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Applying a non-deterministic conceptual life cycle costing model to manufacturing processes Ettore Settanni
Received 11 January 2009 Revised 6 May 2009, 7 February 2010 Accepted 22 February 2010
Dipartimento di Scienze Merceologiche, Universita’ degli Studi di Bari, Bari, Italy, and
Jan Emblemsva˚g Ulstein Verft AS, Ulsteinvik, Norway Abstract Purpose – The aim of this paper is to introduce uncertainty analysis within an environmentally extended input-output technological model of life cycle costing. The application of this approach will be illustrated with reference to the ceramic floor tiles manufacturing process. Design/methodology/approach – Input-output analysis (IOA) provides a computational structure which is interesting for many applications within value chain analysis and business processes analysis. A technological model, which is built bottom-upwards from the operations, warrants that production planning and corporate environmental accounting be closely related to cost accounting. Monte Carlo methods have been employed to assess how the uncertainty may affect the expected outcomes of the model. Findings – It has been shown, when referring to a vertically-integrated, multiproduct manufacturing process, how production and cost planning can be effectively and transparently integrated, also taking the product usage stage into account. The uncertainty of parameters has been explicitly addressed to reflect business reality, thus reducing risk while aiding management to take informed actions. Research limitations/implications – The model is subject to all the assumptions characterizing IOA. Advanced issues such as non linearity and dynamics have not been addressed. These limitations can be seen as reasonable as long as the model is mostly tailored to situations where specialized information systems and competences about complex methods may be lacking, such as in many small and medium enterprises. Practical implications – Developing a formal structure which is common to environmental, or other physically-driven, assessments and cost accounting helps to identify and to understand those drivers that are relevant to both of them, especially the effects different design solutions may have on both material flows and the associated life cycle costs. Originality/value – This approach integrates physical and monetary measures, making the computational mechanisms transparent. Unlike other microeconomic IOA models, the environmental extensions have been introduced. Uncertainty has been addressed with a focus on the easiness of implementing the model. Keywords Accounting, Monte Carlo methods, Input/output analysis, Life cycle costs, Operations and production management Paper type Research paper Journal of Modelling in Management Vol. 5 No. 3, 2010 pp. 220-262 q Emerald Group Publishing Limited 1746-5664 DOI 10.1108/17465661011092623
The authors are grateful to Marco Martelli, Mariano Paganelli and Graziano Busani who kindly shared their expertise in ceramic tile manufacturing, two anonymous referees who gave their contribution, and Mary Mininni who checked the language throughout the paper.
1. Introduction This paper applies a concept of life cycle costing (LCC) based on an input-output technological model. Such concept has been discussed recently, reflecting the emerging and lively debate on the use of LCC in environmental management accounting (EMA) practices (Settanni, 2008). Elements of uncertainty analysis have been introduced in the model consistently with the non-deterministic input-output analysis (IOA) that has been used to formalize the procedural steps involved. The paper structure is as follows: Section 2 provides an overview of the techniques addressed here, in order to outline the background, motivation and scope of the proposed application. The structure of a manufacturing system has been described in terms of physical flows in Sections 3 to 5. This serves as a basis for the bottom-up cost assessment, performed in Section 6. Monte Carlo simulations have been carried out in Section 7 to show how the uncertainty associated with the parameters of the processes involved may affect the outcomes of the model. Section 8 deals with issues related to the emission allowances. Finally, a discussion and conclusive remarks are provided. 2. Background, aim and scope The scope of LCC, its uses in both managerial and environmental accounting, and the factors driving its implementation have been investigated thoroughly (Lindholm and Suomala, 2005; Dunk, 2004; Gluch and Baumann, 2004; Fava and Smith, 1998). Instead, its computational structure has been left almost unquestioned. LCC has a long tradition as a discounted cash flow analysis that supports the procurement process of durable goods, and focuses especially on the post-purchase costs the owner is expected to incur due to this perspective investment (Westka¨mper and Osten-Sacken, 1998; Woodward, 1997; Fabrycky and Blanchard, 1991; Dhillon, 1989). Even the environmental meaning of LCC often implies that an ad hoc discounted cash flow analysis must be combined with environmental considerations (Utne, 2009; Lim et al., 2008; Schmidt and Butt, 2006; Reich, 2005; Sampattagul et al., 2004; Norris, 2001; White et al., 1996). However, if not only the perspective of the final user of a product-system is relevant, but also the perspectives of the producer and the supply chain are, then LCC is expected to shed some light on how the costs are influenced by the structure of the manufacturing system (Artto, 1994; Shield and Young, 1991; Durairaj et al., 2002; Asiedu and Gu, 1998). This means that LCC should also be applied to non-durable goods, or to already existing and operating production systems. As it becomes necessary to keep track of resource consumption, the operations chain preceding the stage in which a product-system is used should not be merely summarized in its purchase price, and viewed as a “black box” while carrying out LCC. Also, as costs are evidently a more adequate measure than cash flows to keep track of resource consumption, the cost assignment mechanism should be explicit and accurate in LCC (Dimache et al., 2007; Emblemsva˚g, 2003; Fixson, 2004; Hansen and Mowen, 2003, Chapter 19; Emblemsva˚g, 2001; Kreuze and Newell, 1994; Fabrycky and Blanchard, 1991, Chapter 7). Nevertheless, a frequent assumption made in literature is that cost data can be simply gathered from the existing information systems, and that such systems implicitly take care of the cost assignment mechanism (Hunkeler et al., 2008; Krozer, 2008; Nguyen et al., 2008; Roes et al., 2008; Kicherer et al., 2007; Janz et al., 2006; Bovea and Vidal, 2004; Keoleian and Kar, 2003). Consequently, more emphasis is usually placed on what environmental costs, even those which cannot be quantified easily, are to be included in LCC (Steen, 2007; Roth and Ambs, 2004;
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Kumaran et al., 2003; Shapiro, 2001; Weitz et al., 1994) than on investigating how the material flows can serve as drivers in order to assign costs to different products, and by-products. It has been claimed that the outline of a formalized computational structure of LCC based on enterprise IOA with environmental extensions could help overcoming, at least theoretically, those shortcomings mentioned above (Settanni, 2008; Settanni et al., 2010). The most remarkable effort to link simultaneously IOA, LCC and environmental analysis has been made only in hybrid models, using national accounting as a background for integrated economic-environmental analysis (Nakamura and Kondo, 2009). At the microeconomic level IOA applies to different kinds of analyses, ranging from complex material requirement planning (Grubbstro¨m and Tang, 2000) to the modelling of interlinked manufacturing processes and their environmental consequences, within and beyond the boundaries of the firm (Xue et al., 2007; Heijungs and Suh, 2002; Albino et al., 2002). The principles of IOA have been also used since the 1960s to solve a variety of financial and cost accounting problems (Brioschi et al., 2000; Klook and Schiller, 1997; Dauner and Dauner-Lieb, 1996; Frank, 1974; Staubus, 1971). A well-known example is the allocation of costs among interacting departments within an organization (Williams and Griffin, 1964; Churchill, 1964; Richards, 1960). Although it is not common to find IOA explicitly addressed in the context of widely recognized cost accounting techniques, it can provide such techniques with a formalized computational structure, secured by using matrices. IOA makes the linear equations typically used in accounting more practical to handle, by means of compact matrix notation and matrix operations. This is particularly useful in those applications that, as the one presented here, explicitly address the physical relationships underlying cost assessment in the manufacturing firms, thus fully reflecting the duality of the original approach developed for use in macroeconomics (Gambling and Nour, 1969; Ijiri, 1968). Indeed, several papers sustain that cost accounting may take particular advantage of IOA, to the extent that modelling the structural elements of a manufacturing system serves as a basis for integrating production planning and business process-oriented costing methods (Boons, 1998; Itami and Kaplan, 1980; Butterworth and Sigloch, 1971; Feltham, 1968; Livingstone, 1969; Tuckett, 1969; Gambling, 1968). The same literature, however, clearly points out which assumptions, such as linear homogeneous production functions and fixed process technology, usually limit the application of this approach. In addition to such limitations, only a few business models based on linear equations include the environmental aspects – such as the generation, treatment and disposal of wastes, by-products and other pollutant emissions – and the associated costs along the operations chain (Schmidt and Schwegler, 2008; Hendrickson et al., 2006, Chapter 18; Wu and Chang, 2003; Polenske and McMichael, 2002; Lin and Polenske, 1998; Sushil, 1992). Finally, just like several managerial accounting systems, the application of IOA at the enterprise level is usually deterministic. Considering this background, this paper provides an extensive numerical example based on the manufacturing of ceramic floor tiles, and it shows how an environmentally extended IOA price model potentially applies to LCC. Here, LCC is understood as a foresight-oriented, transaction-based costing method for use in engineering and management (Emblemsva˚g, 2003). Unlike “traditional” LCC, it is not only a cash-flow based, ad hoc analysis. Rather, it handles several cost objects simultaneously while taking care of resource consumption. The proposed application not only illustrates in
detail how IOA can be suitably used to formalize the procedural steps involved in the LCC model taken as a reference; it also introduces elements of uncertainty analysis within IOA. It is not our purpose to give an accurate account of the manufacturing system considered, which would be a cumbersome task and would require more space than what is allotted in this journal. Rather, our aim is to illustrate the computational aspects of the reference model, while taking into account some real-life issues that may rise when integrating cost and production planning in conditions of uncertainty. In particular, one of these issues is how to asses the cost of producing, and then disposing of scraps and wastes. The limiting assumptions that usually affect IOA techniques also apply here. We will discuss later to what extent these assumptions can be dealt with by the proposed model, keeping low levels of complexity. Nonetheless, simple linear algebra is expected to reasonably meet most of the computational needs in situations where the availability of advanced business information systems, supporting, e.g. activity-based costing (ABC) and enterprise resource planning, cannot be taken for granted. Such situations are not unusual in many small and mid-sized enterprises (SMEs) especially in countries like Italy (Bhimani et al., 2007). Indeed, in the authors’ opinion, IOA still serves effectively as a method for conceptual studies when information is scarce making it possible to understand the interdependence that characterizes the major processes within an economic-production system, in terms of physical and cost flows, even in the absence of specific information system requirements. Unlike the previous contributions on similar topics that make reference to specific software applications, more emphasis is placed here on illustrating a rigorous analytical approach that generalizes, through formal evidence for the benefit of transparency and understandability, the logic and hypothesis underlying the methods for carrying out the necessary calculations. 3. Modeling the physical aspects The LCC model that has been exhaustively described in Emblemsva˚g (2003, 2001), Rodriguez and Emblemsva˚g (2007) will be taken as a reference costing technique throughout this paper. It entails the following steps: Step 1. Define the scope of the model and the corresponding cost objects. Step 2. Obtain and clean bill of materials (BOM) for all cost objects. Step 3. Identify and quantify the resources. Step 4. Create an activity hierarchy and network. Step 5. Identify and quantify resource drivers, activity drivers and their intensities. Step 6. Identify the relationships between activity drivers and design changes. Step 7. Model the uncertainty. Step 8. Estimate the bill of activities. Step 9. Estimate the cost of cost objects. Step 10. Perform Monte Carlo simulations.
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These steps will not be discussed in sequential order. Rather, they will be referred to where necessary while discussing the application of IOA to LCC. This section will focus on modelling the requirement of different resources involved in the manufacturing process as a prerequisite for cost assignment (corresponding to steps 1-6). 3.1 Description of the manufacturing system The ceramic floor tile manufacturing system has been chosen here for several reasons: . being vertically-integrated it gives a rather complete picture of the operations involved; . the installations for the manufacture of ceramic products by firing are among those the European Directive 87/2003 (establishing a scheme for greenhouse gas emission allowance trading within the European Community, EU-ETS) applies to; and . within this industry, especially in Italy, production programs are demanding due to product variety and increasing competitive pressures. Firms are thus experiencing considerable risks related to the prevailing practice of an inaccurate assessment of manufacturing costs (Paganelli, 1993). In a productive ceramic line different operations are performed to transform the raw materials (mainly clay, sand and feldspars) into intermediate products and then into the finished marketable tiles. Several plant configurations are possible. The one assumed here prevails in the Italian ceramic sector. It entails the following operations: (A) wet grinding of raw materials; (B) spray drying; (C) powder forming; (D) drying; (E) production of glaze; (F) glazing; and (G) single-firing of glazed tiles. Each operation has a main output, respectively: (a) slip; (b) powder mixture; (c) green tile; (d) dried tile; (e) glaze; (f) glazed tile; and (g) fired tile. For the sake of simplicity, the final selection and packaging process will not be considered. Being an illustrative example based on a well-established manufacturing system, the operations will not be discussed in further details. Nicoletti et al. (2002) provide a comprehensive reference on this topic, including a discussion of the associated environmental aspects.
Along with the production equipment, there are also three pieces of end-of-pipe equipment, namely (H) dust abatement, (I) flue gas treatment, and (L) wastewater treatment. They process the wastes/by-products generated by the other processes. In out example the plant consists of two production lines. Along each line, operations (C)-(F) are carried out by specialized equipments. During the planning period, which is assumed to be one month, three finished tile models, called g(1), g(2) and g(3), are expected to be produced. Models g(2) and g(3) alternate along the same production line. The only difference is that g(2) does not undergo the glazing process. The outputs of process (A) are three intermediate product types. Intermediate product a(1) is obtained by means of dedicated equipment, whereas either intermediate product a(2) or a(3) can be alternatively obtained by means of another piece of equipment. The network representation of this manufacturing system is shown in Figure 1. An activity hierarchy network is thus created, as required by step 4 of the LCC approach. 3.2 System boundaries The processes and both the intermediate and final products are the relevant cost objects within the system boundaries. Those boundaries may then include any sequence of operations to be performed during the planning period by means of given combinations of equipment, within one organization or more organizations along a supply chain. Processes will be seen here as distinct ways of running the equipment in order to make different product models. Processes are mutually linked by supplier/customer relationships, and they can be further broken down into activities, depending on the available level of details and on the scope of the analysis. Here, the focus is on aggregated processes instead of activities. This can be justified due to the lack of detailed information which is expected from many SMEs. Here, we consider the processes and products within one organization only. The inclusion of the upstream processes, though theoretically feasible, would have required facing the problems of interorganizational cost management (Cooper and Slagmulder, 2004) and open book accounting (Kaju¨ter and Suomala, 2005). Downstream the production stage, the use of a certain quantity of one product model during a specific period of time, i.e. one year, has been considered as an additional process. In this way the post-purchase costs have been assigned to that specific product. The final disposal of that product, instead, has been excluded from the system boundaries. Consistently with IOA, it has been assumed that the technology of each process is fixed. In addition, no substitution among processes occurs. This is of no harm since the model applied here is not an optimization model. Moreover, the operations involved are mainly of line and continuous types, thus allowing substitutability to a lesser extent than, e.g. job-shop manufacturing systems. Finally, the assumption of fixed technology will be amended at least in part by treating the uncertainty associated with the model’s parameters. More generally, however, IOA has also been adapted to deal with substitutability and optimization (Itami and Kaplan, 1980; Samuelson, 1951). Also, substitution is allowed to a more limited extent when the analysis considers the physical coordinates rather than non-linear monetary production functions (Heijungs, 2001, Chapter 5). 3.3 Input-output representation of the manufacturing process Here, a technological model, as in Gambling (1968), is built bottom-upwards from the basic operations which it purports to illustrate. This finally results in an input-output
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Figure 1. Network representation of the manufacturing system
8
10
Chemicals
External disposal (111)
4
5
3
7
6
Thermal energy
Frits raw materials
Slack lime
Cement and detergent
2
1
Electric energy
Water
Clay, sands, feldspars, colouring oxides
9
h
11
Crude waste
14
b
i*
Flue gas treatment/
External disposal (l)
15
a
Spray drying Grinding Forming B(1), B(2), B(3) Powder A(1), A(2), A(3) Slip b(1), b(2), c(1), c(2), c(3) a(1), a(2), a(3) b(3)
Dust releases
Dust apatement H
12
Treated water
1
Wastewater treatment L
Production stage
Drying D(1), D(2), D(3)
e*
Production of Glaze E Glaze E
c
Green tile c(1), c(2), c(3)
13
Carbon dioxide
d
Dried tile d(1), d(2), d(3)
Glazing F(1), F(3)
g
Fired tile g(1), g(2), g(3)
J
Use of tile type 2
Processes
Internally recycled secondary products
Flows outwards the system boundaries
Externally purchased input
j**
Used tile type 2
Intermediate and final main products (alternative models)
Firing G(1), G(2), G(3)
* This flow concerns only models 1 and 3 ** This flow concerns only the final product 2
f
Glazed tile f(1), f(3)
Use stage
226
External disposal (11)
Technosphere
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mathematical representation of the manufacturing system. We extend the existing approaches in order to: . include uncertainty analysis with a focus on the model’s ease of implementation; . address the computational mechanisms to assign the cost of end-of-pipe treatment processes to the production processes transparently, also in the presence of closed-loop recycling; and . avoid that the relevant quantities have to be preliminarily balanced against a time period, a product unit or functional unit, before being used for further computations (instead, the top-down approaches in IOA use the balanced figures as a starting point). Following a bottom-up approach, the relevant processes within the system boundaries are described analytically in terms of those parameters that reasonably approximate their real characteristics. Such parameters must be quantified separately for each process, with reference to the basic level of activity that is meaningful for planning decision (e.g. one hour, one shift, the time needed to complete a batch, etc.). A BOM is thus obtained for each process, reflecting its operational characteristics. Data are to be collected and arranged using several matrices of dimensions commodities £ processes. Those commodities that are both supplied and required by the processes as intermediate inputs or meet the market demand (called main products of the system) must be recorded as the elements of a processes £ processes matrix called technology matrix Z. Table I illustrates the technology matrix for the ceramic tiles manufacturing process. The amount of intermediate product i which is required by the base activity level of process j is denoted as zij , 0 and it can be read at the intersection between the ith row and the jth column of Z. Instead, the gross output of process j generated by the same activity level is zjj . 0, assuming that the jth process (column of Z) produces the jth commodity (row of Z) as its main output. The use phase of main product g(2) has been also included in Z as a distinct process ( J), which consists of using 100 m2 of “fired tile type 2” for one year. It should be noted that the amounts recorded in Z are not balanced. At this point of the analysis, indeed, processes are considered as stand-alone entities and they are described according to their technical specifications, as if they were “cooking recipes”. Symbols “I” and “II” have been introduced in Table I, as well as in the other tables, in order to make a distinction among groups of rows and columns that make reference, respectively, to the production and treatment processes. Thus, the partitions of Z and other matrices can be specified by means of subscripts that address the relevant rows and columns to be considered. For example, the partition Z II ;I records the waste treatments (row group “II”) demanded by the production processes (column group “I”). In Table I the entries of Z II ;I are zeroes because they will be calculated according to the overall amount of waste which is not recycled internally, and therefore, undergoes the treatment processes. Besides, the main products, there are other elements that must be taken into account: . The “externally purchased inputs” matrix 2M records the consumption of those resources that are absorbed by one or more processes but are not produced by any of them. It also includes the operating parameters that allow tracing the costs associated with other physical flows than raw materials (e.g. utilities).
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Note: Technology matrix Z
l
0
0 0
ton 37.2 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 ton 0 0 m2
Dust abatement kg Treatment of fluorine kg compounds Wastewater ton treatment
Slip type 1 Slip type 2 Slip type 3 Powder type 1 Powder type 2 Powder type 3 Glaze Green tile type 1 Green tile type 2 Green tile type 3 Dried tile type 1 Dried tile type 2 Dried tile type 3 Glazed tile type 1 Glazed tile type 3 Fired tile type 1 Fired tile type 2 Fired tile type 3 Tile type 2 2 use
Table I. Input-output representation of a manufacturing system
(I) a(1) a(2) a(3) b(1) b(2) b(3) e c(1) c(2) c(3) d(1) d(2) d(3) f(1) f(3) g(1) g(2) g(3) j (II) h i 0
0 0
0 36.4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
B(2)
B(3)
0
0 0 0
0 0 0
0 0 0
0 0
0 23.3 0 0 0 0 2 2.6 0 36.5 0 0 22.7 0 2.1 0 0 0 0 1.50 0 0 0 0 1.50 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A(1) A(2) A(3) B(1)
C(1)
C(2)
0
0 0
0
0 0
0
0 0
0 0 0 0 0 0 0 0 0 0 25.8 2 2.2 0 0 2 0.9 0 0 0 6.3 0 0 0 5.5 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
E
0
0 0
0 0 0 21.9 21.2 21.7 0 0 0 4.8 0 0 0 0 0 0 0 0 0
D(2)
D(3)
F(1)
F(2)
G(1)
G(2)
G(3)
J
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20.27 20.3 0 0 0 0 25.5 0 0 0 0 0 0 0 0 0 23.0 0 0 0 0 0 0 0 0 0 2 4.8 0 0 0 0 0 0 5.0 0 0 25.50 0 0 0 0 0 0 2.6 0 0 0 0 22.9 0 0 0 0 4.3 0 25.4 0 0 0 0 0 0 0 5.55 0 2 2.1 0 0 0 0 0 0 0 5.5 0 0 2 2.5 0 0 0 0 0 0 1.9 0 0 0 0 0 0 0 0 0 2.7 0 2 2.2 0 0 0 0 0 0 0 2.3 0 0 0 0 0 0 0 0 0 100.0
Processes (I) C(3) D(1)
228
Network node
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
(II) I
0
0
42.0 0 0 0.1
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
H
17
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L
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.
.
Matrix 2 H records the non-physical cost drivers that are related to the operation of each process. Examples are the cycle times, expressed as machine hours. The net output of waste and the input of waste are recorded separately in matrices N and 2N, respectively. Finally, matrix R records the emissions released into the environment and the demand for externally provided disposal services.
The above matrices can be stacked and then partitioned as follows: 0
B¼
B †;I
2M †;I
B B 2H †;I B B B †;II ¼ B N†;I B B B 2N†;I @ R †;I
2M †;II
1
C 2H †;II C C C N†;II C C C 2N†;II C A R †;II
ð1Þ
A distinction has been made between the partitions of matrix B referring to either the production or the treatment processes. The symbol “†” has been used within the subscript to indicate that all the rows of a matrix have been considered. Matrix B for the ceramic tile manufacturing system is shown in Table II. Also the flows recorded in B are not balanced, in that they are consistent with those recorded in Z. Some aspects concerning matrix B need further discussion. The net generation of waste k by process j is recorded as the generic element n kj of matrix N, whereas the element 2n kj of matrix 2N represents the input of the same waste into that process. Following Nakamura and Kondo (2009), each process is assumed either to produce a given waste k or to use it as a secondary input, i.e. ;j; ;k : n kj £ n kj ¼ 0. There are other ways to proceed especially in the case of ceramic tile manufacturing (Albino and Ku¨htz, 2004). However, this approach seems most convenient for cost accounting purposes. The flows recorded in matrix R are those released into the natural environment or extracted from it, causing the environmental interventions. They can be seen as cost drivers to assign the “external failure” environmental costs. An example is the cost of purchasing pollutant emission allowances for carbon dioxide (CO2) emissions. The demand for waste treatments purchased externally is conventionally included in matrix R, if known in advance. In our example this concerns the sludge from the wastewater treatment, the dust from dust abatement system, and the by-products from the treatment of fluorine compounds in kiln flue gas, using fabric filters with the addition of reagents (Breedveld et al., 2007). However, also the amount of waste generated by the production processes and the treatment processes which is neither recycled nor treated within the manufacturing system requires that disposal services be purchased externally. Such amount is not known in advance and it must be calculated. In our example this concerns the crude and fired waste generated by different production processes, as well as the secondary water generated by the wastewater treatment. Different rows of matrix 2M have been reserved to these external disposal services (Table II).
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2H
6 6
7 8 3
2 4 5
1
1 1 1 1
10
9
2M
Table II. Other resources generated and used by the system
Network node
External disposal (II) External disposal (III) Clay Sand Feldspar Coluring oxides A Coluring oxides B Water Electric energy Thermal energy Ca(OH) Chemicals Frits raw materials Cement Detergent Cycle time A Cycle time B Cycle time E Cycle time C Cycle time D Cycle time F Cycle time G Cycle time H Cycle time I Cycle time L ton L min. min. min. min. min. min. min. min. min min.
kg ton ton
m MWh GJ
3
ton
ton ton ton ton
ton
ton
2 900
2 11.00 2 1.65
2 8.55 2 4.30 2 8.57
A(1)
2 720
2 12.5 2 1.32
2 6.97 2 4.67 2 7.79 2 0.78
A(2)
2 600
2 12.5 21.10
20.60
27.14 24.50 28.00
A(3)
2 60
2 0.02 2 4.38
B(1)
2 60
2 0.02 2 4.27
B(2)
2 60
2 0.20 2 8.68
B(3)
2 540
2 2.30
2 2.00 2 0.16
E
2 60
2 0.04
C(1)
2 60
2 0.04
C(2)
2 90
2 0.06
C(3)
2 60
2 0.10 2 1.42
D(1)
230
Matrix notation
Processes (I)
260
2 90
2 0.14 2 1.12
D(3)
(continued)
2 0.10 2 1.42
D(2)
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2N _ II ;†
13 14 15
11
2NI ;†
R
12
11
Network node
NII ;†
NI ;†
Matrix notation
Crude waste Fired waste Dust before treatment Solid-water suspension Fluorine compounds Secondary water Crude waste Fired waste Dust before treatment Solid-water suspension Fluorine compounds Secondary water CO2 Dust External disposal (I) ton kg ton
m3
kg
ton
ton ton Kg
m3
2 5.21
2 0.60
1.60
ton kg
42.00
ton ton kg
A(1)
2 4.82
2 0.52
1.58
42.00
A(2)
2 4.87
2 0.52
1.58
42.00
A(3)
0.24
12.00
B(1)
0.23
12.00
B(2)
0.47
12.00
B(3)
2 2.00
E
Processes (I)
0.30
C(1) 0.13
C(2) 0.16
C(3)
0.07
0.07
0.06
0.500
D(3)
(continued)
0.33
D(2)
0.46
D(1)
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Table II.
2H
9
2M
6 6
7 8 3
2 4 5
1
1 1 1 1
10
Network node
Table II.
Matrix notation
External disposal (II) External disposal (III) Clay Sand Feldspar Coluring oxides A Coluring oxides B Water Electric energy Thermal energy Ca(OH) Chemicals Frits raw materials Cement Detergent Cycle time A Cycle time B Cycle time E Cycle time C Cycle time D Cycle time F Cycle time G Cycle time H Cycle time I Cycle time L ton L min. min. min. min. min. min. min. min. min min.
kg ton ton
m3 MWh GJ
ton
ton ton ton ton
ton
ton
2 65
2 1.45 2 0.05
F(1)
2 75
2 1.57 2 0.06
F(3)
2 0.09
G(2)
2 0.09
G(3)
2 82
2 93
2 87
J
Processes
2 10.31 2 11.69 2 10.94
2 0.08
G(1)
(I)
0.05 9.00
2 0.16
2 60 2 60
H
I
2 0.8
2 0.06
(II)
2 0.50
2 24.00
2 1440
L
(continued)
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12
2N _ II ;†
Crude waste Fired waste Dust before treatment Solid-water suspension Fluorine compounds Secondary water Crude waste Fired waste Dust before treatment Solid-water suspension Fluorine compounds Secondary water CO2 Dust External disposal (I)
Note: Flows not balanced
13 14 15
11
2NI ;†
R
12
11
Network node
NII ;†
NI ;†
Matrix notation
ton kg ton
m3
kg
ton
ton ton Kg
m
3
kg
ton
ton ton kg
2 0.10
1.58
0.19
A(1)
2 0.01
1.57
0.19
A(2)
0.40
0.06
0.05
A(3)
0.45
0
0.20
B(1)
0.43
0.04
0.12
B(2)
B(3)
C(1)
0.33 0.04 3 £ 102 9
E
Processes (I)
1.19
16.3
C(2)
C(3)
D(1)
D(2)
D(3)
Life cycle costing model
233
Table II.
JM2 5,3
Finally, matrix C records the percentage of the corresponding plant’s capacity (monthly, daily, etc. depending on the planning horizon that has been chosen) that each process uses when it runs at its base activity level. Capacity is a necessary constrain when the same processes produce different product models (Tuckett, 1969). A numerical example of C is Table III.
234
3.4 Quantification of resources using the balancing procedures The input-output representation of the manufacturing process provides the coefficients of a system of linear equations that can be structured and solved by means of simple matrix operations such as multiplication, inversion, transposition and diagonalization, with the aid of commonly used electronic spreadsheets. For a detailed discussion of the mathematical aspects of IOA (Miller and Blair, 2005, Appendix A; ten Raa (2005)). The unknown variables are the levels of activity the processes are required to operate at so that their net outputs, recorded in matrix Z, meet the exogenous production plan. Once the levels of activity are known, one determines the amount of resources required and waste generated. Let: ! Z A¼
B
C
ð2Þ
Within A only the volume-related variables have been identified and quantified consistently with step (3) of the LCC model. In particular, according to step (5) the resource and activity drivers have been quantified in matrices B and Z, respectively. Besides, the volume-related cost drivers, there are also other drivers that are fixed with respect to the processes’ activity levels throughout the planning period. An example is the thermal energy consumed by the natural gas-fired kilns, i.e. by processes G(1-3), and the corresponding CO2 emissions. Other examples include the fixed quote of the electric energy cost (the variable quote of the same cost is assigned according to the installed power and the operating times of each plant), and some maintenance interventions. The relevant amounts concerning all the fixed drivers, whether physical or not, will be recorded with the appropriate sign in a separate matrix F, rather than in B. This will be discussed further in Section 6. In this section, it is sufficient to note that this is one possible way to deal with the presence of fixed terms in the cost functions, which is usually seen as violating the above discussed assumption of linearity within IOA (Salamon, 1970; Livingstone, 1969; Gambling, 1968). More complex approaches to overcome such issue also exist (Zhao et al., 2006; Sushil, 1992) or have been invoked (Boons, 1998). There are also some costs that cannot be classified as either purely fixed or purely variable, since the event they are associated with is expected to occur after a certain number of process runs. One way to deal with these costs is to assume that each process run requires just a fraction of the amount of resources consumed when the event occurs. In our example, the rotating mills used in process A(1) must be washed every four runs, consuming 5 m3 of water and generating 6.4 ton of clay-water suspension. Hence, to account for this operation the water consumption corresponding to process A(1) in matrix 2M includes additional 1.25 m3, whereas 1.6 ton of clay-water suspension are recorded in matrix N. There are other similar aspects that will not be discussed here, such as the replacement of exhausted fabric filters and kiln rolls.
Process A, plant 1 Process A, plant 2 Process B, plant 1 Process B, plant 2 Process E, plant 1 Process C, plant 1 Process C, plant 2 Process D, plant 1 Process D, plant 2 Process F, plant1 Process F, plant 2 Process G, plant 1 Process L
% % % % % % % % % % % % %
Note: Flows not balanced
C 2.27
A(1)
1.81
A(2)
1.51
A(3)
0.25
B(1)
0.25
B(2)
0.25
B(3)
5.8
E
0.2
C(1)
0.2 0.3 0.2
Processes (I) C(2) C(3) D(1)
0.2
D(2)
0.3
D(3)
0.2
F(1)
0.3
F(3)
0.19
G(1)
0.21
G(2)
0.2
G(3)
J
H
3.00
(II) I L
Life cycle costing model
235
Table III. Use of plant’s capacities
JM2 5,3
236
As to step (6) of the LCC model, a distinction could be made at this stage between design dependent and design independent cost drivers, like in Bras and Emblemsva˚g (1996). In our example, the characteristics of the ceramic tiles heavily depend on the plant settings. However, the choice of raw materials, especially those used in the glaze production process, can have significant repercussions on the composition of the air emissions, including CO2, released during the high temperature treatments, which are among the most crucial interventions (Nicoletti et al., 2002). The parameters in equation (2) are actually subject to uncertainty. Preliminarily, however, the balancing procedure will be illustrated. This is necessary to obtain a deterministic balance of the resources used and generated while meeting the production plan for a given period. Basically, the following matrix operations will gradually modify the initial tabular representation of the manufacturing system (Tables I-III). Not all the intermediate results of that procedure need to be shown in tabular form, however. The production plan in Table IV sets the final demand of both the final products (namely “fired tile 1” and “fired tile 3”) and the intermediate products (“powder type 2”). Instead, the final product “fired tile 2” has been considered in its use stage. The production plan also provides the beginning inventories of the intermediate products (“powder type 1”).
node (I) a(1) a(2) a(3) b(1) b(2) b(3) e c(1) c(2) c(3) d(1) d(2) d(3) f(1) f(3) g(1) g(2) g(3) j (II) h i Table IV. Production plan or final demand (one month)
l
Beginning inventories (2 )
Production plan (þ )
Final inventories (þ)
Final demand (reference flow) yi
Slip type 1 Slip type 2 Slip type 3 Powder type 1 Powder type 2 Powder type 3 Glaze Green tile type1 Green tile type 2 Green tile type 3 Dried tile type 1 Dried tile type 2 Dried tile type 3 Glazed tile type 1 Glazed tile type 3 Fired tile type 1 Fired tile type 2 Fired tile type 3 Tile type 2 – use
ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton m2
0 0 0 2 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 200 0 400 16,550
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
o 0 0 2500 10 0 0 0 0 0 0 0 0 0 0 200 0 400 16,550
Dust abatement Treatment of flue gas Wastewater treatment
m3 kg
0 0
0 0
0 0
0 0
ton
0
0
0
0
The last column in Table IV is the reference flow, or the vector of final deliveries y I . Making reference to the partitions of Tables I and IV that refer to the production processes only (thus excluding the treatment processes at this stage) the following balancing condition must hold: ZI ; I · sI ¼ yI
ð3Þ
equation (3) is simply a compact representation of a system of linear equations using matrices. The reference flow vector y I is known. The unknown is the vector of activity levels, or scaling vector s I . The production processes must operate at these unknown levels to meet the final deliveries, i.e. the entries of s I are the expected number of runs for each process. If Z21 I ;I , the inverse of Z I ; I exists then: Z21 I ; I · yI ¼ sI
Life cycle costing model
ð4Þ
The conditions for the existence of Z21 I ;I especially when the physical measures are involved, have been treated in-depth elsewhere (Suh and Heijungs, 2007; Heijungs and Suh, 2002), and will not be further discussed here. Let s^ I be the diagonalized vector s I . The entries on the left side of Tables I-III can be balanced: 0 1 0 1 ~ I; I ZI ; I Z B C B C ~ †; I C ~ †; I ¼ A †; I · s^ I ¼ B B †; I C · s^ I ¼ B B A ð5Þ B C @ A @ A ~ C †; I C †; I This is only a partial balance which is necessary at this stage in order to calculate the anticipated amount of resources that are wasted while meeting the production plan and the amount of waste that will be recycled internally. The recycling ratio for each waste type k amounts to: Pn j¼1 nkj £ sj r k ¼ Pn ð6Þ kj £ sj j¼1 n where sj is the jth element of vector s I ; nkj and n kj have been described in Section 3.3. In our example there are n ¼ 19 production processes and the waste types are k ¼ 1. . .5. T The outcomes of (6) are collected in a vector r I ¼ 0; 13 0 0 0 0 . (Subscript “I” indicates that we are concerned only with the waste types originated by the production processes; superscript “T” means that the vector has been transposed). Only 13 per cent of the first waste type (“crude waste”) is recycled internally. Let I be the identity matrix of appropriate dimensions and r^ I the diagonalized vector r I . The relative amount of waste that will undergo the treatment processes can be calculated as ðI 2 r^ I Þ. Making reference to the ceramic tile manufacturing system, it is necessary to turn five waste types into the demand of three internally-provided waste treatments (H, I, and L) and one externally provided disposal service. The latter concerns the amount of crude and fired waste that will not be recycled.
237
JM2 5,3
238
The output of a treatment process is in fact a treatment service, measured by the physical amount, expressed as mass, of aggregated waste types processed. This is an example of “activity driver” consumed by the other processes. To calculate such driver, one needs to define an exogenous matrix Q. Its generic element qlk (0 , qlk , 1) indicates the amount of kth waste type which undergoes the lth treatment. The demand of treatment services can then be calculated as follows: 0 1 ~ II ;I Z @ A ¼ 2Q · ðI 2 r^ I Þ · NI ;I · s^ I ð7Þ ~ 2M III ;I ~ III ;I is the demand of waste treatments purchased externally (subscript “III ” where 2M indicates the group of rows in the balanced matrix of externally-purchased inputs that specifically refers to such services); Z~ II ;I is the demand of internally- provided waste treatments; and: Q II Q¼ QIII is shown in Table V. After Z~ II ;I has been determined, the balancing condition must be reformulated as follows, including also the end-of-pipe processes: 0 1 ~ I ;I Z I ;II Z A·s ¼ y ð8Þ X·s ¼ @ ~ Z II ;I Z II ;II ~ I ;I and Z ~ II ;I have been calculated in equations (5) and (7), Within X the partitions Z whereas Z I ;II and Z II ;II (respectively, the input of commodities produced by the production processes and used by the treatment processes, and the main output of the treatment processes) correspond to the right-hand partition of Table I. If s ¼ X 2 1, the inverse of X exists then: s ¼ X 21 · y
ð9Þ
where y corresponds to the entire last column in Table IV. It is not necessary to rescale all the processes since the treatment processes in the ceramic tile manufacturing system use only inputs purchased externally. Thus, the only entries of vector s that are not unities T are those related to the treatment processes. Let s II ¼ 207:9 135:5 14:0 be the
Treatment processes Q II Table V. Waste destination
Q III
H I L External disposal
Waste types Water-solid Dust suspension
Crude waste
Fired scrap
Fluorine compounds
0 0 0
0 0 0
1 0 0
0 0 1
0 1 0
1
1
0
0
0
corresponding partition of s. For example, according to these results, the process that treats fluorine compounds in kiln flue gases is expected to run 135.5 times at its base activity level (1 hour) during the planning period. If the treatment processes had consumed also the outputs of the production processes, then all the scaling factors would have changed. ~ (Table VI) is the final balanced technology matrix obtained by using the Matrix X scaling vector s: ~ ¼ X · s^ X
ð10Þ
The balance of the other resources generated and used in production can be obtained similarly: 0 1 2M †; I · s^ I 2M †; II B C B 2H †; I · s^ I 2H †; II C B C B C B NI ;I · s^ I 0 C B C 1 B C ! 0~ ~ B B B NII ; II C 0 †; I †; II B B C ^ @ A ¼ ð11Þ C·s ~ †; I C †; II · s^ ¼ B ~ B 2NI ;I · s^ I 2NI ; II C C C B C B C B 2NII ; I · s^ I 2NII ;II C B C B R · s^ R †; II C B †; I I C @ A C †; I · s^ I C †; II ~ †;I have been calculated in equation (5), with the exception of the first ~ †;I and C where B ~ †;I that have been obtained in equation (7); B †;II and C †;II correspond to two rows of B the right-hand sections of Tables II and III, respectively. At this point, it should be taken into account that the treatment processes also generate by-products. Assuming that these processes do not use each other’s treatment services, matrix NII;II in equation (11) only records the by-products from the treatment processes that are recycled in the manufacturing system. In our example NII ;II is a row vector because the water that has been processed by the wastewater treatment plant is the only waste that is recycled. Other waste types, namely dust and fluorine compounds from flue gas treatment, need to be entirely disposed of externally, and therefore, they have been recorded in matrix R †;II . The demand of secondary water has been simultaneously calculated in equation (11) within the partition 2NII ;I · s^ I 2NII ;II · s^ . Since there is just one type of recycled waste from the treatment processes, the recycling ratio is a scalar: r ¼ 0:78. This means that 78 per cent of the treated water is recovered, whereas the remaining amount is disposed of in the drainage system. Such amount must be calculated as follows: ð1 2 rÞ · NII ;II · s^ ¼ ð 0
0
249; 4 Þ
ð12Þ The outcome of equation (12) must then be recoded within the partition 2M †;II · s^ obtained in equation (11). As to the use of by-products in the treatment processes we simply assume, instead, that 2NI ;II ¼ 0 and 2NII ;II ¼ 0.
Life cycle costing model
239
Table VI. Balanced flows – system’s main outputs 382.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0.4 0 2 16.4
ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton ton m2
ton kg
ton
2 21.0
20.5 0
0 478.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A(2)
2 13.3
2 0.3 0
0 0 302.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
A(3)
B(2)
B(3)
0
2 1.4 0
0
2 2.1 0
0 0 0 0 0 0 35.1 0 0 0 0 0 0 0 0 0 0 0 0
E
0
0
2 1.3 2 0.009 0 0
2 382.9 0 0 0 2 478.9 0 0 0 2 302.7 246.3 0 0 0 267.9 0 0 0 166.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
B(1)
C(3)
D(1)
D(2)
D(3)
F(1)
F(2)
0
2 0.3 0
0
2 1.3 0
0
20.8 0
0
0 0
0
0 0
0
0 0
0 0 2 58.2 2 129.9 (continued)
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 234.3 2 322.2 2 189.8 0 0 0 0 0 0 2 137.9 2119.9 0 0 0 0 0 0 0 2 166.7 0 0 0 0 0 0 0 0 0 0 0 2 10.0 2 25.1 221.7 0 0 2 221.7 0 0 0 0 0 439.4 0 0 2439.4 0 0 0 0 0 460.0 0 0 2 460.0 0 0 0 0 0 203.2 0 0 2 203.2 0 0 0 0 0 2391.1 0 0 0 0 0 0 0 0 412.1 0 2 412.1 0 0 0 0 0 0 205.0 0 0 0 0 0 0 0 0 420.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
C(2)
240
(I) Slip type 1 Slip type 2 Slip type 3 Powder type 1 Powder type 2 Powder type 3 Glaze Green tile type1 Green tile type 2 Green tile type 3 Dried tile type 1 Dried tile type 2 Dried tile type 3 Glazed tile type 1 Glazed tile type 3 Fired tile type 1 Fired tile type 2 Fired tile type 3 Tile type 2 2 use (II) Dust abatement Treatment of fluorine compounds Wastewater treatment
A(1)
Processes (I) C(1)
JM2 5,3
(I) Slip type 1 Slip type 2 Slip type 3 Powder type 1 Powder type 2 Powder type 3 Glaze Green tile type1 Green tile type 2 Green tile type 3 Dried tile type 1 Dried tile type 2 Dried tile type 3 Glazed tile type 1 Glazed tile type 3 Fired tile type 1 Fired tile type 2 Fired tile type 3 Tile type 2 2 use (II) Dust abatement Treatment of fluorine compounds Wastewater treatment 0
0
0
0 0 0
0
0 26.8
ton
0 0
8.7 0
(II)
0 2 6.7
H
ton kg
J 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
G(3)
Processes
ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 0 0 0 ton 0 2 391.1 0 0 ton 0 0 0 0 ton 2 205.0 0 0 0 ton 0 0 2 420.5 0 ton 200.0 0 0 0 ton 0 364.1 0 2 364.1 ton 0 0 400.0 0 2 0 0 0 16,550.0 m
G(1)
(I) G(2) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0
0 13.5
I
238.9
0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
L
Life cycle costing model
241
Table VI.
JM2 5,3
242
Finally, it is necessary to warrant that the mass balance holds column-wise for each process. The calculated demand of waste treatments should be, therefore, subtracted from the amount of waste generated by the processes. In other words, the latter has to be turned into the so-called “sale of waste”, i.e. the output of waste that has been “sold” as a secondary input to the other processes (Nakamura and Kondo, 2009). This requires that the recycling ratios r I and r are calculated as previously shown: 0 1 NI ;I · s^ I 0 ~ ¼ @ A · s^ Let N NI ;II 0 be the relevant partition in equation (11) and let: ! r^ I 0 r^ ¼ : 0 r ~ The overall balanced The sale of waste can be obtained as the matrix product r^ · N. ~ entries of matrix B have been shown in Table VII. In the last column of Table VII one can also find the predetermined cost coefficients that quantify the variable consumption intensities. This completes the requirements of step (5) of the LCC model. However, these intensities will be used later. The next section will be dedicated to modelling uncertainty. 4. Modelling uncertainty Both the process-related parameters that have been depicted so far in a deterministic manner as fixed technologies (Tables I-III), and the consumption intensities shown in Table VII, are actually subject to uncertainty. For example, the efficiency of a process in converting inputs into outputs may vary. Chasing accuracy of past cost figures as an apparent reduction in uncertainty can increase risk – particularly if the analysis involved is required to say something about the future, possibly before costs are incurred. Thus, uncertainty is to be explicitly addressed in order to allow both backcasting and forecasting to aid management to take informed actions. According to step (7) of the reference LCC model, uncertainty completes the information about the manufacturing process considered. This section illustrates how this can be put consistently with the proposed input-output computational structure. As pointed out by Heijungs and Suh (2002), Chapter 6, and Hendrickson et al. (2006), Appendix IV; within IOA, a change affecting one element of the technology matrix affects all the elements within its inverse and propagates through the scaling factors. If, perturbation is systematically introduced within the technology matrix, each of its elements must then be defined in stochastic terms, using a specific probability distribution and then solved using mathematical methods. Such mathematical analysis might be, however, cumbersome and unnecessary. Indeed, it might not be possible to describe the variability of each model’s parameter in terms of frequency of occurrence, which is a common approach for establishing probability distributions. Instead, it may be appropriate to describe the uncertainty associated with the subjective degree of plausibility of such values, relying on a limited sampling or even pure guesswork. Even in matrix-based computational structures, a certain level of vagueness about the
External disposal (II) External disposal (III) Clay Sand Feldspar Coluring oxides A Coluring oxides B Water Electric energy Thermal energy Ca(OH) Chemicals Frits raw materials Cement Detergent Cycle time A Cycle time B Cycle time E Cycle time C Cycle time D Cycle time F Cycle time G Cycle time H Cycle time I Cycle time L Crude waste (sale) Fired waste (sale) Dust (sale) Solid-water suspension (sale) Fluorine compounds (sale Secondary water (sale) Crude waste (in) Fired waste (im) Dust (in) Solid-water suspension (in) Fluorine compounds (in) Secondary water (in) CO2 Dust External disposal (I)
m3 ton kg ton
kg
ton ton N m3 ton
m3
kg
ton ton ton ton ton ton ton m3 MWh TJ ton ton ton ton L h h h h h h h h h h ton ton kg ton 2 59.2 2 37.3 2 66.3 2 4.9 2 103.7 2 9.1
2 82.9
2 4.3
2 40.4
2 91.7 2 61.4 2 102.4 2 10.2
2 164.4 2 17.3
2 157.9
2 6.8
2 63.4
2 87.8 2 44.1 2 88.0
2 112.9 2 16.9
2 154.1
2 53.5
2 12.8
A(3)
A(2)
A(1)
27.9
2115.6
2 2.3 2 0.5
B(1)
42.1
2178.6
23.5 20.7
B(2)
53.3
2111.2
22.2 20.9
B(3)
211.2
250.2
212.8
211.1 2 0.9 0
E
2 146.3
2.5
2 40.3
1.6
2 5.4 0
2 16.5
2 10.5
2 1.4 0
C(2)
C(1)
2.0
2 143.7
2 5.7 0
2 13.3
C(3)
(I)
3.2
2.4
2 40.3
2 3.8 2 0.05
2 16.1
D(1)
11.5
6.3
2 146.5
213.9 2 0.2
241.9
D(2)
5.9
6.2
2 143.7
212.9 2 0.1
241.6
D(3)
Processes
2 3.7
0.9
2 40.0
2 53.5 2 1.8
2 6.1
F(1)
2 7.6
1.9
2 95.4
2 119.8 2 4.2
2 12.6
F(3)
40.7
2 138.0
2 8.2
2 5.0
G(1)
61.6
2 209.0
2 12.5
2 26.9
G(2)
73.0
2247.9
2 14.8
2 20.5
G(3)
28.2 21,489
J
69.9 8.7
2207.9
2 33.2
H
16.8
179.8
2 337.4
2 7.0
2135.5
2 337.4
2 8.1
2 49.4
L
2108.4 0
(II)
5 £ E 2 07
I
£ 2 1.2 £ 17.0 £0 £ 400.0
£0
£ 2 1.2
£ 2 37 £ 29 £ 2 152 £ 2 22 £ 2 32 £ 2 26 £ 2 24 £ 2 13 £ 2 56 £ 2 1.4 £ 2 12 £ 2 2,400 £ 2 30 £ 2 1,715 £ 2 17.1 £ 2 25 £ 2 20 £ 2 18 £ 2 12 £ 2 12 £ 2 15 £ 2 33 £ 2 13 £ 2 16 £ 2 20 £0
Cost coefficients (e/unit)
pR
p
p
pM
Life cycle costing model
243
Table VII. Balanced flows – resources generated and adsorbed by the system, including the externally purchased disposal services (with sale of waste)
JM2 5,3
244
phenomenon can be retained and the uncertainty can be described in terms of either bounded intervals or fuzzy numbers. Fuzziness is in fact one main type of uncertainty, which occurs whenever definite, sharp, clear or crisp distinctions are not made (Emblemsva˚g, 2003 Chapter 3; Emblemsva˚g and Kjølstad, 2002). The main difference between bounded intervals and fuzzy numbers is that, in absence of detailed information, the former assumes all values within an interval to be equally plausible – i.e. a uniform distribution; the latter, instead, introduces subjectively-defined distributions – often triangularly shaped, but in principle it can have any shape. The solution to the model is then approximated by employing numerical algorithms, which may have different efficiencies (Tan, 2008; Peters, 2007; Wu and Chang, 2003). Here, the uncertainty is modelled as fuzzy numbers and the model solved numerically by employing Monte Carlo simulation techniques. As Emblemsva˚g (2003) points out, no difference exists between the various approaches of modelling uncertainty when employing numerical approximation techniques. For simplicity, we therefore, simply use the term ‘uncertainty distribution’ in the remainder of this paper. Before continuing, we would like to illustrate this approach using a very simple example. In the example, we simply add two source variables called assumption cells (“Direct Labor” and “Material”) to obtain a so-called forecast cell called ‘Product Cost’, which is a response variable. The example is shown in Figure 2, and the term cell refers to the fact that the model is implemented in an MS Excel spreadsheet. The two input variables are modelled using triangular- and elliptical uncertainty distributions. The Monte Carlo simulation starts by randomly picking numbers in such a fashion that if an infinite number of trials were performed a histogram of the picked numbers from each uncertainty distribution would look exactly like the uncertainty distribution. However, performing an infinite number of a complete computational sequence – often called trials – is rather impractical. Hence, we typically settle for 10,000 trials to be sure that the random error is small enough to produce statistically significant results. The first three trials would then work like this: Assumption cells
Forecast cells Statistical distribution of a forecast cell
Chosen statistical distribution for an assumption cell
Trials £4 £ 12 £ 20 etc. Direct labor
Figure 2. Example of the Monte Carlo simulation
+
Propagation through model
£6 £8 £ 15 etc. Material Source: Bras and Emblemsvåg (1996)
Results £ 10 £ 20 £ 35 etc.
Product cast = Direct labor + Material The forecast cell is shown here as a histogram for simplicity
Trial 1. £4 is picked as “Direct Labour” and £6 is picked as “Material” producing a “Product Cost” of £10.
Life cycle costing model
Trial 2. £12 is picked as “Direct Labour” and £8 is picked as “Material” producing a “Product Cost” of £20. Trial 3. £20 is picked as “Direct Labour” and £15 is picked as “Material” producing a “Product Cost” of £35. When all the trials have been performed, the calculated values of a forecast cell will form a new statistical distribution (see the product cost distribution in Figure 2). Owing to the randomness, the numbers that have propagated through the model can be used in ordinary statistical analysis as if we were running a real experiment, e.g. to construct confidence intervals, perform t-tests, ANOVA, sensitivity analyses, etc. This approach can be applied to any size model of any computational complexity (Emblemsva˚g, 2003), only limited in practical terms by the memory of the PC. Models containing more than 1,000 variables are common. It is important to recall that the historical context for developing Monte Carlo methods was the development of nuclear power plants after WWII which produced mathematical problems of such complexity that the ordinary mathematics using differential methods simply became insufficient. Now, let us return to the manufacturing system in this paper. The information about the manufacturing system has been collected and arranged in a tabular form. The uncertainty distributions can be assigned at the earliest stage to most uncertainties associated with the cost drivers and the consumption intensities described so far, using the assumption cells in the spreadsheet equivalent matrix A (equation (2)) that will serve as source variables. In particular, the uncertainty distributions will apply to the following parameters that are relevant for the decision process, especially in the process/product design phase or while defining scenarios (Bras and Emblemsva˚g, 1996): . The gross main output and the amount of waste/scrap generated by each process, in order to reflect the different process efficiencies (also, a negative correlation should be specified between the main output of processes and the amount of scrap they produce, which is nearly 2 1: in this way the uncertainty in one process output is assumed to be mainly linked to the amount of scrap produced). . The activity drivers, that determine the reciprocal relationships among processes and therefore their cost. . The resource drivers and intensities (cost coefficients), that determine the contribution of the externally-purchased inputs to the overall manufacturing cost. It should be noted that the first and the second issue can affect the balancing procedure described in Section 3.4, involving the technology matrix inverse, which yields the scaling factors. Specific examples of uncertainty attached to the parameters, as in the case discussed here, have been shown in Tables VIII and IX, regarding, respectively, some cost drivers and some consumption intensities. All the distributions are triangularly shaped because the example has been carried out in absence of detailed historical information. The cost of emission allowances has been also associated with uncertainty, but this will be discussed in Section 8.
245
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246
Table VIII. Example of uncertainty modeling for some cost drivers
Finally, in our example the forecast cells which act as response variables correspond to the unit costs of the intermediate and final products. These costs are the outcome of the input-output model as it will be shown in Section 6. 5. Process inefficiencies One further procedural step, although not mandatory, should be carried out in order to estimate by means of the model applied here the value of the resources used by one or more processes only to produce wastes/by-products, that must be treated or disposed of ( Jasch, 2003). Emblemsva˚g and Bras (2001) pointed out that capturing waste generation and the costs associated with waste is one of the core environmental dimensions in the LCC model herein assumed as a reference. The process inefficiencies must then be explicitly addressed. The first type of inefficiency affects the requirement of raw materials and other resources. The entries of Tables I and II recording the process inputs are based on the amounts specified within the BOM. Yet, the efficiency of the conversion of inputs into outputs may be affected by spoilage, scrap and several other factors. In our example, one important factor is the moisture content of clay raw materials (Rebecchi, 2002). In particular, If we consider process A(1) and specify the moisture content of clay as 0 , h , 1, then the input requirement as specified by the BOM must have been divided by ð1 2 hÞ before being recorded in Table II. The amount of wasted material is expected to be recorded alternatively in matrix R or N. Moreover, each process jointly produces its main output and some waste/by-product. Therefore, the latter requires resources as well. One way to estimate the value of “wasted” resources is to imagine that a process can be split into two independent processes, one producing the same output as before, and a new one fictitiously producing the former by-product as its main output. Let l (0 , l , 1) be the relative amount of such process’ main output, measured in units of mass, compared with the total mass of that main output and the corresponding by-product (other criteria are also possible). We call l and (1 2 l) the “allocation factors”. The two process vectors can be obtained from the same relevant column of the former matrix A by multiplying its entries by l and (1 2 l), respectively, – with the exception of those entries that correspond to the main products and the waste types. In order to assign and trace costs according to a cause-effect criterion, the following is also required:
Process
Cost driver
Distribution
Min
Likeliest
Max
G(2) B(1) D(3)
Fired tile type 2 (ton) Cycle time B(1) (hrs) Crude waste (ton)
Triangular Triangular Triangular
2.43 0.90 0.45
2.70 1.00 0.50
2.97 1.10 0.55
Consumption intensity Table IX. Examples of uncertainty modeling for some consumption intensities
3
Natural gas (e/m ) Overhead rate C (e/h) Detergent (e/L)
Distribution
Min
Likeliest
Max
Triangular Triangular Triangular
0.04 10.80 0.90
0.05 12.00 1.00
0.12 13.20 3.10
within the fictitious process vector producing the former by-product, the same amount is entered twice, both as a main output and as a by-product exactly as before; and the downstream processes using the former main output must also use the main output of the new fictitious process (the former by-product).
Life cycle costing model
In our example an assignment criterion based on mass has been adopted to split processes D(2) producing the dried tile “type 2”, and process G(2) producing the fired tile “type 2”. The next section will show that producing a scrap downstream is likely to be costly. The corresponding entries in Tables I to III (as well as in the table which records the amount of fixed cost drivers), should be modified as described. For example, l ¼ 0; 89 for D(2) whereas l ¼ 0; 93 for G(2). Also to the production plan in Table IV two additional rows should be added, respectively, after products d(2) and g(2), in order to record the waste types now considered as fictitious main products. For these products the final demand is obviously zero. The balancing procedures described in Section 3 must then be carried out using the new tables.
247
.
.
6. Assessing the direct process cost and the unit product cost An estimate of direct costs of each process can be obtained multiplying the balanced amounts of the relevant resource drivers by their consumption intensities, shown in Table VII. In this way, the direct material costs as well as the conversion costs (i.e. labour and production overheads) can be assigned to each process directly by means of the input-output scheme obtained in Section 3. Selected cost items, however, must be discussed further: An estimate of predetermined overhead cost rates can be calculated as usual, dividing the annual expected overhead costs by the expected annual amount of the cost driver chosen. In Table VII a different overhead cost rate has been determined for each piece of equipment involved. In our example, the conversion costs have been assigned on the basis of the cycle time of each process, measured as machine hours. As to the post-purchase costs, the unit cost of direct materials in the use phase has been calculated as the present value of an annually recurring uniform amount of, say 1e/L for detergent and 100e/ton for cement, using a time frame of 40 years and a discounting factor of 5 per cent. A cost function should be used instead of a cost estimate for the resources that have been purchased in different periods of times at different costs. Assume that the beginning inventory of a certain raw material is q (0) and its unit cost is p (0). If q * is the total planned consumption of that resource obtained as a row sum from Table VII, and p (1) is the expected unit purchase price that will be applied to that commodity during the planning period, then the cost that should be applied ( p *) is a function like: 8 * < p ¼ p ð0Þ e=ton *
: p ¼ p ð1Þ e=ton
if 0 , q , qð0Þ *
if qð0Þ , q , q
ð13Þ
Within the supply chain of production processes, a waste will be sold, and consequently purchased, at an exogenous price (Nakamura and Kondo, 2009) recorded in vector p (Table VII). In our example this occurs only for the secondary water: being
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p k , 0 (for k ¼ 6) such price is an income for the process selling the waste and a cost for the processes receiving it. However, it may also happen that p k $ 0. In Section 3.4 we have anticipated that some overhead costs are period-related rather than volume related. They can be assigned by means of specific cost drivers (even not physical) recorded separately in a matrix that we called F. Such drivers can be taken into account only after the material flows and the volume-related cost drivers will have been balanced against the production plan for the period considered. Note that the number of rows of matrix F depends upon the overhead issues that are to be assigned. A numerical example is provided in Table X. Fixed costs can be assigned to the processes on the basis of various, necessarily subjective criteria. The natural gas consumed by the firing processes is a typical example of a fixed cost driver, since the kilns used in the firing process must be kept turned on independently from the process being idle or not. In our example this cost has been assigned proportionally to the operating (i.e. not idle) time of the firing processes during the planning period. Table X takes also into account the fixed emissions of CO2 associated with the fixed consumption of natural gas. The beginning inventory of the intermediate product “powder type 1” is another fixed cost driver that can be seen in Table X, and that will be useful later in this section. The way the overall amount of beginning inventories originally recorded in the production plan has been attributed to the various processes is an exogenous parameter. From Table X one can see that another vector of consumption intensities, p F , has been specified consistently with the number of rows of matrix F. Such intensities are usually the whole period costs, rather than cost coefficients, that will be multiplied by some percentage in order to assign them to processes. It is now possible to calculate in a deterministic way the vector of direct process costs v: ! ~ B v ¼ pTB · ð14Þ F T pT pTR pTF is the transposed vector of consumption where pTB ¼ pM pT intensities shown in Tables VII and X. The direct process costs are shown in Table XI. Once the direct cost of each process has been determined, it is possible to calculate the unit cost of each intermediate and final product, consistently with step (9) of the LCC model. The input-output structure described so far guarantees that the manufacturing cost of the main output of a process be transferred into the downstream processes, as a separate category of direct material costs. The cost of producing each main output is thus assumed to offset the corresponding process direct cost and the cost of those inputs supplied by the other processes, including the treatment processes, which are transferred in at their manufacturing cost. Consequently, the following condition must hold: ~ ¼v pT · X
ð15Þ
~ exists, the vector of unit product costs at each stage of the ~ 21 , the inverse of X If X operations chain, including the use stage (i.e. the life-cycle costs) is: ~ 21 pT ¼ v · X
ð16Þ
Beginning inventory of Powder type 2 Natural gas Fixed energy cost Setup Fixed CO2 emission
no. kg
% %
ton
3.28
3.36
E
1.77 0.45 0.69 0.43 0.18
A(1) A(2) A(3) B(1) B(2) B(3)
C(2)
C(3)
0.29 1
1.05 2
1.11
2100.00 2250.00 2 150.00
C(1)
(I)
3
0.74 2.69 2.51 0.35 0.83
D(1) D(2) D(3) F(1) F(3)
Processes
35 2.43
G(2)
42 2.88
G(3)
45.81 69.36 82.25
23 1.60
G(1)
J
I
(II) L
6.44 1.57 65.3
H
£ 2,500 £ 17
£ 0.05 £ 5.025
£ 2 20
Cost coefficients (e/unit) PF
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249
Table X. Period cost drivers (fixed)
e
Direct process cost
Table XI. Direct process costs
e
23,634 G(1) 6,065
26,141 G(2) 9,899
A(2) 16,143 G(3) 11,314
A(3) 3,651 J 39,757
B(1) 5,595 H 8,360
B(2) 4,631 I 4,004
B(3) 1,507 L 52,750
E 5,470
C(1)
12,725
C(2)
13,096
C(3)
1,466
D(1)
4,714
D(2)
4,367
D(3)
250
Direct process cost
A(1)
1,645
F(1)
3,746
F(3)
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However, in presence of beginning inventories of intermediate products, there are additional operations to be carried out before applying equation (16), so that the unit product costs can be assessed properly. Namely, it is necessary to subtract the inventory of a certain product used by a process, recorded in F, from the overall amount of the same ~ In our numerical product required as an input by the same process, recorded in matrix X. example, the first row of Table VI is modified as shown in Table XII. This reformulated ~ is used in equation (16), the outcomes of which are shown in Table XIII. These version of X results will serve as “forecast variables”, as anticipated at the end of Section 4. Finally, if the allocation procedure described in Section 5 has been also applied, then the former unit cost of producing the “dried tile type 2” (123.6e/ton) and the “fired tile type 2” (162.8e/ton) shown in Table XIII can be decomposed into the unit cost of value-adding activities, respectively, 106.46e/ton and 159.9e/ton, and the unit cost of producing the associated scrap is, respectively, 138.6e/ton and 183.9e/ton. The higher cost of producing one unit of scrap is due to the fact that the disposal costs have been entirely assigned to the processes producing it. Clearly, a unit of scrap generated downstream is associated with a higher cost because it includes the cost of the preceding stages.
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7. Perform Monte Carlo analysis All the procedural steps which are necessary to set up the source and response variables within the non-deterministic model have been illustrated through the preceding sections. In order to include the repercussions of the uncertainties described in Section 4, the appropriate algorithms can now be applied in order to determine how the changes occurring in the source variables affect the response variables. To this purpose, techniques like the Monte Carlo methods allow all the uncertain values in the assumption cells to vary simultaneously. The need to select a relatively important small number of variables has been mathematically discussed in Bullard and Sebald (1977). However, when using Monte Carlo methods this restriction does not apply. Models including thousands of variables are mathematically as straightforward as a model containing just seven variables, see for example Emblemsva˚g (2003), Appendix A. The aspects concerning the computational performance of running such a resource-intensive numerical method as Monte Carlo analysis have also been discussed by Peters (2007). However, since the focus here is on the ease of implementation, a simulation has been carried out by using Crystal Ball 7.3.1, an add-on application that runs on the MS Excel spreadsheet. The Monte Carlo Analysis is a sampling technique, and therefore a number of iterations are performed, using the software, in order to numerically simulate the changes caused to the forecast cells, given the variability of the assumption cells that serve as source variables.
... ~ X F
.. . Powder type 1 ... Powder type 1 (beginning inv.)
ton
...
Ton
...
C(1) .. . 2134.3 .. . 2100
Processes C(2) .. . .. 272.2 . 2250
C(3) ..2 139.7 . 2 150
... ... ...
Table XII. Changes to be made to Table VI to take into account the beginning inventory as in Table X
Table XIII. Unit product costs, included post-purchase costs for one product model (life cycle costs)
Unit e/ cost unit
72.3
65.4
64.1 132.6 145.4 151.8
Slip Powder Type 1 2 3 1 2 3 Unit (ton) (ton) (ton) (ton) (ton) (ton) 42.9
(ton)
Glaze
Dried tile 1 2 3 (ton) (ton) (ton)
Glazed tile 1 3 (ton) (ton)
106.5 99.3 134.7 123.5 123.6 160.9 195.2 237.4 240.4 159.9 282.9
Green tile 1 2 3 (ton) (ton) (ton)
252 5.9
0.9
295.4
Tile Treat prod. Dust of F Fired tile and use abatem. comp. 1 2 3 2 (ton) (ton) (ton) m2 kg kg
220.7
ton
Wastewater treatment
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The unit production costs of each process-stage (Table XIII) serve as response variables. Examples of assumption cells within the spreadsheet equivalent of matrix A have been shown in Tables VIII and IX. As anticipated in Section 4, when all the trials have been performed with the aid of the software, each forecast cell can be described as a new statistical distribution. For illustrative purposes, if we take all the uncertainties as in the case presented here into account the distribution of one response variable, namely “Tile type 2 – production and use”, which is the life-cycle cost of the tile “type 2”, will be as shown in Figure 3(a). From Figure 3(a) one can see, for example, that there is a 10.1 per cent probability that the unit Life-Cycle Cost of the “tile type 2” will not exceed 6e/m2. This kind of information has evidently more managerial relevance than its deterministic equivalent. A sensitivity analysis, like shown in Figure 3(b) completes this information. One can see, indeed, that the unit Life-Cycle Cost of the tile “type 2” is directly correlated to the standard cost of post-purchase maintenance materials (detergent has a higher correlation, though the unit cost of cement is higher). There is a negative correlation instead among the variation in the LCC and those in the discount rate which is used to calculate the present value of an annually recurring uniform amount. As to the environmental cost drivers, the LCC is directly related to the cost of emission allowances and such correlation is higher than that between the LCC and the natural gas consumptions that cause CO2 emissions. Although not shown in Figure 3(b), also the costs of purchasing the waste disposal services and the wastewater originated by washing the mills are among the contributors to the LCC. Similar probability distributions and sensitivity analyses can be obtained for all the forecast cells used in the spreadsheet-based numerical simulation. One can also investigate therefore, which factors are likely to affect the cost of all the intermediate products.
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Figure 3. Life cycle cost of tile “type 2” Notes: (a) Uncertainty distribution; (b) tracing sensitivity chart
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For example, consider process C(2) (forming tile “type 2”) and the associated scrap. The unit cost of product c(2) is reduced by an increase in process efficiency, i.e. an increase of the quantity of the main output which can be obtained from the same amount of externally purchased inputs. Other consumption intensities that directly influence the cost of c(2) include electric energy, conversion costs, setup costs, the cost of the beginning inventories of the intermediate product “powder type 1”, and the cost of CO2 emissions. The cost of the scrap corresponding to the main product c(2), instead, is highly influenced by the external disposal costs, in addition to the other factors discussed above. So far, the purpose of this analysis has been mainly to find out which factors have the greatest impact on the total costs and what information should be paid extra attention to. This has been accomplished by tracing the different contributors using sensitivity analysis, and by mainly choosing bounded and symmetric distributions. This, however, can be seen as only one of the different ways in which Monte Carlo methods can be employed. Indeed, it should be noted, that sensitivity charts, like the one shown in this paper, not only can be used to identify the most critical drivers of performance but also can be a highly effective tool in identifying what information should be pursued in order to increase the quality of the analysis. Emblemsva˚g (2003) distinguishes among tracing models and uncertainty models. The former have been mainly employed here to show that for cost management, and the corresponding continuous improvement efforts, adding uncertainty means providing information about the possible distortion problems in the models. Quoting the author, in such cases “we do not need accurate data. We need satisfactory process descriptions that reflect the cause-and-effect relationships and data that are roughly correct”. On the other hand, uncertainty models aim at finding what information generates the most uncertainty and how this affects the forecasts. This implies that uncertainty is modelled as accurately as possible, in order to see how one issue which may be equal, in magnitude, to another one, actually differs in importance, being associated with a larger uncertainty. Consider for example, the input of detergent. It is used in the usage stage and therefore more uncertainty is given to it (Table IX). Owing to this aspect its cost is more important than other factors in sensitivity analysis. 8. Cost of emission allowances Before we close the paper off, we would like to illustrate briefly how an application of this kind of numerical analysis could concern the accounting implications of the EU Emissions Trading Directive. From an environmental analysis of the ceramic tiles in a life-cycle perspective what emerges clearly is that managing CO2 emissions plays an important role to reach improvements of the environmental performance (Nicoletti et al., 2002). Reduction in these emissions can be achieved especially by reducing the consumption of thermal energy. From a cost accounting perspective the repercussions on the unit product costs of the uncertainty associated with the cost of purchasing emission allowances are also investigated. The release of CO2 into the environment has been accounted for in matrix R, and it has been stechiometrically estimated. The corresponding consumption intensity recorded in Table XII, which we call p *, has been calculated as a predetermined overhead cost rate. Let q be an estimate of the emissions allowances that will be
purchased in the period, and that are not matched by the government grant – consisting in the initial allocation of allowances free of charge, denoted as q *. Now assume that p *, is a function of the following kind: 8 > < p* ¼ q2q* £ p e=ton if q . q* q ð17Þ > : p* ¼ 0 e=ton if q # q* where p is the expected average price of the allowances, which is used to assess their fair value. In other words, for the sake of simplicity, and because of the nature of the matrix operations, it is assumed that the government grant only reduces the average cost of the allowances per ton of CO2 equivalent. If q ¼ 4; 160ton is the overall amount of CO2 emissions expected in a one year period, and q* ¼ 1; 000ton, then the condition q . q * is satisfied. We assumed that p ¼ 22e per ton of CO2 equivalent (tCO2eq). Given the above, the deterministic value of p * is 17e/tCO2 equation (Tables VII and X). In order to perform a sensitivity analysis assume that p is characterized by a triangular distribution ranging from 5e/tCO2eq to 35e/tCO2equation This simple assumption is based on a survey carried out by Point Carbon (2007) as to the price of allowances in 2010. (A more complex analysis of uncertainty in the carbon price can be found in Zhu et al. (2009)). From the discussion in Section 7, the average price of allowances is expected to be among the contributors to the variance of the forecast cells. This result highlights that an increased cost of the emission allowances passes-through and increases the manufacturing cost of the ceramic tiles. It is important not only for cost accounting, but also for financial accounting to obtain a non-deterministic cost for the emission allowances. Indeed, the emission allowances give rise to an asset – and to a liability – which must be recorded at its fair value (Ratnatunga, 2007; Casamento, 2004). This aspect emerges also from an interpretation of the International Accounting Standards Board’s International Financial Reporting Interpretations Committee (IFRIC), even though the European Financial Reporting Advisory Group (EFRAG) has suggested not adopting such an interpretation. 9. Discussion and closure In this paper, a concept of LCC as a tool for use in EMA, based on an input-output technological model, has been applied to a vertically-integrated, multiproduct manufacturing process. Unlike other microeconomic IOA models, particular attention has been paid to modelling the environmental aspects along with cost and production planning, and the uncertainty has been addressed with a focus on the easiness of implementation. The proposed analysis is a conceptual one, but it has been designed while having practical implications in mind. Indeed, especially in a downturn it is important for the manufacturing firm to: . control and possibly reduce the cost of material flows along the operations chain; . assess the efficiency of the currently-adopted production technologies in terms of resources used; and . build scenarios on the impact of possible technological changes on costs.
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Moreover, approximation in product cost assessment may prove to be excessively risky, in particular in the presence of reduced margins, high variety of production, quickly evolving technologies and strategically constraining environmental issues – as it occurs in the case presented here. advanced management accounting tools (especially ABC and LCC) combined with those of Environmental Accounting are often addressed in literature in order to face these issues. Yet, practical limitations in their implementation as both combined and stand-alone tools are currently experienced in many countries. For example, a recent survey on a sample of Italian firms (Cinquini et al., 2008) showed that 40 per cent have never used LCC (in its traditional meaning, as discussed in Section 1 of this paper) and 44 per cent assigned to it a low to limited degree of perceived utility. Moreover, Italian firms are still experiencing difficulties in implementing the well-known ABC. Finally, EMA – meant for internal control, rather than for external reporting – is still in its infancy in Italy as well as in Europe (Bartolomeo et al., 2000). Given the above, the practical implications that may have risen from our analysis are discussed below. The General Manager, the Controller and the Production Manager are offered a stimulus to consider the still unused potential of LCC as a way of facing simultaneously some issues that belong to their respective areas. This has been done by means of an overview of the meanings of LCC (both the traditional and the emerging ones) as well as a thorough procedure and a detailed example. The practitioner is offered an example of making the computational mechanisms underlying EMA transparent, showing how physical and monetary measures can be actually integrated, and also taking the product usage stage into account. Our purpose is to contribute to the open debate on identifying and understanding those drivers that are relevant for both the environmental and cost analysis, especially the effects different design solutions may have on both material flows and the associated life cycle costs. The SME is motivated to explore the potential of integrating production and cost planning transparently and independently from the information system already in place (if any), by using spreadsheets. The paper has explicitly addressed the undeniable role of the uncertainty of parameters in order to reflect business reality and reduce risk while aiding management to take informed actions and also being intelligently able to request more information. Instead of introducing pure mathematical models that could have resulted intractable in business practice, we have briefly discussed the advantages of using numerical simulations by means of spreadsheets. Then, we have applied the Monte Carlo method in order to identify the most critical drivers of performance rather than precisely modelling uncertainty. However, the proposed model is subject to all the assumptions characterizing IOA, although some of them can be amended, at least in part. For example, introducing uncertainty makes the assumption of fixed technology less limiting. Furthermore, the proposed treatment of fixed costs also overcomes some non-linearity concerns in cost functions. Anyway, these limitations can be seen as reasonable as long as (1) the model does not aim at optimization problems and equation (2) it is mostly tailored to situations where specialized information systems and competence about several methods may be lacking, such as in many SMEs. Indeed, in daily accounting/production planning practice of SMEs at least in some countries, such complexity hardly appears to be of
primary concern, whereas handling systems of linear equations using spreadsheets may be sufficient. In theory, the approach can handle any processes in any corporation, but actually it would be impossible to establish all the various matrices necessary to handle the complexity of real corporations. This approach is, therefore, mostly suitable for conceptual studies or for simplified cases involving a small set of products, commodities and processes, as in the case presented. Complex issues such as non-linearity and dynamics of the model have not been addressed, but could be included in further developments of the model, possibly introducing elements of optimization.
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