Optimization/simulation-based Framework for the Evaluation of Supply Chain Management Policies in the Forest Product Industry Wassim Jerbi, Jonathan Gaudreault*, Sophie D’Amours, Mustapha Nourelfath, Sébastien Lemieux, Philippe Marier, Mathieu Bouchard FORAC Research Consortium, Université Laval Québec, Canada * Corresponding author:
[email protected]
Abstract—This work describes a framework for the elaboration and evaluation of management policies for production and transportation supply chains in the forest product industry. The approach deals with the issue of coordination between the tactical and operational decision levels. First, we introduce LogiLab, a software system allowing to model the network and to optimize product flows in the supply chain. We than show how one can use this tactical aggregated plan to identify management policies that will guide day to day operations at the operational level. Finally, a discrete event simulation model allows assessing with more details what would be the impact of implementing these policies at the operational/execution level. Keywords - tactical planning; operational planning; optimization; simulation; supply chain management; forest products industry.
I.
INTRODUCTION
Over the last few years, the forest products industry in Canada has suffered from poor financial performance [1]. This is due to a decline in demand related to the recession in the U.S. which melted the housing starts. Also, the rapid appreciation of the Canadian dollar and an excess of production capacity added to the challenge [2]. In this context, competition is not only within enterprises themselves but also between supply chains which the enterprises belong to.
production/transportation plan from which product flows policies are extracted. The decision-maker then suggests execution policies (ex: rules to be used for truck loading) and the combination of those policies are evaluated using a discrete-event simulation model based on Simio simulation software. The reminder of the paper is organized as follows. Section II introduces basic concepts regarding supply chain management. Section III details the proposed framework. Section IV presents the application of this proposed framework in a real case. Section V concludes the paper. II.
LITTERATURE REVIEW
Simchi-Levi and David [3] define Supply Chain Management (SCM) as "a set of approaches utilized to efficiently integrate suppliers, manufactures, warehouses and stores, so that merchandise is produced and distributed at the right quantities, to the right locations, and at the right time, in order to minimize system wide costs while satisfying service level requirements." Planning decisions can be grouped in three different categories/levels: strategic, tactical and operational [5], as shown in Fig. 1. The major difference between these levels is the time frame of the related decisions.
A supply chain (SC) is a network of organizations, people, activities, information and resources involved in the physical flow of products from supplier to customer [3]. It performs the functions of procurement of raw materials, transformation of these materials into semi-finished product, finished products, and transportation between facilities and to customers. As underline by Jianfeng et al, "Supply Chain Management (SCM) becomes an important management conception for enterprises in the current vehement environment" [4].
The strategic level deals with long term decisions. As an example, it includes the selection of locations for facilities and production technologies to be employed at each facility. Strategic decisions thus determine the network through which production, assembly and distribution serve the marketplace. As a representative example of research related to strategic decision-making in the forest product industry, Vila et al proposed in [6] a market driven approach to design productiondistribution networks for the lumber industry.
Our objective is to propose a framework to identify and evaluate different combinations of production, transportation and execution policies for supply chains in the forest product industry. Within this framework, a software called LogiLab allows modeling the network and performs mathematical optimization in order to propose an aggregated
The tactical level prescribes material flow management policies, including production levels, assembly policy, inventory levels and lot sizes. Typically, it deals with medium term decisions that have planning horizon from a few months to a year. The planning activity at this level usually provides an aggregated production plan. It is established based on
Figure 1. Strategic, tactical and operational decision levels.
forecasts, and using aggregated products family, production capacity and aggregated time bucket (each period of the plan corresponding to a week or a month). Singer and Donoso [7] have worked on the case of internal supply chain management in the Chilean sawmill industry. They proposed a model for production optimization and inventory planning decisions within a system of plants. However, the study neglects the possibility of exchanging intermediary products among plants. Farell and Maness [8] proposed a relational database approach that they used to create an integrated linear programming-based decision support system. It’s used to analyze production planning issues in a wide variety of secondary wood product manufacturers. The operational level deals with the environment created by decisions made at the strategic and tactical levels. It involves short term decisions that provide a daily functioning and efficient organization. It schedules operations to assure in-time delivery of final products to customers, coordinating the logistics network to be responsive to customer demands. As examples of research applied to the forest products industry, Rönnqvist [9] proposed a method for the allocation of wood products in order to optimize the cutting process in real time, and they later integrated defect detection to this approach [10]. Chandra and Fisher [11] presented a single plant, multi-period model that seeks to combine production planning with the vehicle routing problem. Gaudreault et al. [12] proposed models to plan and schedule production operations in the softwood lumber industry according to demand. As already mentioned, the targets set by productiontransportation plan at the tactical level are used to guide operational level. However, the issue of how to implement tactical decisions at the operational level remains an open field of study. In the context of forest products industry there is some work related to tactical/operational forest operations (e.g. [13]) but tactical/operational wood transformation supply chain is like missed in the literature. At this point, we need to mention there are two classes of production systems. In a pull system, production at the operational level is planned according to actual customers’ orders. In a push system, production at the operational level is only driven by decisions of the tactical level (salespeople must sell the production forecast).
Throughout this article, we will study the question of tactical/operational integration in a push production system in the softwood lumber industry. We propose a tactical mathematical model optimizing flows in the logistic network. It aims at maximizing profits by increasing production value and reducing transportation, inventory and production costs. This model specifies specific quantities to produce at each mill and to transport from one node to another for every period of the planning horizon in order to achieve maximum profitability. From this aggregated plan, it is possible to extract productiontransportation flow policies (ex: percentage of production from mill A for product 1 that must be shipped to mill B at period T). In the next section, we will demonstrate how they can guide the execution of operations at the operational level. This demonstration is done using a simulator that uses tactical decisions as it in input. However, the actual performance achieve by the network also depends on other policies that a tactical aggregated model does not provide – we call them execution policies. An example of execution policies is truck loading/scheduling policies. Therefore, the proposed framework also helps the decision-makers to identify the best combination of production/transportation flow policies and execution policies. III.
OPERATIONAL FRAMEWORK
The framework we propose for the elaboration and evaluation of tactical management policies of supply chains in the forest products industry is illustrated in Fig. 2. It includes two main activities (A and B) divided into 7 steps (labeled from 1 to 7 in Fig. 2). Activity A (aggregate optimization of the tactical level) is supported by our modeling and optimization software called LogiLab. Activity B (anticipation of operational/execution performance) is supported by a discrete-event simulation model developed using the Simio simulation software. A. Aggregate Optimization at the Tactical Level This activity is supported by LogiLab. It allows decisionmakers to easily design and optimize forest industry supply chain network (SCN) without any background in operations research or mathematical programming. First (Step 1 in Fig. 2), the user sketches the supply chain network and models the mills based on aggregate data. This is done using a schematic or geographic representation of the network. The user places the various elements of its network on the map and defines the inputs and outputs of each production unit, according to the transformation process involved. It also defined the possible product flows between the production units as well as the distances (see Fig. 3). Then, based on demand forecasts, raw material available and the processing capacity of each plant, a multi-period flow optimization (Step 2) is performed by LogiLab in order to maximize the network profits. The detailed mathematical programming model used by LogiLab is provided in the Appendix.
Figure 3. Framework for optimal supply chain management policies.
The results of the optimization provide a tactical aggregated plan (aggregated production and transportation plan) over a multi-period horizon (typically 52 one-week periods). It specifies, for each mill and each product, the manufactured volume per period and the processes to use. For a given product, it also specifies the volume to be transported for one node of the network to another.
X% of the production for product Y from mill A should be shipped to distribution centre B at period T. Similar weight or ratio are computed for production (i.e. usage of production capacity and processes). Such policies are more easily accepted by operations people than a plan stating that we must transfer exactly 234 units of a
The plan can be previewed and analyzed by decisionmakers (Step 3) using user interfaces and reports provided by LogiLab (Fig. 4). In this specific figure, we can see that the volumes to be transported from one node to another are displayed on arcs (colors and weight of the arcs make the analysis easier). Moreover, the decision-maker is provided with expected performance associate with the aggregated plan, such as costs (transportation, production, and inventory), profit, used capacity for each business unit, etc. Once the tactical plan is obtained, the next question that arises is: how to use the decisions taken at the tactical level in day-to-day operations? The answer is provided by Step 4 which consists in the automatic extraction of production & products flow policies that will guide the operations at the operational level. Instead of using the “absolute” values obtained by the tactical optimization, we extract weight (or ratios) associated to the different arcs. As an example, the policy will specify that
Figure 2. Supply chain modeling using LogiLab.
for modeling discrete event systems that provides accurate 3D animated models. While aggregate data were sufficient for flow optimization, the simulation requires more detailed information. For each business unit, we must specify the number of machines and their properties, incoming and outgoing products, etc. For transportation, we characterize the transportation mode (number of trucks and capacities). Then we integrate the policy developed in Activity A which provides production and transportation periodic targets on percentage of each product. This is made easy, thanks to how Simio implements alternative “routing” for products: for each alternative Simio asks us to provide a “weight”. During simulation, Simio selects stochastically which alternative routing should be used each time a batch is available.
Figure 4. Visualization of aggregate production & transportation plan using LogiLab.
given product from mill A to mill B. Optimization results are based on aggregated information; we cannot be sure that 234 units will actually be available. However, a guideline taking the form of a percentage is generally well accepted. B.
Detailed simulation of operational/execution level In real life, the actual performance will differ from the performance anticipated by the tactical aggregated model. This is related to two main factors: (1) real life is stochastic, and (2) tactical models work on aggregated data. An example of aggregated processes is transportation. In practice, performance will not only depend on product flow policies, but also from execution policies (ex: rules to be used for truck loading and dispatching). Those execution policies cannot be extracted from our tactical plan; however the decision maker can easily formulate a set of alternative policies to be tested (Step 5).
Finally, simulation results must be analyzed by the decision maker (Step 7). Results are provided for different sets of policies. The decision-maker has access to a wider range of indicators than those obtained from the tactical optimization (e.g. average stocks level over time, etc). Based on this analysis the decision maker can suggest changes on execution policies and production/transportation flow policies and evaluate them again. IV.
EVALUATION OF THE FRAMEWORK (ONGOING WORK)
This section presents preliminary results obtained with the proposed approach. The case study is a network constituted by a group of sawmills (Fig. 5) in Canada that produce lumber. These mills are owned by one company. Lumber production involves three main processes which must be performed in sequence: (1) sawing, (2) drying and (3) planing. The reader is referred to [12] for a through description of softwood lumber industry. Some of these mills may only have the required equipment to process the sawing of the logs. Others only have the required equipment for lumber drying and
Using simulation (Step 6), these execution policies can then be evaluated in conjunction with the product flow policies extracted from the tactical plan. This simulation also provides us with a better evaluation of expected performance (in comparison to the tactical model) as stochasticity is introduced by the simulation. Simulation, according to Banks et al. [14], is “the imitation of the operation of a real-world process or system over time. (…) Simulation modeling can be used both as an analysis tool for predicting the effect of changes to existing systems and as a design tool to predict the performance of new systems under varying sets of circumstances." Today, most software available to simulate stochastic manufacturing operations are based on the discrete-event simulation model. A discrete-event simulation model is defined as one in which the state variables change only at those discrete points in time at which an event occurs [15]. Our framework use a detailed simulation model we developed using the Simio software [16] (see Fig. 6). It is a tool
Figure 5. Processes and localizations of the mills.
Figure 6. Network modeling with Simio.
some others have facilities to saw, dry and plane the wood, as shown in Fig. 5. When a sawmill does not have the drying or planing equipment or capacity, the lumber has to be moved to another location to continue its processing.
TABLE I.
PERCENT CHANGE IN VALUES FROM CURRENT SITUATION TO OPTIMAL SOLUTION
In the context of this study, we do not have control over the sawing process. This activity has been planned by the company taking into consideration log availability and sawmills capacity. As a result, the volume of green rough lumber produced by each mill at each period (for 12 one-month periods) is already determined. First, the network was sketched and optimized using LogiLab and a multi-period optimization was performed. An aggregate production-transportation plan was determined for 52 weeks horizon. The optimal solution was compared to the actual supply chain plan used by the company (Table 1). In the base case, the network is unable to use all the available capacity of the mills: despite an average capacity utilization of 71% for the drying operations and 69% for planing operations, 9% of the potential product volume could not be completed and sold. In contrast, the optimal solution completely processes all the possible lumber volume to completion and the difference between revenues and costs (we do not use the term “profit” as some fixed costs are not taken into account in our study) is increased by more than 14%. In the optimal solution, the mill’s capacity utilization is increased on average by 11% as more lumber is dried and planed.
Within the optimal solution, no ending inventory or work in process exists in the network at the end of the planning horizon. The initial inventory of green and dry rough lumber is decreased to zero in the first few periods, and the inventory cost is thus decreased by 83%. In this optimal solution, much more green wood is transported. The increase in green wood transportation is explained by the global increased volume of lumber processed. The next step was to build the detailed model of the network with Simio. As this is an ongoing work, we are not able to provide simulation results at present time. However, we already benefits from the simulation models as it allows to demonstrated industrial partners how tactical decisions can be implemented at the operational level. Being able to show 3D animations of flows of trucks and products is priceless.
V.
CONCLUSION
This paper proposed a framework for the selection of supply chain management policies that best operate a lumber supply chain network. The framework is based on two phases. The tactical phase is supported by software called LogiLab. It facilitates to model the supply chain and determine the aggregate production-transportation plan. From this plan, production & products flow policies is automatically extracted. In the second phase, the user evaluates this policy at the operational/execution level on combination with execution policies, using a discrete events simulation supported by Simio software. The goal is to allow identification of the best combination of production-transportation flow and execution policies. One may ask why is it needed to perform optimization at the tactical level if a more precise evaluation can be done using the simulation model? A simple answer is that there exist an infinite number of products-flow policies; it would not be possible to evaluate them all using the detailed simulation model. However, the optimization at the tactical level allows identifying the ones that must carefully studied using the simulation model. Providing this simulation also illustrates how the decisions provided by the tactical model could be implemented at the operational level in the real world. As for future work, we intend extending the framework in order to study and support tactical/operational integration in a pull production system where operations are driven by customer orders.
f etpu
: Maximal flow of product p passing through the
cw
link e at period t . : Maximal flow of all products passing on link e at period t . : Cost of process w .
f cetp
: Transportation cost of product p on link e if the
letp
transportation begins at period t . : Delay of transportation of product p on link e if
f etu
α pw
the transportation begins at period t . : Delay of production of product p with the process w . : Quantity of product p required by the process w .
γ pw
: Quantity of product p made by the process w .
λkuw dtup
: Quantity of units of capacity type k ∈ K of the business unit u consumed by the process w . : Demand for product p at business unit u at
ρtup
period t . : Sale value of product p at business unit u at
β tup
period t . : External supply of product p at business unit u
σt
at period t . : Discount factor at period t .
sw
Decision variables:
Dtup
: The quantity of the process w performed in business unit u and ending at period t . : The quantity of product p sold by business unit
: The set of business units.
Fept
: The
K
: The set of types of capacity (machine capacity, limits of stocks).
Objective function:
W
: The set of processes (machines, inventories).
APPENDIX - MATHEMATICAL MODEL Ensembles:
T
: Number of time periods.
U
Wtu ⊂ W : The set of processes that can be performed in business unit u at period t .
P E δ u+ ⊂ E
: The set of Products. : The set of links between business units. : The set of incoming links to u .
δ u− ⊂ E
: The set of outgoing links from u .
Maximize f σ t ∑ ∑ ρtup Dtup − ∑ cwYtuw − ∑ ∑ cetp Fetp (1) ∑ e∈E p∈P u∈U p∈P dtup>0 t∈T w∈Wtu Constraints:
γ pwYt1up + ∑ ∑ Fet2 p − ∑ t1 ∈T w∈Wt1u |t1 + sw t = e∈δ u+ t2 ∈T |t2 + let2 p t =
β tup + ∑
: Capacity of type k ∈ K of the business unit u at period t available.
w∈Wtu
∑λ
w∈Wtu
f etpl
u at period t . flow of product p on link e at period t .
∑α
Parameters:
qktu
Ytuw
: Minimal flow of product p passing through the link e at period t .
Y
pw tuw
Y
kuw tuw
Dtup ≤ dtup
(2)
− ∑ Fetp − Dtup = 0 ∀t ∈ T , u ∈ U , p ∈ P. e∈δ u−
≤ qktu
∀t ∈ T , u ∈ U , k ∈ K .
∀t ∈ T , u ∈ U , p ∈ P.
(3) (4)
∑F p∈P
etp
≤ f etu
∀t ∈ T , e ∈ E.
(5) [13]
f etpl ≤ Fetp ≤ f etpu
∀e ∈ E , t ∈ T , p ∈ P.
D, F , Y ≥ 0.
(6) (7)
[14] [15]
The objective function (1) maximizes profit in the network (sales revenue minus cost of production, storage and transport). The constraint (2) ensures the conservation of flow through the network. The constraint (3) ensures compliance with production capacity. The constraint (4) limits the satisfied demand with potential demand. The constraint (5) respects flows capacities on the links. The constraint (6) guarantees the limit of flow capacity of each product relative to a given link. It should be noted that in this model, the inventory is modeled as a process that consumes a product p at period t and gives the same product p at period t + 1 . Inventory limits are the limits of resource consumption qktu , where k represents the capacity of inventory. REFERENCES [1]
Forest products association of Canada. Available on line: http://www.fpac.ca/index.php/en/industry-outlook (Accessed January 2012)]. [2] L. Benoit, " Canada's forest industry: recognizing the challenges and opportunities," Report of the Standing Committee on Natural Resources, House of Commons, 2008. [3] D. Simchi-Levi, P. Kaminski, Designing and managing the supply chain–concepts, strategies and case studies, New Jersey: McGraw-Hill, 2006. [4] J. Li, W. Li, Y. Li, "Port supply chain simulation model under interactive analysis," in 2011 International Conference on Advanced in Control Engineering and Information Science, CEIS 2011, August 18, 2011 - August 19, 2011, Dali, Yunnam, China, 2011, pp. 2082-2086. [5] R.H., Ballou, Business Logistics Management, Prentice-Hall, Englewood Cliff, NJ, 3rd edn, 1992. [6] D. Vila, A. Martel, R. Beauregard, "The strategic design of forest industry supply chains," INFOR, vol. 47, pp. 185-202, 2009. [7] M. Singer and P. Donoso, "Internal supply chain management in the Chilean sawmill industry," International Journal of Operations & Production Management, vol. 27, pp. 524-41, 2007. [8] R. R. Farrell and T. C. Maness, "A relational database approach to a linear programming-based decision support system for production planning in secondary wood product manufacturing," Decision Support Systems, vol. 40, pp. 183-196, 2005. [9] M. Rönnqvist, "A method for the cutting stock problem with different qualities," European Journal of Operational Research, vol. 83, pp. 57-68, 1995. [10] M. Ronnqvist and E. Astrand, "Integrated defect detection and optimization for cross cutting of wooden boards," European Journal of Operational Research, vol. 108, pp. 490-508, 1998. [11] P. Chandra and M. L. Fisher, "Coordination of production and distribution planning," European Journal of Operational Research, vol. 72, pp. 503-17, 1994. [12] J. Gaudreault, P. Forget, J. M. Frayret, A. Rousseau, S. D'Amours, "Distributed operations planning in the softwood lumber supply chain: Models and coordination," International Journal of Industrial
[16]
Engineering : Theory Applications and Practice, vol. 17, pp. 168-189, 2010. D. Beaudoin, J. M. Frayret, L. LeBel, "Hierarchical forest management with anticipation: An application to tactical-operational planning integration," Canadian Journal of Forest Research, vol. 38, pp. 21982211, 2008. J. Banks, J.S. Carson, B.L. Nelson, D.M. Nicol, Discrete-event system simulation, Prentice Hall, fifth edition, 2010. Averill M. Law and W. David Kelton. Simulation Modeling and Analysis. McGraw-Hill, Inc., third edition, 2000. C. D. Pegden and D. T. Sturrock, "Introduction to Simio," in 2011 Winter Simulation Conference (WSC 2011), 11-14 Dec. 2011, Piscataway, NJ, USA, 2011, pp. 29-38.
