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Variety Management M t in Manufaacturing. Prooceedings of o the 47th CIRP C Confeerence on Manufacturin M ng Systems
Investiga I ating Beest Capaccity Scaling Poliicies forr Different Reconnfigurabble Mannufacturing Systtem Scennarios Shady y S. Elmasrry, Ayman M. A. Youussef*, Mo ohamed A. Shalaby Department of o Mechanical Deesign and Producction, Faculty of Engineering, E Caiiro University, Giiza 12613, Egypt * Corresponding autthor. Tel.: +1-2266-975-5603; fax: +1-519-973-7053 + 3 E-mail address:: ayman.youssef@ @alumni.uwindsoor.ca
Abstract Thiis research pressents a System Dynamics appproach to modeel and analyze a single stage Reconfigurable R e manufacturingg system (RMS S). The model is a continuuous time modeel. The system is i exposed to a random demannd that is assum med to follow a normal distribuution pattern. Scaling S pacity up or dow wn is assumed unrestricted, annd no outsourciing is allowed. New modificattions to the exissting state of thhe art capacity scaling s cap model are appliedd in order to brring it closer too reality. A costt model for evaaluating differeent scaling policies is introducced and a modu ule for con nsidering seasonnal demand is added. a The fulll-fledged simulaation model waas developed annd tested using Vensim DSS Double D Precisioon 5.2a pacckage. Comprehhensive experim mentation and analysis a are appplied to evaluatee the performannce of five capaacity scaling poolicies under different system scenarios. The unit cost is i the performaance measure coonsidered for policies p assessm ment. Experimen ntations are appplied on three stages; s preeliminary experrimentation to select s the effecctive factors am mong all factorss, Taguchi fracctional factoriall design to seleect significant factors f 4 among the effectivve factors, and d 2 full factoriaal design to connduct multiple system scenariios that are useed in the policyy assessment prrocess. d results to t help a practittioner in decidiing the best scaaling policy acccording Pollicy selection ruules are produced based on thee full factorial design to the t existing sysstem scenario. The results shoow that chasingg demand policcy and inventorry-based policyy have the best performance inn most system scenarios. 22014The Authoors. b open by Elsevier B.V V.article under the CC BY-NC-ND license © © 2014 Elsevier B.V.Published This is an access Sel lection and peerr-review under responsibility of o the Internatio onal Scientific Committee C of “The 47th CIRP P Conference onn Manufacturingg (http://creativecommons.org/licenses/by-nc-nd/3.0/). Sys stems” inand thepeer-review peerson of theunder Con nference Chair Professor Hodaa ElMaraghy. Selection responsibility of the International Scientific Committee of “The 47th CIRP Conference on
Manufacturing Systems” in the person of the Conference Chair Professor Hoda ElMaraghy” Keyywords: Capacityy scaling policy, Manufacturing M syystem, System dyynamics
1. Introduction I t The historyy of manufaacturing systeems shows their evo olution over tthe years as a response too an increasingly dyn namic and gloobal market with a greater need n for flexibbility and d responssiveness. Recently, Reconfigurrable maanufacturing system (RM MS) was intrroduced. It is i a maanufacturing syystem that proovides exactlyy the functionnality and d capacity nneeded, when it is needed [1]. RMS is inteended to combine the high h throughpput of dediccated maanufacturing lline (DML) with w the flexiibility of flexxible maanufacturing ssystem (FMS)) and react too changes quiickly and d efficiently [2]. It alllows repeateed changes and reaarrangements of the com mponents of a manufactuuring sysstem in a cost--effective wayy. One of the key features of o RMS is caapacity scalabiility.
Simply, it is the ability too adjust systeem capacity to t meet variable demaand. Capacityy scaling is coonsidered a classical problem in many industrries, and it was known as the capacity expaansion problem m to satisfy inncreasing dem mand in a cost-effecttive way. Thhe first studdy of the capacity c expansion problem p wass conductedd by Mann ne [3]. Representativ ve review of the classical capacity exppansion problem was conducted by Luss [4]. [ Since demand d ncreases and technologicaal advancemeents are uncertainty in faster, the neeed to address the t capacity scaling s problem m from a dynamic view point wheere capacity can c be increassed and ment. Key issuues that decreased beccomes an esseential requirem capacity scalaability problem m addresses arre: when, wheere, and by how mucch should thee capacity off the manufaacturing system be scaled s [5]. A dynamic model m for capacity c scalability analysis in reconnfigurable maanufacturing systems s
2212-8271 © 2014 Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). Selection and peer-review under responsibility of the International Scientific Committee of “The 47th CIRP Conference on Manufacturing Systems” in the person of the Conference Chair Professor Hoda ElMaraghy” doi:10.1016/j.procir.2014.01.116
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was introduced by Deif & W. ElMaraghy [6]. This model is associated with minimizing the delay in scaling the system’s capacity and thereby improving the RMS performance in response to sudden demand changes. Wang et al. [7] presented a scalability planning methodology for RMS that can incrementally scale the system capacity by reconfiguring an existing system. They developed an optimization algorithm, based on Genetic Algorithm, to determine the most economical way to reconfigure an existing system by adding or removing machines to match the new throughput requirements. An integer programming technique was used by Niroomand et al. [8] to explore how a firm should optimally allocate its capacity investments among different manufacturing systems considering the capacity evolution in ramp up period. Spicer et al. [9] developed an integer programming optimization tool to investigate the optimal scenario plan for a scalable RMS. They defined another scaling capacity cost that includes more details as the number of modules sold and bought. A new methodology based on a control loop approach was offered by Azab et al. [10] for the required planning, evaluation, restructuring and utilization of a reconfigurable manufacturing system. They portrayed manufacturing systems reconfiguration as a controller that minimizes the deviations between current values of reconfigurability, including capacity scaling, and their respective reference values. Kim and Duffie [11] presented a multi work station production system model that is based on control theory. They applied proportional control policy, with a delayed control gain, that represents realities of hiring/firing labor force and other issues that prevent instantaneous adjustment of capacity. Deif and H. ElMaraghy [12] proposed a system dynamics approach for a single stage scalable capacity model. The model objective was to examine different scalable policies using multiple performance measures. Further analysis for the same capacity scalable model focusing on a market-capacity integration policy was proposed [13]. The objective of this research is to evaluate capacity scaling policies under different system scenarios. The state of the art capacity scaling model, introduced and enhanced by Deif and H. ElMaraghy [12] & [13], is further developed in this paper to include more practical aspects. Two novel realistic modules are added. The first module includes a new method to evaluate the cost of implementing different capacity scaling policies. The second module introduces seasonal capacity scaling. Comprehensive experimentation methods are implemented to generate different system scenarios. These scenarios are used to evaluate different capacity scaling policies. The evaluation is based on determining the scaling policy that achieves the minimum cost/unit. Finally, policy selection rules are introduced to assign the best scaling policy for each system scenario. 2. A Cost-Based Model for Capacity Scaling In this section, a cost-based system dynamics model for capacity scaling is presented. The model is considered an extension to the original model introduced by Deif and H. ElMaraghy [12] by adding two modules in order to bring it closer to reality. The original model is a single stage RMS
subject to random demand that follow a normal distribution. Further details can be found in the original reference. Additional modules are introduced, which represent the extension to the state of the art model. The first module is dedicated to evaluate the total cost to help in the assessment of different scaling policies. It involves different manufacturing costs and capacity scaling costs, namely; Capacity Cost CC(t), Scaling Cost SC(t), Backlog Cost BC(t) and Inventory Cost IC(t). The total cost module (Figure 1) is presented as the summation of the four components. The first component evaluates Scaling Costs SC(t), which is composed of fixed scaling cost FSC and physical scaling costs. The fixed scaling cost FSC represents overheads of stopping production to rescale capacity, lost production, and salaries of labors involved in ordering and estimating new capacity. FSC is assumed to be independent on type of capacity scalability (up or down). The physical scaling cost represents the costs incurred to increase or decrease capacity levels including adding/removing another spindle to a machine, adding/removing a machine, and hiring/firing workers. Physical scaling cost is assumed to be proportional to the change in capacity. It is further assumed that scaling up unit cost is equal to scaling down unit cost and no outsourcing is allowed. Here, two conditions may exist. The first condition is when capacity level C(t) is not equal to the required capacity RC(t); scaling cost SC(t) will be formulated as the difference between required capacity RC(t) and the existing capacity C(t) multiplied by scaling unit cost SUC and added to the fixed scaling cost FSC. The second condition is when capacity level C(t) is equal to the required capacity RC(t), scaling cost SC(t) will be equal to zero (equation 1).
SC(t )
SUC * | RC(t) - C(t) | FSC, if RC(t) z C(t)
(1)
Otherwise SC(t) = 0 The second component is Capacity Cost CC(t), which is defined as the cost of operating full capacity at time t. It includes costs of salaries involved in the production process and overheads. It is formulated as the result of multiplying capacity level C(t) by capacity unit cost CUC (equation 2).
CC(t ) CUC * C (t )
(2)
The third component is backlog cost BC(t) which reflect penalties of late delivery costs. It is simply presented as backlog level B(t) multiplied by backlog unit cost BUC (equation 3).
BC(t )
BUC * B(t )
(3)
The last component is inventory cost IC(t) which represents cost of holding goods in stock. It includes physical cost of space, taxes and insurance, breakage and opportunity cost of alternative investment. Inventory cost is directly proportional to inventory level I(t) (equation 4). Where IUC is the inventory unit cost
IC (t )
IUC * I (t )
(4)
Total costs TC(t) are estimated by summing up capacity, scaling, backlog, and inventory costs (equation 5) at each
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tim me period. In order to calcculate the average cost for any tim me horizon, neew stock for sttoring and addding total costs
Figu ure 1: Total Cost module
is introduced i as cumulative cost. c It is form mulated to integrate totaal costs until the final timee (equation 6). Consequentlly, the aveerage total coost is determin ned by dividinng cumulative cost by the final tim me (equation 7). 7 To comparre between poolicies witth different time horizonss, the unit coost measurem ment is req quired (equatioon 8, 9), wherre D(t) is the demand d at tim me t.
TC C (t ) CC (t ) SC (t ) BC (t ) IC (t )
Cu ummulative cos c t Avveragecos t
T
³
0
Cummulative cos t T
Cu ummulative ddemand Un nit cos t
TC t
T
³ D t 0
Cuummulative coos t Cum mmulativedemand
(5)
impplemented to the t model throough adding fixed f scaling period p FSP P and seasonaal index SI (Figure 2); Fixeed Scaling Perriod is deffined as the number n of peeriods per seaason, and Seaasonal Inddex SI presentt a pulse funcction that allow ws capacity sccaling onlly at the beginnning of a seaason and bloccks capacity sccaling witthin the seasoon (equation 10, 1 11). For siimplicity, the value of the seasonal capacity will be considerred as the deemand vallue for the starrting period inn the season.
(6) (7)
(8) Figure 2: Seasonal capacity c scaling module. m
(9)
One of the assumptions in i the originall model is thee need r capaccity each timee period. This issue requires high to readjust effforts and costss to achieve itt. However, iff we investigaate the reaal life, we willl find many inndustries charaacterized by having h a fixed fi period-byy-period demaand within a specific s season. For theese industries there is no neeed to rescale capacity level each tim me period. Ottherwise, cappacity planninng takes placce on quaarterly (everyy three mon nths) or seasonal basis while dem mand is updated period d-by-period. Seasonal cappacity scaaling is based on maintaininng capacity at a constant levvel for a fixed fi number of o periods or a season, whiile demand remains perriodic. At thee end of seaason, capacityy will be resscaled acccording to the average deemand of the following seeason. Neew variables were added to the originnal model [1 12] to ach hieve this prroperty. Thesse variables are responsibble to deffine number of periods thhat represent the season and a to preevent capacityy scaling withhin season perriods. This lo ogic is
SI (t )
PULSETRAIN T (FSP,0, FSP, finaltim me)
(10)
( RC(t ) C (t )) * SI (t ) (11) SDT Whhere: PULSE TRAIN is a function fu in Veensim DSS, SR R(t) is thee scaling rate and a SDT is thee scalability delay d time. SR R(t )
3. Experimenta E ation The objectiive in this section s is to generate diffferent sysstem scenarioss. These scenaarios were prooduced based on o the ideentified signifficant factors that affect thhe total cost. Three typpes of experim mentation are used in orderr to select fou ur key facctors from all system factorrs that may affect the totall cost. Firrst, a preliminaary experimen ntation is condducted to deteermine thee “effective faactors” (factorrs that are worth investigaation). Seccond, four “significant “ factors” f are selected from m the “efffective factoors” by conducting a Taguchi T Fracctional Facctorial Design n. Finally, a Full Factorial Design (2 24) is
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applied to generate the 16 possible system scenarios using the significant factors. In the experimentation stage, a preliminary number of runs are conducted. A set of 16 possible factors that have an effect on costs for any policy were considered. Two levels (high H and low L) for each factor were selected to investigate the impact of changing the level of this factor on the average total cost. One reference scenario was simulated by setting the values of all proposed factors at the low level, while the other 16 scenarios were simulated one by one by setting the value for exactly one of the proposed factors at high level H while keeping other factors at low level L. Five scaling policies are investigated in this experiment; chasing demand policy, inventory-based policy, WIP-based policy, hybrid policy [12] and Kim policy [11]. These policies were ranked at both the low level factor value L, and at high level factor value H relatively based on the Total Cost. Both
rankings for a given policy are compared to determine the factor effect in deciding the best scaling policy. If the policy ranking at a factor’s low level value L is the same at its high level value H, then this factor is considered “ineffective” and will be excluded from the following step. On the other hand, if the policy ranking at the factor’s low level value L is different from its ranking at high level value H, then this factor is considered “effective” and will be included in the following step for further analysis. Accordingly, The “effective” factors are: Demand Standard Deviation SD, Average Demand AD, Target Responsiveness Time TRT, Manufacturing Lead Time MLT, Inventory Adjustment Time IAT, Minimum Order Processing Time MOPT, Fixed Scaling Period FSP, Safety Stock Coverage SSC, Backlog Unit Cost/ Capacity Unit Cost BUC/CUC and Inventory Unit cost/Capacity Unit Cost IUC/CUC.
Trial No.
MLT
IAT
MLT*IAT
MOPT
SD
IUC/CUC
BUC/CUC
TRT
SSC
AVD (103)
FSP
MOPT* TRT
IUC/CUC * FCP
BUC/CUC*SSC
SD * AVD
Table 1: Factors Assignment in L16 OA.
1
2
2
-
1
0.1
0.1
0.1
1
2
10
1
-
-
-
-
2
2
2
-
1
0.1
0.1
0.1
3
5
50
3
-
-
-
-
3
2
2
-
3
0.5
1
1
1
2
10
1
-
-
-
-
4
2
2
-
3
0.5
1
1
3
5
50
3
-
-
-
-
5
2
5
-
1
0.1
1
1
1
2
50
3
-
-
-
-
6
2
5
-
1
0.1
1
1
3
5
10
1
-
-
-
-
7
2
5
-
3
0.5
0.1
0.1
1
2
50
3
-
-
-
-
8
2
5
-
3
0.5
0.1
0.1
3
5
10
1
-
-
-
-
9
5
2
-
1
0.5
0.1
1
1
5
10
3
-
-
-
-
10
5
2
-
1
0.5
0.1
1
3
2
50
1
-
-
-
-
11
5
2
-
3
0.1
1
0.1
1
5
10
3
-
-
-
-
12
5
2
-
3
0.1
1
0.1
3
2
50
1
-
-
-
-
13
5
5
-
1
0.5
1
0.1
1
5
50
1
-
-
-
-
14
5
5
-
1
0.5
1
0.1
3
2
10
3
-
-
-
-
15
5
5
-
3
0.1
0.1
1
1
5
50
1
-
-
-
-
16
5
5
-
3
0.1
0.1
1
3
2
10
3
-
-
-
-
Next, Taguchi Fractional Factorial Design is conducted to select the “significant” factors among the ten “effective” factors. To select the orthogonal array (OA) two arguments must be defined: the number of factors, and the number of levels for the factors of interest [14]. Since 10 factors are considered and each factor has 2 levels, the total degrees of freedom DOF required for the entire experiment is 10 (degree of freedom is equal to 102-1). Considering that the DOF of the two-level orthogonal array must exceed the required DOF of the experiment [14], L16 OA is selected (Table 1). It includes 16 different experiments in which the factors impact could be inspected. The 16 experiments are replicated for the five scaling policies. According to the results of running these experiments and by applying ANOVA to calculate the factors main effect (data not shown), four significant factors are selected; BUC/CUC, IUC/CUC, MOPT and TRT. Finally, A 24 factorial design is conducted to produce different system
scenarios. A system scenario is generated by selecting “H, L” levels for each of the four significant factors. The average cost/unit for each run is determined which represents the system response for each scenario under specific scaling policy (Table 2).
4. Selection of Best Scaling Policy Results of the Full Factorial Design FFD revealed that relative costs for a given policy differ from one system scenario to another. This observation indicates that a particular policy may be a good selection for a specific scenario but not necessary for another. A system scenario, in this study, is defined by the values of the four significant factors. Thus, a scenario defined as “HLLH” is a manufacturing system that has high BUC/CUC value, low IUC/CUC value, low MOPT value, and high TRT value. Accordingly, the FFD includes the 16 different system
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scenarios that are used in this assessment. For investigating the performance of the scaling polices, two different selection rules are presented. The first selection rule considers policy X and policy Y as the best scaling policies if the difference between their performance is 1% of the minimum cost/unit. Otherwise, policy Y is not considered as a best scaling policy for the same system scenario. The second selection rule considers policy X and policy Y as the best scaling policies if the difference between their performance is 5% of the minimum cost/unit. Otherwise, policy Y is not considered as a best scaling policy for the same system scenario. Results for the application of the first and second selection rules are shown in Table 3 and Table 4 respectively. The reason of defining two selection rules with different selection criterion is to offer the planner more flexibility to apply policy X or policy Y while sacrificing only a very small difference in cost/unit. This will help in taking better
decisions due to increasing available alternative policies for the same system scenario, which improves the applicability for different industries. According to the new criterion (1% margin in cost/unit) used in ranking of policies shown in Table 3, Chasing demand policy is found to be the best policy in 10 out of 16 scenarios. Inventory based policy becomes the best policy in 4 out of 16 scenarios. WIP based and hybrid policies become the best policy in 3 out of 16 scenarios. At the end, Kim policy is found the best in only 1 policy. For the other criterion (5% margin in cost/unit) used in ranking of policies shown in Table 4, Inventory based policy becomes a best scaling policy in 14 out of 16 scenarios. Chasing demand policy is found to be the best in 11 out of 16 scenarios. Hybrid and WIP based policies becomes the best in 8 out of 16 scenarios. Kim policy is found the best in 2 out of 16 scenarios.
Run
BUC/CUC
IUC/CUC
MOPT
TRT
Table 2: Full Factorial Design.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
L H L H L H L H L H L H L H L H
L L H H L L H H L L H H L L H H
L L L L H H H H L L L L H H H H
L L L L L L L L H H H H H H H H
Chasing Demand policy
Inventory based policy
WIP based policy
Hybrid policy
Kim policy
73.1 120 118.7 165.6 92.4 226 224 358 92 224.3 223 355 92.5 226.6 225.3 359.5
75.4 125.1 120.5 170.2 94.6 193.9 228 327.2 84.9 226 132 273 98.6 237.2 233 371.4
76 164.5 120.6 209 95.2 270 226.1 401 85.8 218 174 306.4 95.2 270 226 401
76.3 162.5 120.8 207 96 266 227 396.8 83.8 216 152 248.4 96.1 266 227 397
79.8 201.8 124.7 246.7 91.5 213.7 226.3 348.6 343.7 478.4 2,707 2,842 359 494 2,858 2,993
Run
BUC/CUC
IUC/CUC
MOPT
TRT
Table 3: First Policy Selection Rule.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
L H L H L H L H L H L H L H L H
L L H H L L H H L L H H L L H H
L L L L H H H H L L L L H H H H
L L L L L L L L H H H H H H H H
Chasing Demand Policy
Inventory Based Policy
WIP Based Policy
Hybrid Policy
¥ ¥ ¥ ¥ ¥
¥ ¥
¥
¥ ¥ ¥
¥ ¥
¥
¥
¥ ¥ ¥ ¥ ¥ ¥
Kim Policy
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Run
BUC/CUC
IUC/CUC
MOPT
TRT
Table 4: Second Policy Selection Rule.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
L H L H L H L H L H L H L H L H
L L H H L L H H L L H H L L H H
L L L L H H H H L L L L H H H H
L L L L L L L L H H H H H H H H
Chasing Demand
Inventory Based Policy
WIP Based Policy
Hybrid Policy
¥ ¥ ¥ ¥ ¥
¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥
¥
¥
¥
¥
¥
¥
¥ ¥ ¥ ¥
5. Summary and Conclusions This paper presented a cost-based model for capacity scaling of a manufacturing system characterized by capacity scalability. Modeling was based on a system dynamics approach to reflect the dynamic behavior of capacity scaling process. The manufacturing system was assumed to have a random demand that follow a normal distribution. Five capacity scaling policies were presented to scale capacity level to accommodate the random demand. New modules were introduced to the existing state of the art model to make it closer to reality. It includes adding total cost module and seasonal capacity scaling module. The performance of the five capacity scaling policies was evaluated through a statistical design of experiment to specify the best scaling policy for different system scenarios According to the results, two policy selection rules were introduced. The first rule shows that chasing demand policy and inventory-based policy have the best performance in most system scenarios. Kim policy produces high costs especially for high values of target responsiveness time. WIP-based and hybrid policies have an intermediate performance for all system scenarios. However, the second selection rule, which have more tolerance to consider a policy from the best, shows a common ranking for four policies in multiple scenarios. This observation could be justified by considering that computing capacity in these policies is based on the same factors but with different weights. Also, the second selection rule emphasize that Kim policy produces high costs relative to the other policies. As an extension to this work, new capacity scaling policies could be investigated to produce better performance. Also, the proposed scaling policies could be examined under different demand scenarios. References [1] Mehrabi, Mostafa G., A. Galip Ulsoy, and Yoram Koren. Reconfigurable Manufacturing Systems: Key to Future Manufacturing. Journal of Intelligent Manufacturing; 2000. p. 403-419.
¥ ¥ ¥
¥
Kim Policy
¥
¥
¥
¥ ¥
¥ ¥
¥
¥ ¥
¥
¥
¥
[2] Koren, Yoram, Uwe Heisel, Francesco Jovane, Toshimichi Moriwaki, G. Pritschow, G. Ulsoy, and H. Van Brussel. Reconfigurable Manufacturing Systems. CIRP Annals-Manufacturing Technology; 1999. p. 527-540. [3] Manne, Alan Sussmann. Investments for Capacity Expansion: Size, Location and Time-Phasing. MIT Press; 1967. [4] Luss, Hanan. Operations Research and Capacity Expansion Problems: A Survey. Operations Research; 1982. p. 907-947. [5] Deif, Ahmed M. and Hoda A. ElMaraghy. A Control Approach to Explore the Dynamics of Capacity Scalability in Reconfigurable Manufacturing Systems. Journal of Manufacturing Systems; 2006. p. 1224. [6] Wang, Wencai and Yoram Koren. Scalability Planning for Reconfigurable Manufacturing Systems, Journal of Manufacturing Systems; 2012. p. 8391. [7] Deif, Ahmed M. and Waguih ElMaraghy. Effect of Reconfiguration Costs on Planning for Capacity Scalability in Reconfigurable Manufacturing Systems. International Journal of Flexible Manufacturing Systems; 2006. p. 225-238. [8] Niroomand, Iman, Onur Kuzgunkaya, and Akif Asil Bulgak. Impact of Reconfiguration Characteristics for Capacity Investment Strategies in Manufacturing Systems. International Journal of Production Economics; 2012. p. 288–301. [9] Spicer, Patrick and Hector J. Carlo. Integrating Reconfiguration Cost into the Design of Multi-Period Scalable Reconfigurable Manufacturing Systems. Journal of Manufacturing Science and Engineering; 2007. p. 202-210. [10] Azab, A., H. ElMaraghy, P. Nyhuis, J. Pachow-Frauenhofer, and M. Schmidt. Mechanics of Change: A Framework to Reconfigure Manufacturing Systems. CIRP Journal of Manufacturing Science and Technolog; 2013. p. 110–119. [11] Kim, Jin-Hyung and Neil A. Duffie. Design and Analysis of ClosedLoop Capacity Control for a Multi-Workstation Production System. CIRP Annals-Manufacturing Technology; 2005. p. 455-458. [12] Deif, Ahmed M. and Hoda A. ElMaraghy. Assessing Capacity Scalability Policies in RMS using System Dynamics. International Journal of Flexible Manufacturing Systems; 2007. p. 128-150. [13] Deif, Ahmed M. and Hoda A. ElMaraghy. A Multiple Performance Analysis of Market-Capacity Integration Policies. International Journal of Manufacturing Research; 2011. pp. 191-214. [14] Roy RK, Design of experiments using the taguchi approach: 16 steps to product and process improvement. Wiley-Interscience; 2001.
