A comparison of HK-CONWIP and BK-CONWIP control strategies in a multi-product manufacturing system

Onyeocha, Chukwunonyelum Emmanuel; Wang, Jiayi; Khoury, Joseph; Geraghty, John Article A comparison of HK-CONWIP and BK-CONWIP control strategies in a multi-product manufacturing system Operations Research Perspectives Provided in Cooperation with: Elsevier Suggested Citation: Onyeocha, Chukwunonyelum Emmanuel; Wang, Jiayi; Khoury, Joseph; Geraghty, John (2015) : A comparison of HK-CONWIP and BK-CONWIP control strategies in a multi-product manufacturing system, Operations Research Perspectives, ISSN 2214-7160, Elsevier, Amsterdam, Vol. 2, pp. 137-149, https://doi.org/10.1016/j.orp.2015.07.001 This Version is available at: https://hdl.handle.net/10419/178258 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc-nd/4.0/ Operations Research Perspectives 2 (2015) 137–149 Contents lists available at ScienceDirect Operations Research Perspectives journal homepage: www.elsevier.com/locate/orp A comparison of HK-CONWIP and BK-CONWIP control strategies in a multi-product manufacturing system Chukwunonyelum Emmanuel Onyeochaa,∗, Jiayi Wanga, Joseph Khouryb, John Geraghtya aEnterprise Process Research Centre, School of Mechanical & Manufacturing Engineering, Dublin City University, Dublin 9, Ireland bMethode Electronics International, Germany article info Article history: Available online 29 July 2015 Keywords: Production control strategies Kanban allocation policies Multi-product manufacturing systems Hybrid Kanban CONWIP abstract This paper evaluates the performance of the Hybrid Kanban Constant Work-In-Process control strategy and Basestock Kanban Constant Work-In-Process control strategy operating Shared Kanban Allocation Policy (S-KAP) and Dedicated Kanban Allocation Policy (D-KAP) in a multi-product serial flow line. We explored the effect of an increase of product types on the WIP inventory in the system. A simulation-based optimisation technique was used in determining the optimal settings for the strategies. The strategies were compared via pairwise comparison technique and Nelson’s ranking and selection procedure. S-KAP responds quicker to demand than D-KAP. BK-CONWIP outperforms HK-CONWIP in a serial manufacturing system. It was shown that an increase in the number of product-type increases the number of PAC and WIP inventory. ©2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction CONWIP control strategy is one of the most studied Pull Production Control Strategies (PCS); Scopus (accessed 14th January 2015), a multi-disciplinary abstracting and indexing database, documents that the paper [1], that introduced CONWIP has been cited 440 times. CONWIP combines the high throughput of a push strategy and the WIP control mechanism of a pull strategy [1–3]. The merits of CONWIP prompted comparisons by researchers to other pull production control strategies. A CONWIP controlled system has been shown by various researchers to be superior to Kanban systems [4–7]. Additionally, CONWIP was reported outperforming other pull control strategies in terms of minimising Work-In- Process (WIP) while maximising the service level [8–11]. However, loose co-ordination between stages in the CONWIP strategy has led some researchers to propose modifications of the CONWIP control strategy. Bonvik et al. [12] proposed a Pull/Push control strategy called Hybrid Kanban CONWIP (HK-CONWIP) control strategy, which integrates Kanban control mechanism in each of the stages of a traditional CONWIP except for the last stage of the system. The Kanban controls the inventory level at every stage in the production line ∗Corresponding author. E-mail address: [email protected] (C.E. Onyeocha). except for the final stage while the CONWIP controls the inventory of the entire system. HK-CONWIP was shown to have a reduction in inventory levels at each stage when compared with KCS and CONWIP [10,12]. On the other hand, Wang et al. [13] developed a HK-CONWIP strategy that combines the Theory of Constraints (TOC), which focused on solving bottleneck issues in a production line. The proposed HK-CONWIP with TOC outperformed traditional HK-CONWIP and traditional CONWIP, while the traditional HK-CONWIP outperformed CONWIP. The study of Gaury et al. [14,15] generalised HK-CONWIP and showed that HK-CONWIP outperformed the Kanban and CONWIP strategies. Also, Geraghty and Heavey [16] evaluated the performance of HK-CONWIP and hybrid push/pull systems and showed that the control mechanism of the hybrid push/pull strategy found in Hodgson and Wang [17,18], is the same as that of HK-CONWIP. These studies [12–18] showed that HK-CONWIP is superior to KCS and CONWIP. A majority of these studies are based on single product manufacturing environments with the assumption that the research findings in single product manufacturing systems are scalable to multi-product manufacturing systems. With this assumption in mind, several studies in multi-product manufacturing systems implemented only D-KAP in their studies because it is the only production authorisation card policy found in single product manufacturing systems [19]. Prior to the findings of Baynat et al. [20], studies in multi-product manufacturing systems gave attention to issues such as planning and scheduling, optimisation of the CONWIP card [21]. Some of these studies proposed techniques for http://dx.doi.org/10.1016/j.orp.2015.07.001 2214-7160/©2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4. 0/). 138 C.E. Onyeocha et al. / Operations Research Perspectives 2 (2015) 137–149 Table 1 Acronyms used in this work. Acronym Description Acronym Description PCS Production Control Strategy KAP Kanban Allocation Policy BK-CONWIP Basestock Kanban CONWIP control strategy D-KAP Dedicated Kanban Allocation Policy BSCS Basestock Control Strategy S-KAP Shared Kanban Allocation Policy CONWIP Constant Work In Process control strategy PCS +KAP A specified PCS and specified KAP combination EKCS Extended Kanban Control Strategy Other Other abbreviations used in paper GKCS Generalised Kanban Control Strategy MPME Multi-Product Manufacturing Environment HK-CONWIP Hybrid Kanban CONWIP control strategy PAC Production Authorisation Card KCS Kanban Control Strategy WIP Work In Process inventory Table 2 Description of symbols. Symbol Description Symbol Description D1,2,... Demand card for stage 1,2, . . . CC CONWIP card in a S-KAP PCS D1,2,... Demand for product 1,2, . . . CC1,2,... CONWIP card for product 1,2, . . . in a D-KAP PCS D1,2,... 1,2,... Demand card for product 1,2, . . . at stage 1,2, . . . MP1,2,... Manufacturing process unit at stage 1,2, . . . K1,2,... Kanban card for product 1,2, . . . I1,2,... 1,2,... Inventory output buffer for product 1,2, . . . at stage 1,2, . . . K1,2,... 1,2,... Kanban card for product 1,2, . . . at stage 1,2, . . . I1,2,... 0Raw material inventory output buffer for product 1,2, . . . RM1,2,... Raw material for product 1,2, . . . solving scheduling issues that arise when production authorisation cards for two or more product types are waiting in a queue and a decision is required to ascertain which product-type should be released first [22–25]. Additionally, a number of studies [26,27] developed mathematical or simulation models for optimisation of production authorisation card in order to minimise the inventory, production and shortage costs in a multi-product system, while certain studies [28–31] evaluated the effect of the WIP cap of CONWIP in multi-product manufacturing systems. To address the issue of selection of an appropriate pull control strategy, researchers compare and rank the performance of various pull control strategies [32–37]. Baynat et al. [20] proposed a shared production authorisation card policy that is applicable only to multi-product systems. The application of S-KAP in GKCS and EKCS improved the WIP control of the strategies [20]. Olaitan and Geraghty [36] implemented D-KAP and S-KAP on five PCS in a two-product, three-stage multiproduct manufacturing system with minimal blocking policy to evaluate the performance of five PCS under negligible setup and similar manufacturing processes. The findings of Olaitan and Geraghty [36] agree with that of Baynat et al. [20] that S-KAP outperforms D-KAP, but suggested that under robust conditions D-KAP outperforms S-KAP. KCS, CONWIP, HK-CONWIP and BSCS cannot operate naturally in S-KAP mode [20,21,36]. Onyeocha and Geraghty [21] proposed a modification approach that enables PCS that is not capable of operating S-KAP naturally to operate it. The approach was implemented on HK-CONWIP and they developed a new pull production control strategy called BK-CONWIP. However, the performance of both strategies (HK-CONWIP and BK-CONWIP) in both policies (S-KAP and D-KAP) in a multi-product manufacturing environment is yet to be evaluated. In this study, we investigate and compare the performance of HK-CONWIP and BK-CONWIP in a multi-product, three-stage manufacturing serial line under high demand variation. The multiproduct serial line is similar to the model proposed by Olaitan and Geraghty [36]. However, we introduced no minimal blocking policy in our models. The line is highly automated with negligible setups. The remainder of this paper is organised by first presenting an overview of the production authorisation cards policies and the production control strategies under investigation in Section 2. The research methodology is presented in Section 3. The experimental results are provided in Section 4. The results are discussed in Section 5and Section 6provides the conclusion of the study. 2. Background An overview of the multi-product production authorisation card policies and the pull production control strategies being investigated is hitherto presented to guide the reader through the subsequent sections. Table 1 describes the acronyms used in this work for easy readability and comprehension while Table 2 defines the symbols used in this paper. 2.1. Description of the production authorisation card policies A majority of pull production control strategies use a signal card known as production authorisation card (sometimes referred to as Kanban) in order to release a product type into a manufacturing system, while few others such as Basestock Control Strategy (BSCS), use the actual demand to trigger the release of product type into a manufacturing system. In single product manufacturing environments, the production authorisation card is rigid such that it is dedicated to a specific product type. However, in multi-product manufacturing environments, the production authorisation cards could be shared among product types or dedicated to a specific product type [20]. The procedure in which the shared and dedicated production authorisation cards are implemented in a pull production control strategy is considered the production authorisation card policy. The two main production authorisation card policies found in the literature are the D-KAP and S-KAP. D-KAP is applicable to both single and multi-product systems. Each product type in a system has a designated number of production authorisation cards assigned for releasing of such a product type into a manufacturing system [19–21,36]. Therefore, the total number of production authorisation cards in a stage is given by the summation of the total number of production authorisation cards of all the product types in that stage. This implies that a system having a large number of product types with erratic demand will require planning a large number of production authorisation cards for each of the product types in a stage or a system. The issue of such a large number of PAC in a manufacturing system is that it results in a proliferation of WIP in the system which causes line congestion, long lead times and low throughput [19,21]. Furthermore, optimising the PAC for each product type in multi-product systems is complex in nature and takes a long period of time [36]. The complexity of the optimisation process is more prevalent in C.E. Onyeocha et al. / Operations Research Perspectives 2 (2015) 137–149 139 Fig. 1. D-KAP and S-KAP in a multi-product stage. multi-product manufacturing systems. In multi-product manufacturing systems, D-KAP is extended single product systems [19–21,36]. S-KAP was proposed by Baynat et al. [20], as PAC policy that allocates and distributes its resources among the product types in a system. There is only a single resource pool containing the total number of the PAC that is shared among all product types in a stage or a system. The allocation of PAC to product types in S-KAP in a multi-product system depends on the scheduling policy in the system. Onyeocha and Geraghty [21] suggested that sharing PAC in a multi-product system enables the PCS to rapidly respond to demand variations. Additionally, a decrease in a specific product type with a corresponding demand increase of another product type in the same system can be catered for without alteration or re-configuration of the control parameters [21]. However, in some PCS, S-KAP could also behave as D-KAP such that when a specific PAC is released from a finished product type. The released PAC is used to re-authorise a replacement of the same product type. The control mechanism of D-KAP and S-KAP, as implemented in a multi-product single stage manufacturing system is shown in Fig. 1. 2.2. Pull production control strategies under investigation HK-CONWIP uses CONWIP cards (a global set of cards) to control the inventory of the entire production system and Kanban cards (an individual signal cards) to tightly control the inventory of a stage in a system except for the last stage of the system that is push controlled. A vital feature of the CONWIP is that it sets an upper limit on the inventory of a system, which is referred to as WIP cap. However, CONWIP has a poor control of an individual stage inventory causing large inventory in front of the bottleneck stages in a system. Conversely, HK-CONWIP combines Kanban in its control mechanism in order to control each stage WIP excluding the last stage. The addition of Kanban controls in HK-CONWIP proffers a solution to the problem of a large buildup of inventories and bottleneck issues in a multi-product manufacturing system. The initial state of the final product inventory buffer of HK-CONWIP has a predefined number of basestock with CONWIP cards attached to them. The control mechanism of the D-KAP HK-CONWIP in a multi-product manufacturing system is presented in Fig. 2. In Fig. 2,MP1...3denotes the manufacturing process where the subscript signifies the stage number. Also, K1 1. . . K2 2are the stage Kanbans, the superscript refers to the product type and the subscript represents the stage number. CC1...2signifies the CONWIP card, while the superscript denotes the product-type that the card authorises. Finished product types in the final product inventory I1 3or I2 3 have CONWIP cards attached to them. When a demand for a product-type occurs, a finished product in the finished product inventory corresponding to the product-type is released to satisfy the demand. Simultaneously the attached CONWIP card on the released product is detached and sent back upstream to authorise a replacement of the similar product-type. In the first stage, the CONWIP card CC1...2is attached to a raw material RM1...2and a stage Kanban K1 1. . . K2 2and then transferred to the manufacturing process for production of the replacement product-type in the system. The finished product-type is stored in the output buffer of that stage I1...2 1. For production to begin in the next stage, the following factors must be available, next stage manufacturing process MP2, the next stage Kanban K1...2 2and a semi-finished product-type with CONWIP card CC1...2in the current stage output buffer I1...2 1. These parameters are synchronised together while the current stage Kanban is detached and sent back to its initial position. The synchronised semi-finished product-type is processed in the manufacturing process of the next stage. The finished product is then transferred to the output buffer of that stage m+1. When the product-type completes the processes in the next stage, it is then stored in the output buffer of that stage. The process continues in a similar manner until the last stage. If the last stage manufacturing process is available, the semifinished product-type in the output buffer of the previous stage is transferred into the last stage manufacturing process via a push control mechanism. The finished product is stored in the final product inventory. Traditional HK-CONWIP does not operate S-KAP. In order to develop HK-CONWIP in S-KAP mode, the modification approach proposed by Onyeocha and Geraghty [21] was implemented on HK-CONWIP. The control mechanism of HK-CONWIP S-KAP is similar to that of HK-CONWIP D-KAP, except for the modification at the last stage of the strategy. The modification is such that the CONWIP card is detached from the finished product, immediately the product-type leaves the manufacturing process of the last stage to enable the sharing of the CONWIP cards. Therefore, the base stock level of the final product inventory is used to trigger off demand information to the first stage of the system. Fig. 3 illustrates the control mechanism of HK-CONWIP S-KAP in a multiproduct manufacturing system. When a demand occurs in HK-CONWIP S-KAP, finished producttype (no CONWIP card attached) is released from the output buffer of the last stage to satisfy the demand. During the process of satisfying a demand, demand information D1or D2is transmitted to the first stage to authorise a replacement of a product-type. BK-CONWIP was recently developed by Onyeocha and Geraghty [21]. HK-CONWIP was modified owing to the need for rapid response to demand variability. The choice to modify HK-CONWIP was based on their review that it is a better strategy in comparison to Kanban Control Strategy (KCS), CONWIP and Basestock control strategy [21]. However, it has a tight coupling between demand information and the CONWIP cards such that it does not 140 C.E. Onyeocha et al. / Operations Research Perspectives 2 (2015) 137–149 Fig. 2. The control mechanism of HK-CONWIP D-KAP. Fig. 3. The control mechanism of HK-CONWIP S-KAP. Fig. 4. The control mechanism of BK-CONWIP D-KAP. operate S-KAP. Also, when a demand occurs, the demand information is transferred from the last stage output buffer to the first stage for replacement of the product-type. The demand information is transferred from the first stage to the subsequent stage until it reaches the last stage. This causes a slow response to demand in HK-CONWIP. BK-CONWIP combines the merits of BSCS (global transmission of demand information to all stages at the same time), KCS (stage inventory controls) and CONWIP (high throughput rate while maintaining a small quantity of WIP inventory). Figs. 4 and 5provide descriptions of the control mechanism of the D-KAP and C.E. Onyeocha et al. / Operations Research Perspectives 2 (2015) 137–149 141 Fig. 5. The control mechanism of BK-CONWIP S-KAP. Phase 1 Modelling Phase 2 Optimisation Phase 3 Comparison Fig. 6. A pictorial description of the methodology. S-KAP of BK-CONWIP in a multi-product manufacturing system respectively. The control mechanism of BK-CONWIP has three parameters (basestock, CONWIP and Kanban). The initial state of BK-CONWIP has a predefined number of basestock with no CONWIP cards and Kanbans attached to them, at the output buffer of the final stage. Also, resource pools of CONWIP cards and Kanbans have a pre-planned number of CONWIP cards and Kanbans. When a demand for a product-type occurs, the demand splits into the total number of stages +1 demand information. The demand information is transmitted to each of the stages while the last demand information is transmitted to the last stage output buffer for the release of a finished product-type in order to satisfy the demand. If the manufacturing processes of the stages are available and the raw material/semi-finished product types are available, production of the product types begins in all of the stages simultaneously. However, if any of the elements are unavailable, the production will be delayed. In the last stage, a push control mechanism controls production and the CONWIP cards are released immediately after the manufacturing process of the last stage. 3. Research methodology In this study, the performance metrics of interest are the level of WIP inventory and the service level achieved by the pull control strategies operating D-KAP or S-KAP. The three fundamental procedures used here are modelling, multi-objective optimisation and comparison techniques. The system entities, their interactions and outcomes were identified in order to model the system. The identified entities were conceptually designed and translated into simulation models. The control parameters (Kanbans and CONWIP cards) of the simulation models were optimised using a multi-objective optimisation block developed for ExtendSim [38]. The models were simulated and the outcome was compared using all pairwise comparison technique and Nelson’s ranking and selection technique. Fig. 6 shows a pictorial description of the research methodology used in this study. This section provides a description of the system modelled, the modelling assumptions, the verification, the validation of the models, the parameters of the system, the optimisation and comparison techniques. 3.1. A description of the system modelled The system studied is a two-product three-stage serial flow line described by Olaitan and Geraghty [36]. The flow line was modified to have no minimal blocking policy as shown in Fig. 7. The structure of the flow line was rearranged to produce three products and four products. The two product serial flow line is referred as Case 1 while the three and four product flow lines are referred as Case 2 and Case 3 respectively. The production capacity, loading and the level of variability were considered in selecting the processing times, Mean Time Between Failures (MTBF), and the Mean Time to Repair (MTTR). The models were initially run for 20 replications using a simple push control strategy with infinite demand and 100% manufacturing process availability in order to determine a realistic level of loading of the production capacity. The mean outputs (13 593—case 1, 13 601—case 2 and 13 587—case 3) and the mean time between demands were recorded. The mean time between demands for 100% manufacturing process availability of the push model was used to determine the mean time between demands for 90% manufacturing process availability in each of the cases. For instance, in case-1, the mean time between demands for product 1 is given as 5.61 h and for product 2 as 5.72 h obtained 142 C.E. Onyeocha et al. / Operations Research Perspectives 2 (2015) 137–149 Fig. 7. Case-1 two-product three-stage manufacturing system. Table 3 The system configuration. Stage Product 1 processing time (hours) Product 2 processing time (hours) Product 3 processing time (hours) Product 4 processing time (hours) MTBF exponential distribution mean (hours) MTTR exponential distribution mean (hours) Case 1 (2-product system) 1 1.50 3.00 N/A N/A 90.00 10.00 2 1.50 3.00 N/A N/A 90.00 10.00 3 1.50 3.00 N/A N/A 90.00 10.00 Demand ∼N(5.61,2.81)∼N(5.72,0.57)N/A N/A Case 2 (3-product system) 1 1.50 3.00 1.50 N/A 90.00 10.00 2 1.50 3.00 1.50 N/A 90.00 10.00 3 1.50 3.00 1.50 N/A 90.00 10.00 Demand ∼N(8.48,0.92)∼N(8.63,4.63)∼N(8.38,6.54)N/A Case 3 (4-product system) 1 1.50 3.00 1.50 3.00 90.00 10.00 2 1.50 3.00 1.50 3.00 90.00 10.00 3 1.50 3.00 1.50 3.00 90.00 10.00 Demand ∼N(11.32,2.76)∼N(11.33,8.43)∼N(11.28,1.11)∼N(11.35,5.62) from the push model analysis. The standard deviation of product 1 is set at 2.805 h (50% of its mean) while that of product 2 is set to 0.572 h (10% of its mean). This corresponds to 90% capacity loading level of the system. The same method was used for determining the mean and standard deviation of product demands in cases 2 and 3. The products are set to have low to high demand variability and the system is required to deliver a high service level with the least possible WIP inventory. MTBF and MTTR are exponentially distributed. MTBF with a mean of 90 h and MTTR with a mean of 10 h were modelled such as to represent a 90% manufacturing process availability. A summary of the processing times, demand, MTBF and MTTR is provided in Table 3 for cases 1, 2 and 3. StatFit (www.promodel.com) application software was used to fit an appropriate distribution to the data. Normal distribution ranked highest under the lower bound condition and was selected. According to Olaitan and Geraghty [36] a normal distribution is suitable for modelling distributions, which combine two or more events. The importance of the use of a normal distribution is because the values of the mean and standard deviation would simply combine to represent various levels of variations in demand. Therefore, values for the standard deviation for the two products were set to correspond to a low and a high level of demand variations. The demand information is provided in Table 3. 3.2. Modelling of the system Modelling in this study is the representation of a system via a logical framework. In manufacturing system analysis studies, simulation is widely used to model systems owing to its advantages over analytic techniques, especially its computation time [39–41]. Simulation modelling uses logical objects (icons) or program instructions (codes) to represent entities of a system and their interactions. These objects are constructed and configured to mimic the behaviour of the system modelled. The accuracy of designing and configuring the model determines the extent to which the model represents the actual system. In this study, an object-oriented simulation tool (Extendsim) from Imagine That Inc. (www.extendsim.com) was used to model the manufacturing system. The process followed in modelling the system is (i) the identification of the relevant entities, (ii) the designing of the entities’ structure and (iii) the linking of the entities’ interactions with each other as the actual system. The system entities modelled include the manufacturing processes, buffers, demands, operators, finished-products, WIP levels, and PAC. The events captured in the modelling are the demand arrival, starting and finishing point of part processing, manufacturing process failure and repair. Owing to the complexity of manufacturing system entities and their interactions, assumptions were made to minimise the challenges in modelling. The complexity of the system was simplified in the model by removing some of the characteristics of the systems that have an insignificant effect on the results of the model. Hence, the following assumptions were made: •Two to four product types are produced in a three-stage serialline via the same manufacturing process. •The demand profile is stochastic in nature and unsatisfied demand within a defined period is logged as backlog and is served in the next period before satisfying the demand of the next period. •There are three stages in the manufacturing system with each having a similar manufacturing process. •The three stages are assumed to have negligible setup. •The manufacturing processes are assumed to have an operation dependent breakdown such that a manufacturing process can only breakdown during processing of a part-type. •The time for loading and unloading a manufacturing process is negligible. •The information flow in the system occurs within a negligible time. The demands and the production authorisation cards’ information are instantaneous. •Any negative output generated due to a normal distribution used in representing the demand arrival event will produce arrival of demand. C.E. Onyeocha et al. / Operations Research Perspectives 2 (2015) 137–149 143 Table 4 WIP results for model validation. PCS +KAP Average total WIP from Olaitan and Geraghty [36], with minimalblocking policy at 95% SL Average total WIP from current models with minimal blocking policy at 95% SL Average total WIP from current models with no minimal blocking policy at 95% SL Confidence interval of differences between average total WIP of columns 2 and 3 CONWIP D-KAP 47.000 47.000 Not applicable 0.000 KCS D-KAP 47.764 47.557 Not applicable 0.207 ±0.284 EKCS D-KAP 46.835 46.609 Not applicable 0.226 ±0.272 EKCS S-KAP 46.252 46.112 Not applicable 0.140 ±0.153 GKCS D-KAP 44.278 44.187 Not applicable 0.091 ±0.116 GKCS S-KAP 43.832 44.024 Not applicable −0.192 ±0.207 HK-CONWIP D-KAP Not applicable 36.376 32.204 Not applicable HK-CONWIP S-KAP Not applicable 36.529 32.101 Not applicable BK-CONWIP D-KAP Not applicable 33.877 31.633 Not applicable BK-CONWIP S-KAP Not applicable 33.25 30.051 Not applicable •A warm-up period of 15 000 h, 50 000 h run-length and 30 simulation replications as described by Olaitan and Geraghty [36] were used in carrying out the experiments in this study. The model was verified to ensure accuracy with the system. A structural walk through and a stage by stage examination of the models were conducted. Corrections were made to the models, wherever errors or inaccuracies were found. The production capacities and the throughput of the models were tested. The validation of the models was based on the study of Olaitan and Geraghty [36], which confirms the accuracy of the models used here. Table 4 shows the comparison of WIP results from models developed by Olaitan and Geraghty [36] and the models used in this work. 3.3. Performance measures The performance measures often used in Pull production control strategy comparison are the average WIP inventory in the system and the average service level that the system achieved after a defined length of time [12,36,39,40]. The use of targeted service level at a minimum WIP inventory level has been widely used in pull production control strategy comparisons [36]. For instance, Geraghty and Heavey [40] based their comparison on the level of WIP inventory of a system that would achieve targeted service levels. In this study, a minimum WIP inventory that would achieve targeted service levels of 95%, 98% and 100% was used as the performance measure for comparison of the pull production control strategies and production authorisation card policies. 3.4. Optimisation The performance of pull control strategies significantly depends on the settings of the parameters. Setting control parameters to their best values before comparing pull control strategies highlights the outcome of the strategies [36,41]. Khojasteh-Ghamari [39], defines the optimal setting of the production authorisation cards of a strategy as a minimum number of production authorisation cards required by the system to achieve maximum or targeted throughput. Additional production authorisation cards to the optimal value will increase the WIP inventory in the system. A majority of real-life manufacturing problem consists of immediate optimisation of numerous objectives that are difficult to measure and at the same time are conflicting. On the other hand, the single objective optimisation has a well-defined single target for the optimal solution such that any good combination in the search space within the targeted objective function is considered a solution, while in multi-objective optimisation, a set of alternative tradeoffs, referred to as Pareto-optimal solutions is generated. These solutions are non-dominated such that they are superior to all other solutions within the search space. The control parameters of the model were optimised to operate in their best performance. A scenario manager block combined with a multi-objective optimisation block [38] of ExtendSim were used in the optimisation. The Extendsim optimisation searches for a solution via genetic algorithms. The mutation rate, the crossover, the number of generations, the number of replications, the production authorisation cards and the basestock level of the strategy are the variables that affect the percentage of the search space and the number of solutions produced. The aim of the multiobjective is to establish a trade-off between conflicting objectives such that a set of non-dominated solutions would become a guide or support a decision process for managers or production personnel to co-ordinate production authorisations and manage inventory in a multi-product system while maintaining targeted or higher service levels. In this work, the multi-objective optimisation block developed by Kernan and Geraghty [38] for Extendsim was used. The multiobjective optimisation method is iterative and requires a check by the user in order to express preferences of iterations based on the user’s defined interest (e.g. a low WIP level, while achieving a high service level) for a solution. The steps followed are (i) a pre-defined mutation rate (0%–20%) and crossover rate (0%–100%) expected to achieve a high service level with the lowest WIP inventory was determined by varying the settings, (ii) the search was set to termination after 150 generations if the search failed to find optimal solutions, (iii) the number of PAC and the basestock level are defined, (iv) the Extendsim multi-objective optimisation block is simulated and the solutions were recorded. The parameters of the multi-objective optimisation block were configured as follows: (i) the mutation rate of 10% was selected for the experiments after testing various mutation rates ranging from 0% to 20% on the HK-CONWIP D-KAP and BK-CONWIP S-KAP models. During the trial test for the selection of a mutation rate, it was observed that higher mutation rates of up to 15% reduced the outcome with respect to the number of generations obtained. (ii) The crossover rate of 70% was selected after testing a range of crossover rates of 0%–100% at 10% mutation rate. (iii) The number of specific generation before termination of the search is 150 generations. According to Kernan and Geraghty [38], a generation of 150 is significantly large enough to achieve a good solution search. (iv) The number of replications is 30. 30 replications were found to have statistically a high confidence level from similar and relevant experiments [12,36]. 3.5. Comparison techniques To understand the difference between the strategies, the pairwise comparison analysis and Nelson’s ranking and selection technique were adopted in this study. The performances (minimum WIP required to achieve targeted 95%, 98% and 100% service levels) of the strategies for cases 1–3 were screened and ranked. Pairwise comparison is useful for evaluating the criteria of systems. It is used where differences between systems are 144 C.E. Onyeocha et al. / Operations Research Perspectives 2 (2015) 137–149 subjective and unclear [36]. The technique matches the mean of each system to the mean of each of the alternatives. A system is awarded a point for outperforming an alternative in each oneon-one comparison. A system is awarded half of a point for a tie with an alternative. The system with the highest total points is the superior system to its alternatives. Pairwise comparison satisfies the Condorcet (fairness) criterion in selecting a superior system. A pairwise comparison was used in this study to screen the strategies for an overall 95% confidence level for nine sets. The Bonferroni Approximation was used such that an individual confidence level is adjusted to 99.17% confidence level. The difference of means of the samples (t-statistics) and the confidence interval for the t-statistics was determined. Nelson’s ranking and selection technique [42] authorises the removal of poorer performing PCS +KAP during screening without additional simulations. Survivors of the screening are gathered into a set for further comparison based on additional simulations. However, if the survivors’ set contains only one survivor, it is selected as the superior PCS +KAP. In this study, the two-stage ranking and selection (combined) procedure for systems proposed by Nelson et al. [42], was used to select the superior strategy. The parameters of Nelson’s combined procedure used in this work are as follows: k=4, where kis the number of systems for screening and selection. The initial number of replication is denoted as n0 such that n0=30. An additional number of simulation replications in cases of further screening is Ni.¯ Yiis the mean of the sample data. The variance of the sample data is represented as S2 i, the overall confidence level (α) is 90% for the combined procedure, that is α= 0.1, also confidence level of 95% for each of the two-stage sampling procedures is given as α0=α1=α 2=0.05. A practical significant difference of 0.2 unit quantities is reasonable [36]. Rinott’s integral h is given as h=h(1−α1,n0,k)=3.129. Wij =t(S2 i no+S2 j no)0.5, where t=t 1−(1−α0) 1 k−1,no−1 ,t=2.5336. 4. Experimental results In this section, the outcome of the simulation-based optimisation experiments is presented. Also, the analysis of the performance of the strategies in terms of the WIP inventory and service levels achieved is provided. 4.1. Optimal solution In this study, the main optimisation parameter with significant influence on the performance metrics of the system is the production authorisation cards (CONWIP and Kanban cards). The search range for the optimal parameters is 1–90. The result of the decision setting obtained at 95% service level while maintaining minimum WIP inventory is presented in Table 5. The result of the search solution shows the decision set that achieves the 95% service level. Table 5 shows that strategies combined with S-KAP have the least number of production authorisation cards. BK-CONWIP has a smaller proportion of production authorisation cards and basestock levels than HK-CONWIP. Similarly, BK-CONWIP combined with S-KAP has the least proportion of production authorisation cards and basestock levels in the system. 4.2. WIP inventory and service level The simulation results of the average total WIP inventory at 95%, 98% and 100% average service levels of the strategies are presented in Table 6 for case-1, while the results of the average total WIP inventory of the strategies for cases 2 and 3 are presented in Tables 7 and 8respectively. An observation of the data presented in Table 5 (PAC and basestock level optimal values) and Tables 6–8 (average total WIP) indicates that BK-CONWIP S-KAP has the least production authorisation cards and maintained the least WIP inventory in the experiments. BK-CONWIP S-KAP was observed to outperform its alternatives. Similarly, HK-CONWIP S-KAP outperformed HK-CONWIP D-KAP in terms of WIP control. In contrast, HK-CONWIP D-KAP has the highest level of WIP inventory in the system. BK-CONWIP D-KAP has better WIP control than both HK-CONWIP S-KAP and HK-CONWIP D-KAP. In general, BK-CONWIP outperformed HK-CONWIP while S-KAP outperformed D-KAP. Furthermore, the WIP inventory, production authorisation cards and throughput of the strategies at varying number of product types were investigated. The outcome of the WIP inventory and the throughput (total finished product output) of the strategies in cases 1–3 are presented in Table 9. The result (Table 9) shows that the number of product types has similar throughput (mean output) with different proportions of production authorisation cards and WIP inventory levels. Also, the WIP inventory level varies across strategies. For instance, strategies have the least production authorisation cards and WIP inventory levels when the system produces two product types. The proportion of production authorisation cards and WIP inventory levels is at the highest level when the system produced four product types. Again, BK-CONWIP S-KAP has the least production authorisation cards and it is the best performer. BK-CONWIP outperformed HK-CONWIP while S-KAP outperformed D-KAP. 4.3. Selection of the superior strategy The result of the pairwise comparison is presented in Table 10. Any positive confidence interval without zero between the upper and lower bounds indicates the strategy on the row-level has significantly a smaller number of WIP inventory (better performer) than the strategy on the column-level. However, a negative confidence interval without zero between the upper and lower bounds shows that the strategy on the column-level has statistically a smaller proportion of WIP inventory than the strategy on the rowlevel. If zero exists between the lower and upper bounds, the two strategies have no significant difference (ties). Table 10 shows the outcome of the pairwise comparison analysis of the WIP inventory level achieved by the strategies at different service levels. From the table, there are no zeros between the upper and lower bounds of the confidence intervals for all the tests. In each comparison, a point is awarded to the best performer and the strategy with the total highest points is the superior. The strategy with the total highest points is ranked 1 (the best performer) and the strategy with the least points is ranked 4 (the worst performer). BK-CONWIP S-KAP has a total of 27 points (9 in each case), followed by BK-CONWIP D-KAP with 18 points (6 in each case), and next is HK-CONWIP S-KAP with 9 points (3 in each case). HK-CONWIP did not win any comparison test and has zero points. A summary of the ranking of the strategies owing to the confidence intervals is presented in Table 11. BK-CONWIP S-KAP is superior to its alternatives in terms of maintaining the least average total WIP inventory in the system. The outcome of the application of Nelson’s combined procedure is presented in Tables 12–14.Table 12 shows the result of the best strategy at 100% service level for case-1, while Tables 13 and 14 show the results of the best strategy at 100% service level for cases 2 and 3 respectively. The results of the application of Nelson’s combined procedure of the sampled data (WIP at 100% service level for the three cases— Tables 12–14) show that only one strategy (BK-CONWIP S-KAP)