An Investigation of Pull Control Strategies and Production Authorisation Cards in a Multi-product Plant in the Presence of Environmental Variability

Transcription

1 Comput. Sci. Appl. Volume 1, Number 2, 2014, pp Received: June 30, 2014; Published: August 25, 2014 Computer Science and Applications An Investigation of Pull Control Strategies and Production Authorisation Cards in a Multi-product Plant in the Presence of Environmental Variability Chukwunonyelum Emmanuel Onyeocha Enterprise Process Research Centre, School of Mechanical & Manufacturing Engineering, Dublin City University, Dublin 9, Ireland Corresponding author: Chukwunonyelum Emmanuel Onyeocha (chukwunonyelum.onyeocha2@mail.dcu.ie) Abstract: Pull control strategies are sensitive to uncontrolled environmental variations. Therefore, selection of appropriate pull control strategies and Kanban allocation policies in risk prone multi-product systems has become widespread issue in production systems engineering. This paper investigates the behaviour of pull control strategies in dedicated and shared Kanban allocation policies with consideration of robustness of optimal solutions to environmental and system variabilities. Discrete event simulation and evolutionary multi-objective optimisation approach were utilised to develop sets of non-dominated optimal solutions for the control parameters in the shared Kanban allocation policy and dedicated Kanban allocation policy. Simulation experiments were carried out via ExtendSim simulation application software. The outcomes of the experiments were compared via Nelson s ranking and selection technique for superior strategy and policy under negligible environmental and system variabilities. To determine superior strategy and policy under systems and environmental variability, the optimal solutions were tested for robustness using Latin hypercube sampling technique and stochastic dominance test. Basestock Kanban CONWIP control strategy in combination with shared Kanban allocation policy outperforms the alternatives when the system is not prone to uncontrolled variabilities, while the Basestock Kanban CONWIP control strategy in combination with dedicated Kanban allocation policy is the best strategy and policy in a risk prone system when service level is the major factor for selection of a strategy. However, if the proportion of work-in-process inventory is the criteria for selection of a strategy and a policy, Basestock Kanban CONWIP control strategy in combination with shared Kanban allocation policy is selected as the best strategy and policy in both robust and non-robust conditions. Key word: Pull control strategies, production authorisation card policies, multi-product manufacturing systems, robustness analysis. 1. Introduction Selection and implementation of an appropriate pull control strategy and production authorisation card policy for multi-product systems that would effectively respond to customers demands in the shortest possible time and at a reduced cost are complex especially in risk prone systems. In pull controlled multi-product systems, operations personnel plan a large number of PAC (production authorisation cards) to respond to demand variability resulting in proliferation of WIP (work-in-process) inventory in the system. Proliferation of WIP in multi-product systems undermines the principles of pull control strategies. A majority of studies in multi-product manufacturing systems such as Refs. [1-3], focused on planning and scheduling issues and optimisation of system control parameters [4, 5]. In these studies, PAC was assumed to function in a dedicated mode only. Conversely, in a study by Baynat et al. [6], it was shown that the PAC can be dedicated and shared. In a pull controlled system operating D-KAP (dedicated Kanban allocation policy), a predefined proportion of PAC is assigned to individual product type, while S-KAP

2 68 An Investigation of Pull Control Strategies and Production Authorisation Cards (shared Kanban allocation policy) uses a shared resource pool to allocate PAC to all the product type based on the availability of PAC and demand information. The performance of D-KAP and S-KAP has been studied in both serial and assembly line to provide clear understanding of the behaviour of these policies in multi-product systems [4, 5, 7, 8]. A performance analysis of PCS (production control strategies) and KAP (Kanban allocation policies) is examined here under non-robust solutions using a health care manufacturing plant found in Ref. [8]. The strategies considered here are three pull PCS that operate S-KAP and D-KAP naturally: (1) two exciting pull PCS namely, GKCS (generalised Kanban control strategy) and EKCS (extended Kanban control strategy), (2) a newly developed BK-CONWIP (Basestock Kanban CONWIP control strategy) with capability of quick respond to demand variability and high flexibility [5]. A multi-objective optimisation using genetic algorithm was used to optimise the control parameter of the multi-product system for simulation examination of the behaviour of each combination of either D-KAP or S-KAP and PCS (PCS+KAP). WIP and service levels are the performance metrics used in comparing PCS+KAP based on their optimal solutions, when the system operates under negligible environmental and system variabilities. The literature shows that optimal solutions to real manufacturing problems are essential for operational performance of manufacturing systems [8]. However, the question on how robust these solutions are has been of concern especially to operations personnel. Several studies like Refs. [6, 8-13] suggested that environmental variabilities in manufacturing systems affect the performance of pull control strategies. A clear understanding of the robustness of PCS+KAP is a worthwhile innovation in the field of production systems engineering. Studies like Refs. [4, 5, 8] studied D-KAP and S-KAP in multi-product systems did not consider D-KAP BK-CONWIP in a multi-product environment. Similarly, evaluation of the performance of BK-CONWIP under system and environmental variabilities has not been conducted. This paper would examine the performance of the three pull strategies (in D-KAP or S-KAP mode) in the presence of environmental and system variabilities. The study will deliver a robust study covering a range of PCS+KAP and its outcome will provide knowledge on selection and implementation of a suitable PCS+KAP in serial multi-product manufacturing flow lines. The remainder of this paper is organised as follows: Section 2 gives a brief account of the pull control strategies and production authorisation card policies in multi-production systems; In Section 3, a description of the research methodology, the multi-product system under investigation and the experimental conditions were provided; Section 4 presents the simulation result and analysis; while the discussion and conclusion of the study are presented in Section Background The regulation of material flow in a manufacturing system determines the level of efficiency of the system in terms of throughput rates and work-in-process inventory in a system. Material flow comprises the process of production authorisation, part flow, raw material arrival routine, control semi-finished and finished products in a system, priority settings, quality control, and part transportation [14-17]. The control of production authorisation and part flow in a manufacturing system is often referred to as production control strategy. The function of a production control strategy is the authorisation of part release and regulation of the flow of parts in a system. The need to effectively control the flow of parts in different manufacturing systems and conditions led to variations of production control strategies. These variations led to divisions in the classification of production control strategies. PCS could be classified based on their control mechanism.

3 An Investigation of Pull Control Strategies and Production Authorisation Cards 69 For instance immediate release, input, output, input-output and bottleneck control mechanisms [18]. Fernandes and Carmo-Silva [18] observed two classifications in the literature owing to (1) the manner of authorisation of parts release and (2) the material flow in a system. The classification of production control strategy based on the authorisation of parts into a system has five groups, which are referred to as the immediate release control mechanisms, input control mechanisms, output control mechanisms, input-output control mechanisms and bottleneck control mechanisms. However, the widely used classification found in the literature is based on how the flow of material is controlled in a strategy [19]. Production control strategy classifications by material flow are called push and pull production control strategies. A push production control strategy requires demand forecast in order to develop a production schedule and release parts into a system to ensure that production meets the anticipated demand. Conversely, pull production control strategies use actual demand to authorise material release into a production system. Pull utilises a feedback loop to communicate and regulate the work-in-process inventory of a system while monitoring the throughput. Push production control strategies aim at providing order processing, data handling and inventory management, however, advanced push strategies support planning. It regulates the throughput of a system from the view of the first workstation [20]. The accuracy of the forecasted demand and production scheduling evaluates the effectiveness and efficiency of the production flow. Noticeable and major implementations of the concept of push production control strategy are noted in the Material Requirement Planning [21], Manufacturing Resource Planning [21, 22], and Enterprise Resource Planning [20, 22]. The primary advantage of push control strategy is producing substantial enough throughput to meet demand based on forecast. Push incurs large work-in-process inventory in a system. Furthermore, it was observed that environmental and system variabilities cause changes in production scheduling resulting in long lead times and capacity infeasibility [23-25]. These instabilities generate (1) an increase in the cost of production, (2) reduction of the service level and (3) productivity losses [24]. The concept of pull production control strategy is based on the principles of automation and just-in-time production [20, 26]. Automation aims at establishing the optimal approach to carry-out a task and brand the approach as the standard method to perform such a task. It stops production to correct any problem in the production line. The standard approach eliminates the requirement for rework lines and scraps. Just-in-time production establishes the use of signal cards (often referred to as Kanbans) to authorise the release of parts into a system, as well as the application of production levelling in a system. The goals of these two principles are to eliminate numerous wastes in a manufacturing system and drastically reduce changeover times. The concept of pull production control strategy is implemented in several strategies including Kanban control strategy [27], Basestock control strategy [28], constant work-in-process control strategy [29], generalised Kanban control strategy [30, 31], extended Kanban control strategy [32], hybrid Kanban CONWIP control strategy [9, 33], Basestock Kanban CONWIP control strategy [34]. Pull production control strategies have been favoured in the literature over push production control strategies, owing to their documented performance and effectiveness in manufacturing systems with stochastic demand [35-38]. The benefits of these pull production control strategies over push production control strategies include reduced production cost, minimum material waste, improved quality control and just-in-time delivery of products [20, 39-41]. Despite these benefits, pull production control strategies have drawbacks for instance; it exhibits a poor response to instabilities such as product mix and volume variations [42, 43]. The poor performance of

4 70 An Investigation of Pull Control Strategies and Production Authorisation Cards pull under instabilities is more pronounced in multi-product systems [8, 34]. Feng et al. [44] observed a growing interest in research studies on multi-product manufacturing environments. Akturk & Erhun [1] and Hum & Lee [2] developed a technique for scheduling in multi-product systems. Their findings were shown to solve scheduling issues requiring a decision on how and which part type should be released first when two or more part types are waiting in a queue. Park and Lee [45] analysed a multi-product CONWIP system having correlated external demands via an approximation technique. Bard and Golany [3] used an analytical model to optimise production authorisation cards to solve the problem of huge inventory in multi-product systems. To proffer a solution to a large inventory in pull controlled multi-product systems. Studies like Ref. [46-49] evaluated the WIP cap effect of CONWIP. Gurgur and Altiok [50] examined inventory and service level performance of pull by an approximation algorithm. Li and Huang [51] estimated a split and merge routing technique via a recursive approach. These studies provided significant insights into the performance of pull in multi-product systems especially in the areas of scheduling, planning, routing and optimisation of control parameters [4, 5, 34]. An additional area in the study of multi-product systems with extensive attention is set-ups and finite buffer issues [44]. Altiok and Shiue [52] investigated the effect of sequence-independent set-ups in a multi-product system. Krieg and Kuhn [53] evaluated a sequence-independent set-ups, cyclic scheduling policy and Kanbans in multi-product systems. Dasci and Karakul [54] developed an iterative technique for evaluation of finite buffers and sequence-dependent set-ups. Feng et al. [55] compared the performance of sequence-dependent set-ups, finite buffer and scheduling policies. These studies improved the general understanding of the effect of finite buffers and changeovers in multi-product systems. Prior to the study of Ref. [6], production authorisation cards policy (dedicated Kanban allocation policy) found in single product systems adapted to multi-product systems as the sole production authorisation card policy. This is largely attributed to the assumption that the findings of studies in single product systems are adaptable to multi-product systems [4-6]. Baynat et al. [6] proposed a shared Kanban allocation policy for a multi-product system capable of reducing the inventory level of a multi-product system with a lower number of production authorisation cards. A few studies that considered the performance analysis of the D-KAP (dedicated Kanban allocation policy) and S-KAP (shared Kanban allocation policy) showed that S-KAP outperformed D-KAP [4, 5, 8]. Olaitan and Geraghty [8] compared the performance of D-KAP and S-KAP of five pull production control strategies. Their paper showed that S-KAP combined with GKCS (generalised Kanban control strategy) outperformed the alternatives when the system is stable. When a system is subject to instabilities, D-KAP combined with EKCS (extended Kanban control strategy) outperformed the alternatives. Onyeocha et al. [5] compared the performance of performance of GKCS in S-KAP and D-KAP mode, EKCS in S-KAP and D-KAP mode and BK-CONWIP in S-KAP mode. Their paper showed that BK-CONWIP in S-KAP mode outperformed the alternatives. The paper did not consider robustness of solutions for systems prone to instabilities. Robustness of solutions has become an important issue in production systems engineering because of the competitiveness and changing nature of the global market. Despite the importance of robust solutions to industrialists, only a few research studies were noted in the literature on with interest in robustness or related topic [44]. Kang and Gershwin [56] considered the effect of inaccurate data in inventory systems. The paper showed that a small probability of stock loss influences the process of replenishment in a system.

5 An Investigation of Pull Control Strategies and Production Authorisation Cards 71 Feit and Wu [57] examined the performance of a transfer line under uncertainty in data. They developed an analytic technique that reduces the effect of uncertainty by identifying critical data for design performance. Li et al. [58] developed an approximation technique to minimise erroneous data in computing the reliability data of feeder lines. The study improved the level of accuracy in throughput estimation. Li et al. [59] evaluated the robustness on the design of repair and rework systems in automotive paint shop. Their findings indicated that robustness analysis enhances the quality of products and delivery performance in a system. Studies like Refs. [60-64] have shown that robustness of the solution improves the operational performance of a manufacturing system. A preponderance of these studies did not consider robustness of solution in multi-product systems. However, few studies that considered robustness of solutions in multi-product systems include Refs. [8, 44] focused on scheduling policies in multi-product systems with finite buffers and sequence-dependent changeover times. The paper suggested that cyclic policy and longest queue policy are relatively robust over a wide range of parameters than the alternatives. Olaitan and Geraghty [8] investigated the robustness of production authorisation card policies in pull control strategies. The paper showed that D-KAP is preferable to S-KAP when combined with EKCS. None of these papers considered BK-CONWIP (Basestock Kanban CONWIP control strategy). This pull control strategy has been reported to have effective WIP control and rapid response to demand variations. This paper examines the robustness of D-KAP and S-KAP when operating in GKCS, EKCS, and BK-CONWIP via a two-product three-stage serial manufacturing line with low to high demand variations, having negligible set-ups. 3. Experimental Settings and Simulation Results The procedure adopted in this paper for analysis of the performance of the pull production control strategies under investigation includes simulation, design of experiments, optimisation, Nelson s screening and selection techniques and stochastic dominance test. It provides the methodology for investigating the application and behaviour of the pull production control strategies in multi-product manufacturing systems. To conduct the experiment the manufacturing system under investigation was modelled. The conceptual models were converted to simulation models via ExtendSim V8 simulation application software. A multi-objective block developed by Kernan & Geraghty [65] was used to conduct an optimal solution search. When robustness was not considered in the system, the results of the experiments were screened and the best strategy and policy were selected using the Nelson s ranking and selection technique. The results of the optimal solutions achieved by strategies and policies were screened via Latin hypercube sampling technique and stochastic dominance test to determine the level of robustness of the control parameters of strategies and policies. 3.1 System Description The system studied in this paper is a two-product three-stage serial flow line found in Olaitan and Geraghty [8]. The system has a negligible setup times with low to high demand variability, infinite buffer sizes, minimal blocking policy, cyclic scheduling policy. The machines are similar with deterministic processing times. The system unreliability is set at 90 hours MTBF (mean time between failures) and 10 hours MTTR (mean time to repair). A schematic diagram of the system is shown in Fig. 1, while a description of the system configuration is provided in Table 1. A description of the symbols and abbreviations used in this paper is provided in Table Modelling and Assumptions The ability to capture the conceptual ideas of the actual systems is essential for accurate analysis of the

6 72 An Investigation of Pull Control Strategies and Production Authorisation Cards Fig. 1 Two-product three-stage system. Table 1 Case-1 manufacturing system configuration. Stage Product 1 Product 2 MTBF exponential MTTR exponential Processing time Processing time distribution mean distribution mean hours 3 hours 90 hours 10 hours hours 3 hours 90 hours 10 hours hours 3 hours 90 hours 10 hours Demand ~N(5.61,2.805) ~N(5.72,0.572) Table 2 Description of symbols and acronyms used in this paper. Symbol/Acronym I,,,, I,, RM,, MP,, PCS KAP D-KAP S-KAP PCS+KAP WIP PAC BK-CONWIP HK-CONWIP CONWIP BSCS KCS PPCS Description Inventory buffer for product 1, 2, Inventory buffer for product 1,2, at stage 1, 2, Raw material for stage 1, 2, Manufacturing process unit at stage 1, 2, Production control strategy Kanban allocation policy Dedicated Kanban allocation policy Shared Kanban allocation policy A specified PCS and specified KAP combination Work in process inventory Production authorisation card Basestock Kanban CONWIP control strategy Hybrid Kanban CONWIP control strategy Constant work in process control strategy Basestock control strategy Kanban control strategy Pull production control strategy behaviours of the systems under investigation. Adequate representation of all the entities that would affect the outcome of the system is required for good judgement on the system s behaviour. Input parameters (e.g., modelling parts inter-arrival rate) and experimental conditions should be modelled to mimic the behaviour of the actual system with negligible preconception to minimise error during test. However, it is difficult to model real-world production systems owing to the complexity of these systems and their interactions. To model such complexity, assumptions are made to simplify and model only entities, interactions, behaviours and performances that have significant effect on the system performance with respect to the objective for study. In the study, the following assumptions were made:

7 An Investigation of Pull Control Strategies and Production Authorisation Cards 73 The production process is monitored in a continuous time period. Two products are manufactured in a three-stage serial line via related machines Demand is generated randomly and is modelled via a probability distribution. Unfulfilled demand in a given production period is logged as backlog. Backlogs (if any) are served first before the actual demands of a given period. The system operates under negligible setup, infinite buffer size and cyclic policy. Raw materials are assumed always available. The machines have operations dependent failure. The transfer time is negligible. 3.3 Performance Measures The trade-off between Service Level (fill rate) and Work-In-Process (WIP) inventory has been widely used in the comparison study of production control strategy [7, 8, 33, 66]. Alternative performance metrics for pull comparison include cycle time, throughput rate, and demand backlog [29, 67, 68]. Service Level is the ratio of satisfied demands to the total demands in a production period while WIP refers to the raw materials, semi-finished parts and finished parts that are released into the system and have not left the system. Studies such as Geraghty and Heavey [66], Olaitan and Geraghty [8] compared pull control strategies using the level of WIP required in pull control strategies to achieve targeted service level. Similar to their work, the proportion of WIP that pull control strategies used to achieve 100% service level is used in this paper to compare pull performances. 3.4 Control Mechanisms The concept of Generalised Kanban control strategy is centred on the combination of KCS and BSCS to harness their merits into one control strategy [30]. GKCS uses two parameters (base stock and Kanban) in each stage of the production line to control inventory and authorise production. The basestock of the finished parts controls the total stage inventory while the number of Kanban controls the quantity of products to be stored in a stage s output buffer. The inventory level of each stage is initialise to a pre-set level and the demand information is transmitted to each stage. The flow of product in the system is controlled by Kanban just as in the case of the KCS system. The actual market demand information is transmitted as demand cards to the last stage of the production line and if a Kanban match with the demand card, then a demand card is sent to the next stage upstream. Extended Kanban control strategy has the same control parameters as GKCS in a simpler way. It was designed to control process time variations [32]. The base-stock of finished parts in EKCS is initialise with a pre-defined value to respond to demand, while Kanbans are stationed at each stage production authorisation card pool for authorisation of parts into a stage or system based on the availability of raw material/semi-finished parts and demand information. Demand information is globally transmitted to all stages in a system, resulting in quick response to demand. BK-CONWIP was developed for quick response manufacturing [4, 5, 34]. The control mechanism of BK-CONWIP uses three parameters (Kanban, CONWIP and basestock level) to manage the material flow in a system. Global information flow is used in the strategy such that information is transmitted to all stages instantaneously. CONWIP controls the WIP level of the entire system by putting a limit on the maximum WIP level (WIP Cap) in the system. The Kanbans regulate the stage WIP except for the last stage that operates a push mechanism. BK-CONWIP operates S-KAP and D-KAP naturally. A detailed description of the control mechanism of BK-CONWIP is provided in Refs. [4, 5, 34]. 3.5 Optimisation The selection of the control parameters of pull production control strategies affects the operational

8 74 An Investigation of Pull Control Strategies and Production Authorisation Cards performance of a system. To determine the best performance of a strategy requires setting and operating the system with the optimal values of the strategy s control parameters [13]. The optimal values of the control parameters are the least number of parameter assigned to a system that achieved the maximum outcome [7]. Simulation based-optimisation is widely used in complex system design to search for optimal solutions of problems [13]. It is a method of connecting an optimisation technique with a simulation model to compute suitable settings of the relevant control parameters, in order to maximise the simulated system s performance [69]. Single and multi-objective optimisation techniques are the two simulation based optimisation approaches found in Refs. [70, 71]. Multi-objective optimisation technique searches for optimal solutions of problems with multiple conflicting objectives. While the single objective optimisation searches for optimal solutions of a problem with one unknown objective while the other objective(s) is clearly defined. Multi-objective optimisation is often favoured owing to its capability of generating a set of non-dominated solutions. A Pareto optimiser block for ExtendSim developed by Kernan and Geraghty [65] using genetic algorithms was adopted for conducting a multi-objective optimisation in this paper. 3.6 Comparison of Systems without Consideration for Robustness The performance comparison of the PCS+KAP alternatives was conducted using a ranking and selection technique proposed by Nelson et al. [72]. The technique allows the elimination of inferior performing PCS+KAP via its screening approach without further simulations. A set of the survivors of the screening is collected and the further simulation and screening are conducted until the best PCS+KAP is selected. In a case where only one survivor emerged from the first screening, it will be selected as the best strategy and policy. The WIP level of the PCS+KAP was used for the screening and selection of best PCS+KAP in this paper. 3.7 Comparison of Systems with Consideration for Robustness To determine the performance of the optimal solutions of PCS+KAP in the presence of instabilities, the robustness analysis technique developed by Kleijnen and Gaury [60] was used to conduct a robustness test in this paper. The technique generates practicable sets of control factors via LHS (Latin hypercube sampling). In LHS, a minimum of 100 samples are needed for robustness test. Comparisons of PCS+KAP are conducted by means of a stochastic dominance test and cumulative distribution functions on the results of PCS+KAP performances. The result of a stochastic dominance test and is presented as the first or second degree dominance or inconclusive owing to the level of the significant difference between the compared PCS+KAP. For instance, the cumulative distribution functions of two systems A and B are given by ( ) and ( ). If the objective of the stochastic dominance test is to maximise the value of, then system A is said to have first-order stochastic dominance over system B if ( ) ( ), for all (1) While system A stochastically dominates system B in a second order degree if ( )d ( )d, for all (2) When the two systems have insignificant difference, the stochastic dominance test result is presented as inconclusive. 4. Experimental Results and Analysis The outcome of the multi-objective optimisation for all PCS+KAP is shown in this section. A description of the results of the simulation experiments conducted for the performance evaluation of the PCS+KAP.

9 An Investigation of Pull Control Strategies and Production Authorisation Cards Optimisation Results ExtendSim application software was used to conduct the simulation based optimisation experiments in this paper. The control settings for the Pareto optimiser block used in conducting the search for optimal solutions of PCS+KAP are given as follows: (1) the mutation rate was set to 10%, (2) the number of generation was set to 150 and (3) the number of simulation replications was set to 30. Search range values were selected by means of one-factor sensitivity analysis. The run length for the simulation experiments is configured to 50,000 hours. Table 3 provides a comprehensive summary of the control parameters that achieved 100% service level. The total number of production authorisation cards (Table 3) implemented in the S-KAP models is smaller than the proportion of production authorisation cards implemented in the D-KAP models. The S-KAP BK-CONWIP model has the lowest number of primary production authorisation cards and basestock level. The D-KAP GKCS has the most production authorisation cards and basestock levels. The trade-off points of the average work-in-process inventory versus the service levels of PCS+KAP are provided in Fig. 2. The figure shows that service levels from 90% to 100% and the WIP level required by individual PCS+KAP to achieve the service levels. Direct observation of the optimal solutions (Fig. 3) shows that S-KAP out performed D-KAP. S-KAP BK-CONWIP is reckoned as the best PCS+KAP owing to the level of WIP it achieved at any given service level. BK-CONWIP in both D-KAP and S-KAP modes outperformed its alternatives. GKCS is the worst performer at high service levels above 95%. The GKCS models (D-KAP and S-KAP) were noted to perform better than EKCS (D-KAP and S-KAP) at service levels less than or equal to 95%. The finding of Olaitan and Geraghty [8] agrees with this observation that at 95% service level, GKCS outperformed EKCS. 4.2 Performance Comparisons of PCS+KAP without Consideration for Robustness The simulation experiments were conducting using Table 3 Results from application of Pareto optimiser at 100% service level. Pareto decision set at 100% Service Level CONWIP Kanban Basestock (RV) & [O.S] (RV) & [O.S] (RV) & [O.S] Total Stage PCS KAP Product 1-90 (RV) 1-80 (RV) 0-80 (RV) GKCS EKCS BK-CONWIP D-KAP S-KAP D-KAP S-KAP D-KAP S-KAP 1 N/A [28] [23] [57] [0] [0] [57] 2 N/A [22] [19] [28] [0] [0] [34] 1 [0] [0] [62] N/A [44] [34] [28] 2 [0] [0] [28] 1 N/A [26] [22] [34] [0] [0] [64] 2 N/A [25] [19] [30] [0] [0] [29] 1 [0] [0] [58] N/A [42] [20] [43] 2 [0] [0] [28] 1 [44] [23] [27] N/A [0] [0] [44] 2 [40] [21] [25] N/A [0] [0] [40] CON-WIP Kanban Basestock N/A N/A N/A N/A [82] [43] [52] N/A [0] [0] [51] [0] [0] [31] [O.S] Optimal values for the control parameters, (RV) Range value of search, N/A Not applicable.

10 76 An Investigation of Pull Control Strategies and Production Authorisation Cards the optimal values achieved via the optimisation of individual PCS+KAP. The simulation run length is set to 50,000 hours with a warm-up period of 15,000 hours, while the number of simulation replications is set to 30. The average WIP level of the entire system was computed and the result of the WIP level at 100% service level is presented in Table 4. The result of average total WIP shows at 100% service level, the S-KAP BK-CONWIP model had the lowest quantity of WIP in the system. S-KAP BK-CONWIP with the least amount of production authorisation cards outperformed the alternatives. This is attributed to the level of flexibility of S-KAP and quick respond to variability of BK-CONWIP [4, 5, 34]. This observation was confirmed using the Nelson s ranking and selection technique for the best PCS+KAP. To conduct the Nelson s screening and selection technique, the following control parameters 90 Inventory-service level trade-off points 80 Work-In-Inventory % 91% 92% 93% 94% 95% 96% 97% 98% 99% 100% Average total service level Fig. 2 S-KAP BK-CONWIP D-KAP BK-CONWIP S-KAP EKCS D-KAP EKCS S-KAP GKCS D-KAP GKCS Service level vs. WIP trade-off points. Cumulative Probability Cumulative average total service level Fig. 3 Average total service level D-KAP BK-CONWIP D-KAP EKCS S-KAP GKCS S-KAP BK-CONWIP S-KAP EKCS D-KAP GKCS Cumulative distribution function of total service level. Table 4 Average total WIP with 95% confidence interval half widths at 100% service level. GKCS EKCS BK-CONWIP D-KAP S-KAP D-KAP S-KAP D-KAP S-KAP ± ± ± ± ± ± 0.279

11 An Investigation of Pull Control Strategies and Production Authorisation Cards 77 values were used: the number of PCS+KAP for screening k is given as k = 6, the initial number of replication, is set to n 0 = 30., is the variance of the sample data, while the mean of the sample data is + denoted by. = ( )., where t = is the overall confidence level and it is 90% for the combined procedure, implying that α = 0.1, where each of the two stage sampling procedures confidence level is 95% and is given as α 0 = α 1 = α/2 = i denotes the number of PCS+KAP, while j represents PCS+KAP alternatives. The significant difference ɛ is given as ɛ = 0.2 units [8]. Rinott s integral h is given as h = The result of the application of the Nelson s combined procedure on the WIP level of PCS+KAP at 100% service level is provided in Table 5. The outcome of the ranking and selection technique showed that PCS+KAP with inferior WIP performances were eliminated during the initial screening test. S-KAP BK-CONWIP was the lone survivor after the screening. The S-KAP BK-CONWIP model was chosen as the best PCS+KAP owing to its capability of maintaining the least WIP level in the system. Therefore, in multi-product manufacturing environments with negligible environmental variability, S-KAP BK-CONWIP should be selected and implemented for the best WIP performance. 4.3 Bottleneck Locations The stage in a system that slows down the flow of material or parts of the system is referred to as the bottleneck. Bottleneck stage decreases the operational performance of a system by increasing the WIP level of the system, while decreasing the throughput and service level of that system. In this paper, the stages of the system were studied to identify a stage with possible bottleneck effect. Statistics of the incoming WIP (i.e., WIP in before a stage manufacturing process unit, waiting to be processed) at each stage of the system were observed and the result is presented in Table 6. The incoming WIP in stage one is the raw material inventory. It is modelled to be constant with value of one (always available). The stage two incoming WIP is the inventory at the output buffer of stage one waiting to be processed in stage two. The stage three incoming inventory is the inventory at the output buffer of stage two, while the final goods inventory is the inventory at stage-three output buffer. The result demonstrates that the stage-two of the system for EKCS (S-KAP and D-KAP) and GKCS (S-KAP and D-KAP) has more proportion of WIP, indicating possible bottleneck. However, the difference between stage-two and stage-three WIP levels is relatively small indicating that both stages slowed down the flow of parts in the system. This is attributed to the stock-piling of semi-finished parts found in Kanban control mechanism, which is utilised in GKCS and EKCS. Onyeocha and Geraghty [34] reported that KCS has large WIP in multi-product system owing to semi-finished parts required in each stage in the system. For BK-CONWIP (S-KAP and D-KAP), the final goods inventory is the inventory position with the highest WIP. The primary production authorisation card in BK-CONWIP is CONWIP cards. The CONWIP cards push parts through the system and are stored in the finished goods inventory position. The large WIP in the final goods inventory is ascribed to the push mechanism of CONWIP and in the final stage of the BK-CONWIP controlled system. 4.4 Performance Comparisons of PCS+KAP with Consideration for Robustness External (demand variability) and internal (system variability) instabilities require adequate consideration in designing a production system. This study concentrated on the failure rate in a system and demand variability as possible factors for robustness study. To examine the behaviour of PCS+KAP when there is an increase and/or decrease of the failure rate

12 78 Table 5 An Investigation of Pull Control Strategies and Production Authorisation Cards Application of Nelson s combined procedure for selection of the best PCS+KAP. PCS+KAP i n 0 j W ij +max 0, Keep? N i D-KAP GKCS Eliminate S-KAP GKCS Eliminate D-KAP EKCS Eliminate S-KAP EKCS Eliminate D-KAP BK-CONWIP Eliminate S-KAP BK-CONWIP Keep Table 6 Stage incoming WIP statistics of PCS+KAP at 100% service level. PCS GKCS EKCS BK-CONWIP KAP D-KAP S-KAP D-KAP S-KAP D-KAP S-KAP Stage Stage Stage Final goods inventory Total WIP

13 An Investigation of Pull Control Strategies and Production Authorisation Cards 79 or demand profile, ±5% of the simulated values was selected for design of experiments. The experiment was designed with ten factors with four factors for demand variability, while six of the factors are for system variability. The base values, upper and lower bound values of the factors are detailed in Tables 7 and 8. In designing the experiment, 100 samples of each factor were computed within ±5% range of the base values via the Latin hypercube sampling technique of JMP design of experiment software ( from SAS. The simulation run length is hours and the number of replication is 30. The stochastic dominance tests were conducted via ModelRisk from Vose software ( The performance metrics was used in the comparison of the PCS+KAP are the service level and work-in-process inventory. 5% step by step incremental procedure was used in creating the cumulative distribution function of the service level and the work-in-process inventory. The cumulative distribution functions of the PCS+KAP were compared. A description of the comparison graph of the cumulative average total service level of the PCS+KAP is provided in Fig. 3. The cumulative distribution function comparison graph (Fig. 3) and the stochastic dominance tests of the average total service level showed first order dominance and second order dominance. D-KAP BK-CONWIP stochastically dominates D-KAP EKCS in second degree dominance. While it dominates S-KAP BK-CONWIP, S-KAP EKCS, D-KAP GKCS and S-KAP GKCS in a first degree dominance. The D-KAP EKCS model dominates S-KAP BK-CONWIP, S-KAP EKCS, D-KAP GKCS and S-KAP GKCS in first degree dominance. The S-KAP BK-CONWIP model has opening degree dominance over S-KAP EKCS, D-KAP GKCS and S-KAP GKCS. S-KAP EKCS has first degree dominance over D-KAP and S-KAP GKCS. While, D-KAP GKCS has second order dominance over S-KAP GKCS. The ranking of the PCS+KAP based on the service level performances under robust conditions with 1 indicating the best performer is shown in Table 9. It was demonstrated that if the decision makers are concerned with the service level in a system, D-KAP is preferred to S-KAP when robustness of solution is considered. BK-CONWIP is preferred over EKCS and GKCS. D-KAP BK-CONWIP is the superior PCS+KAP to the alternatives. Table 7 Base values, upper and lower bound values of demand variability factors. Demand (environmental variability) factor Product 1 Product 2 Mean (normal distribution) 5.61 [5.26, 5.96] 5.72 [5.65, 5.79] Standard deviation (normal distribution) [2.52, 3.09] [0.29, 0.86] [R.V] Range values for the factors (range from -5% to +5% of base value) Table 8 Base values, upper and lower bound values of system variability factors. Processing (system variability) factor Stage 1 Stage 2 Stage 3 Mean time before failure (exponential distribution) 90 [78.5, 103] 90 [78.5, 103] 90 [78.5, 103] Mean time before failure (exponential distribution) 10 [8.72, 11.5] 10 [8.72, 11.5] 10 [8.72, 11.5] [R.V] Range values for the factors (range from -5% to +5% of base value) Table 9 Robustness analysis ranking for service level. Performance metrics D-KAP BK-CONWIP S-KAP BK-CONWIP D-KAP EKCS S-KAP EKCS D-KAP GKCS S-KAP GKCS Service level

14 80 An Investigation of Pull Control Strategies and Production Authorisation Cards A description of the results of the cumulative distribution functions of the average total work-in-process inventory is shown in Figs. 4 and 5. These figures show that under robust conditions, S-KAP is preferable to D-KAP when WIP is a concern to the decision makers. BK-CONWIP is preferred over its alternatives. S-KAP BK-CONWIP is the best PCS+KAP. The stochastic dominance tests showed first degree dominance and second degree dominance for minimisation of WIP. S-KAP BK-CONWIP has first degree dominance over the alternatives. It was selected as the best PCS+KAP in terms of minimisation of WIP under robust condition. D-KAP BK-CONWIP has first degree dominance over S-KAP EKCS, D-KAP EKCS, S-KAP GKCS and D-KAP GKCS. S-KAP EKCS has first degree dominance over D-KAP EKCS, S-KAP GKCS and D-KAP GKCS. D-KAP has first degree dominance over S-KAP GKCS and D-KAP GKCS. S-KAP GKCS has second degree dominance over D-KAP GKCS. D-KAP GKCS is the worst performer in terms of WIP. The ranking of the PCS+KAP based on their capability to minimise WIP under robust conditions with 1 indicating the best performer is shown in Table 10. Average total WIP probability distribution 1 Cumulative probability Fig. 4 Average total WIP S-KAP BK-CONWIP D-KAP BK-CONWIP D-KAP EKCS S-KAP EKCS D-KAP GKCS S-KAP GKCS Cumulative distribution function of average total WIP. 0.2 Average total work-in-process inventory probability Probability Fig. 5 Average total WIP S-KAP BK-CONWIP D-KAP BK-CONWIP D-KAP EKCS S-KAP EKCS D-KAP GKCS S-KAP GKCS Average total WIP probability histogram. Table 10 Robustness analysis ranking for WIP. Performance D-KAP S-KAP D-KAP EKCS S-KAP EKCS D-KAP GKCS S-KAP GKCS metrics BK-CONWIP BK-CONWIP Service level

15 An Investigation of Pull Control Strategies and Production Authorisation Cards 81 In both service level and WIP performance metrics comparison, BK-CONWIP outperformed the alternatives under environmental and system variability. D-KAP outperformed S-KAP in terms of higher service levels under instabilities. This is attributed to the larger proportion of production authorisation cards in D-KAP models, generating large WIP and satisfying more demands under lumpy demand profile (demand profile higher than the base-demand profile) than S-KAP models. S-KAP models performed better than the D-KAP models in terms of WIP level. 5. Discussion and Conclusions Observation from the multi-objective optimisations (Fig. 2) shows that BK-CONWIP achieved lowest total inventory (WIP) at any service level in the range 90% to 100%. The result showed that S-KAP models will achieve any given service level with less WIP than D-KAP models. While S-KAP BK-CONWIP is the best PCS+KAP. The results of the application of the ranking and selection procedure confirmed the direct observation by selecting S-KAP BK-CONWIP as the superior PCS+KAP to its alternatives. S-KAP is preferable to D-KAP, while BK-CONWIP is preferred over EKCS and GKCS. The choice of S-KAP over D-KAP when the system is considered stable agrees with the findings of Ref. [4-6, 8]. Instability affects the operational performance of PCS+KAP. The performance of PCS+KAP for service level showed that D-KAP models are preferable to S-KAP models. Similarly, findings of Ref. [8] agree with this finding that D-KAP is a better performer than S-KAP under instabilities. D-KAP BK-CONWIP outperformed the alternatives. When minimisation of WIP was the concern, S-KAP outperformed D-KAP. BK-CONWIP outperformed the alternatives, owing to its capability of using the lowest number of low production authorisation cards and the flexibility in its control mechanism. The GKCS models are the least preferred due to its high WIP level resulting from the manner in which demand information is transmitted in its control mechanism. Generally, BK-CONWIP is shown in this study to be a promising pull production control strategy with the capability of maintaining high service levels while minimising work-in-process inventory in a multi-product manufacturing system. S-KAP was found to be the best policy when a multi-product system operates under predictable demand and system failure rates. In systems that are subject to instabilities, D-KAP is preferred to S-KAP, when service level is a concern. When WIP is a matter of concern, S-KAP is preferred to D-KAP. This is attributed to the flexibility of S-KAP. S-KAP uses less production authorisation cards than D-KAP. Least production authorisation card in S-KAP reduces the level of WIP in S-KAP than in D-KAP. The findings in this paper provide additional indication that S-KAP is a promising Kanban allocation policy for allocating production authorisation card in multi-product systems under predictable demand and system failures. However, under environmental and system instabilities, D-KAP is the preferred to S-KAP for high service level, while S-KAP is preferred to D-KAP for low WIP level. Lastly, S-KAP BK-CONWIP was suggested to have superior flexibility and responds to demand variations without control parameters reconfigurations [34]. Further research on the performance of BK-CONWIP to product mix and demand volume variations in a complex multi-product system will provide a clearer understanding on the flexibility of BK-CONWIP. References [1] M.S. Akturk, F. Erhun, An overview of design and operational issues of Kanban systems, International Journal of Production Research 37 (1999) [2] S.H. Hum, C.K. Lee, JIT scheduling rules: A simulation evaluation, Omega 26 (1998) [3] J.F. Bard, B. Golany, Determining the number of Kanbans in a multi-product, multi-stage production

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