Job shop management of products under internal lifespan and external due date

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Production Research, Vol. 56, Issue 16, on January 2018, available at: https://doi.org/10.1080/00207543.2018.1430908 © 2018 Informa UK Limited, trading as Taylor & Francis Group. En idUS Licencia Creative Commons CC BY-NC-ND Job shop management of products under internal lifespan and external due date PedroL. Gonzalez-Ra*, Marcos Callea and Jose L. Andrade-Pinedaa aIndustrial Management, School of Engineering, University of Seville, Seville, Spain *Corresponding author. Email: [email protected] Preprint submitted to INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH January 3, 2018 DOI: 10.1080/00207543.2018.1430908 Job shop management of products under internal lifespan and external due date Deteriorating items are found in a wide variety of productive environments and have been extensively reported in the literature. However, the evolution of markets demand the development of new products and new forms of work are made necessary to adapt production systems to those changes. The present work focuses on the production control of perishable products in a job-shop environment. Specifically, in those products that have an expiration date within the production interval (internal caducity) that must be delivered before a certain date. As far as we know, there are no previous works that focus on the internal caducity of products at the production-control level. Two systems of different nature have been compared: Workload Control (WLC) and Kanban. WLC is usually a benchmark in job-shop and made to order environments. Recent studies show that Kanban, traditionally used in JIT (Just in Time) environments, performs similarly or even better than WLC. The study was performed by discrete events simulation using Python© language, SimPy© and DEAP© modules, and considering several responses of the systems. The results show that both systems have a good performance in a variety of scenarios, with overall performance of Kanban in terms of internal caducity and tardy deliveries. Keywords: product lifespan; perishable product; job-shop; pull systems; work load control; kanban system; production control 1. Introduction A common hypothesis in research studies about production planning and control is to consider that the properties and physical-chemical characteristics of processed products remain unchanged throughout the entire process, or the changes are a controlled phase within the product production lifecycle. In this case, the modifications in the products are not important enough to be considered as something special in the performance of the productive system, and therefore in management decisions. In other cases, the properties of the products are altered. One of the most wellknown effects is the change in properties of the products over time. As time passes, the product degrades, so the due dates required by customers are usually quite important in production management decisions, in order to reach the market on time and sell the product with the quality characteristics established by customers. This is usually the case in which the product to be manufactured is perishable. Examples of such problems are found in floriculture, agri-food, food manufacturing, medicine and pharmacy, blood banks, or in ready-mix concrete paste companies. Although they are totally different products, they keep the relation as far as lifecycle is concerned. In some cases, the products have a certain lifespan, while in others the quality of the products decreases with time before the end of the lifecycle. For example, products harvested by horticultural companies begin to deteriorate once the product is collected, as it begins to lose moisture. See 𝑡0 in Figure 1 (a). The product lifespan (𝐿𝑆) ends at the Expiration Date (𝐸𝐷) after the time required to manufacture the product or Lead Time (𝐿𝑇) at instant FD (Finish Date). Under normal conditions the product is already in the hands of the customer before the Due Date (𝐷𝐷) required by the customer. We say in this case that the production system has an "External Caducity", since the caducity of the product occurs outside the manufacturing system. A list of acronyms and notations is provided in the Appendix to facilitate understanding and readability of the document. Another different case of the deterioration phenomenon occurs e.g. in the manufacturing of fibre-reinforced plastic structures where a material called prepreg (contraction of 'pre-impregnated') has become the standard technology. The lifetime of a prepreg is limited, due to the self-reacting nature of the resin (see Pansart 2013). The composite material must be kept cold at very low temperatures until it is used. Subsequently, when the material leaves such conditions, at time 𝑡𝑜 in Figure 1 (b), it has a time slot to be used, therefore a fixed lifespan. That is, the pieces should be prepared in a certain time limit and taken to the curing process, in order to stabilize the piece in an autoclave and to give it the physical properties for which it has been designed. The available time window to stabilize the product is represented in the graph as 𝑆𝑇, which coincides in this case with the 𝐿𝑆 interval. Once stabilized, the product continues the process until its completion time in 𝐹𝐷. There is also a commitment to the customer to finish the order before a certain date, 𝐷𝐷. In this case the effect of the deterioration of the product is framed within the production process, so we denote this case as "Internal Caducity". Figure 1. (a) External caducity timeline (b) Internal caducity timeline As is argued later in the literature review, the management of deteriorating products within the production process has been approached very briefly and never from the point of view of production control. Classically, production control systems play a very important role in short-term decisions and their correct operation will produce 𝑡 Internal Process 𝐿𝑆 𝑡𝑜 𝐸𝐷 𝐷𝐷 𝑆𝑇 𝐹𝐷 External Process 𝐿𝑇 𝑡 Internal Process 𝐿𝑆 𝑡𝑜 𝐸𝐷 𝐷𝐷 𝐹𝐷 External Process 𝐿𝑇 𝑆𝑇 (a) (b) different responses of the system in terms of: Work in Process (WIP), lead time and order delays. In addition to the above, and in the context of internal caducity, it is also necessary to correctly manage the deterioration of products within the production system. We could then formulate the Research Question as follows: How does the joint phenomenon of caducity and due date affect the management of production control systems? To address this question, we compare the two alternatives that are most suitable for this type of environments: The WLC system and the Kanban system. WLC has proven to be a benchmark in made-to-order (MTO) products in job shops. A different approach is given by a recent version of Kanban that has proven to achieve a similar or even better performance than the most advanced implementation of the WLC. There are several novel aspects in this paper: i) the product has an internal lifespan, that must be managed by the production control system, ii) the WLC system is compared to a recent and unstudied version of the Kanban system in job-shop environments, and iii) priority rules are adapted to meet lifespan and external due dates. The rest of the chapter is organised as follows: Section 2 presents the review of the literature on the products deterioration concerns in production, as well as reviewing the production control systems in job-shop environments. Section 3 describes the implementations of the WLC and Kanban used in this work. Section 4 provides a detailed description of the shop floor under study, as well as the computational experience. Section 5 describes the simulation analyses, and discusses the results. Finally, the last section is devoted to drawing conclusions and pointing out possible research directions. 2. Literature review 2.1 Deteriorating products: definition and previous works Usually companies work with products that do not always maintain the physicalchemical characteristics for which they have been conceived and which must remain stable over time. It is said in this case that the products are deteriorating items (Mirzaei and Seifi 2015). Deteriorating items refer to items that become decayed, damaged, evaporative, or expired through time (Li, Lan, and Mawhinney 2010). Products that have a maximum usable lifetime are known as perishable products (e.g. meat, green vegetables, human blood, medicine, flowers, and films). Commodities such as alcohol and gasoline which have no shelf-life are known as decaying products (Goyal and Giri 2001). The effect of perishability on the products is a phenomenon already studied previously. In fact, as far as we know, there are 17 reviews on this phenomenon. In addition to the reviews mentioned above the following revisions stand out: Nahmias (1982), Karaesmen, Scheller-Wolf, and Deniz (2011), Bakker, Riezebos, and Teunter (2012), Amorim et al. (2013), and Janssen, Claus, and Sauer (2016). In the latter, the main contributions of each of the revisions, differences and evolution over time are assessed and explained. 2.2 Perishable products at production and distribution Deteriorating items impact on decisions at the production level, as much as on decisions in long, medium and short term. It should be noted that the major body of literature on perishability is concerned with inventory management, although there has been a growing interest in its effect on supply chain management problems (Amorim et al. 2013). Distribution networks and centres are responsible for managing the complex problem of distribution and storage of products. In the case of perishables, the problem is even more complicated, since the distribution and storage of perishable items usually requires consideration of the limited lifetime of the items. See for example recent studies by Miner and Transchel (2017) on the effect of order variability in the supply chain of perishable goods. Distribution plans that need refrigeration are of particular interest within the supply chain, since distribution planning tasks are one of the main activities in cold supply chains (see Hsiao, Chen, and Chin 2017). In a recent publication Keizer et al. (2017) address aspects of network design when product quality can be categorized and thus split flows. Other issues addressed in the context of the supply chain are localization problems, including ILDN (Integrated Logistic Distribution Network) distribution problems integrated with location of facilities and allocation of retailer to the open facilities. See in this regard Wu, Shen, and Zhu (2015) where the backlogging of a perishable product is also considered. The integration of inventory control and vehicle routing produces a complex optimization problem called IRP (Inventory Routing Problem) which aims to minimize total inventory and transportation costs. Recent works simultaneously study the inventory management problem associated with routing to retailers. Progress in this area is also important in problems which simultaneously optimize inventory management with the associated transport problem VRP (Vehicle Routing Problem). See in this regard Mirzaei and Seifi (2015), which addresses an IRP with lost sales. The IRP that also integrates the variables related to the quantities to be produced of each product yield the IPDS (Integrated Production and Distribution Scheduling Problem) optimization problem. In a recent paper (see Devapriya, Ferrell, and Geismar 2017), the authors study an IPDS to determine fleet size, truck routes, production schedule and distribution sequence, fulfilling a planning horizon. Belo-Filho, Amorim, and Almada-Lobo (2015) carry out new research on the MILP (Mixed Integer Linear Programming) model introduced in Amorim et al. (2013) using the lot sizing approach. The authors proposed solution methods based on the ALNS (Adaptive Large Neighbourhood Search) heuristic to address large instances of the problem. 2.3 Internal Caducity To our knowledge, there are very few jobs which consider that the end of the lifespan occurs internally during the production process. The works by Cai et al. (2008) and Billaut, Della Croce, and Grosso (2015) belong to this category in the context of lot sizing and scheduling problems. Cai et al. (2008) perform a scheduling of perishable products at a seafood manufacturing plant. The products are made from raw material which, for reasons of freshness, must be used before a fixed deadline. The decisions are relative to what type of product is produced, the quantity and the sequence to be processed at manufacturing. Billaut, Della Croce, and Grosso (2015) introduce an interesting problem inspired by the production of chemotherapy drugs for cancer treatment by intravenous injection (an early description of the same problem can also be found in Billaut 2011). The authors address a scheduling problem from the pharmaceutical industry where raw materials have a limited lifetime once they have left the environmental conditions of storage, and therefore, they must be used before a certain deadline. 2.4 Production control systems in job-shop environments In order to select which types of production control systems can achieve a better performance in the management of perishable products, we have taken the WLC system as a reference. WLC is the most widely used method for production control in MTO and job-shop environments (Stevenson, Hendry, and Kingsman 2005), and it is considered 𝑂𝑐𝑐𝑢𝑝𝑎𝑡𝑖𝑜𝑛 = 𝑚𝑒𝑎𝑛 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 𝑡𝑖𝑚𝑒 · 𝑚𝑒𝑎𝑛 𝑟𝑜𝑢𝑡𝑖𝑛𝑔 𝑙𝑒𝑛𝑔𝑡ℎ 𝑖𝑛𝑡𝑒𝑟−𝑎𝑟𝑟𝑖𝑣𝑎𝑙 𝑡𝑖𝑚𝑒 · 𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑠ℎ𝑜𝑝 𝑓𝑙𝑜𝑜𝑟 (1) The due dates are set exogenously by adding to the job entry time, a random allowance factor which is uniformly distributed over the range 40 to 50 time units. As in Thürer and Stevenson (2016), the minimum value will be sufficient to cover a minimum shop floor throughput time corresponding to the maximum processing time (4 time units) for the maximum number of possible operations (8) plus an arbitrarily set allowance for the waiting or queuing times of 8 time units. The value of the maximum waiting time allowance is chosen in order that the basic set of experiments result in a percentage tardy between 5 and 20%, see González-R and Calle (2017). The maximum caducity window is set to 18 time units, in order that the set of basic experiments achieves a percentage of expired products less than 10%. For all orders, the lifespan starts at the beginning of the process in the activation station, which is a fixed work centre (number 5), independently of the position in the route. These settings facilitate comparison with earlier studies on both Workload Control (e.g. Oosterman, Land, and Gaalman 2000, Thürer et al. 2012, Thürer et al. 2014) and Kanban (González-R and Calle 2017). Table 1 shows a summary of simulated shop and job characteristics. Table 1. Summary of simulated shop and job characteristics. Shop Characteristics Routing variability Random routing; no re-entrant flows No. of work centres 8 Interchange-ability of work centres No interchange-ability Work centre capacities All equal Work centre utilization rate 80% Job Characteristics No. of operations per job Discrete uniform [1, 8] Operation processing times Truncated 2-Erlang (mean=1; max=4) Planned throughput time per operation 5 time units Due date allowance Uniformly distributed [40, 50] Inter-arrival times Exp. distribution; mean=0.703125 4.2 Order release As in previous simulation studies on workload control (e.g. Land and Gaalman 1998, Fredendall, Ojha, and Patterson 2010, Thürer et al. 2012, and Thürer, Stevenson, and Qu 2016), it is assumed that all jobs are accepted, materials are available and all necessary information regarding shop floor routings, processing times, etc. is known. Jobs flow into a pre-shop pool to await release according to LUMS COR, as Land, Stevenson, and Thürer (2014). The time interval between releases for the periodic element of LUMS COR is set to 5 time units, as Thürer et al (2014). 4.3 Experimental design and performance measures The experimental factors are: i) the two production control systems (WLC LUMS COR y Kanban), and ii) four dispatching rules at intermediate buffers, which are the FIFO rule (First-In-First-Out rule), the EDD rule (Earliest Due Date), the SRPT rule (Shortest- Remaining-Processing-Time) and the CR rule (Critical Ratio). In the related literature on the WLC system it is usual to implement the FIFO rule as an internal dispatching rule. However, none of these studies addressed the effect of internal caducity of products. Therefore, we consider necessary to study the performance of different priority rules in this work. The FIFO rule gives priority to the next job in the queue. This rule emerges as the best in minimizing the makespan objective in all cases regardless of changing the flexibility of the problem instances. The SRPT rule, where the job with the least slack per remaining process time is chosen for loading, yields the shortest mean flow time, and it is extensively implemented in industry and often used as a benchmark for evaluating tardiness-related measurements. To include the effect of the internal caducity and delivery date we propose two priority rules (EDD and CR) adapted to this problem, and, as far as we know, never proposed before. The EDD rule gives priority to the job with the earliest due date. This rule performs well regarding the mean flowtime, being the most popular due date based rule, and is frequently used as a benchmark for reducing maximum tardiness and variance of tardiness. After the activation station the proposed EDD rule select the minimum value between the due date and the expiration date. Finally, the CR rule tends to prioritise jobs that have less time available, sequencing jobs in non-decreasing order of a ratio defined as the remaining allowance (the time till it is due) of the job divided by its remaining processing time. The CR rule has been tested in a number of studies, mainly for job shops and performs well for objectives based on the due date. In the proposed CR rule, the value of the remaining allowance, used in the evaluation of the critical ratio, is assessed by two alternative procedures: i) before caducity activation, the remaining allowance, for each job 𝑗 waiting in the intermediate buffer, is the remaining time from now to the due date, and ii) after caducity activation, the remaining allowance is given by the minimum value between the remaining time from now to the expiration date, and the remaining time from now to the due date. Evolutionary algorithm toolkit DEAP (Fortin et al. 2012), an abbreviation for “Distributed Evolutionary Algorithms in Python”, is used in the adjustment process of WLC and Kanban systems to find i) the optimum values for the workload norm for each station, in the WLC model, and ii) the optimum number of cards for each station, in the Kanban model. To reduce the area of search, only discrete variables are defined, i.e., the search for the load norms is restricted to integer values. DEAP is an evolutionary computation framework that allows rapid prototyping of diverse genetic algorithms, including genetic algorithms (Mitchell 1998), genetic programming (Banzhaf et al. 1998), evolution strategies (Beyer and Schwefel 2002), covariance matrix adaptation evolution strategy (Hansen and Ostermeier 2001), particle swarm optimization (Kennedy and Eberhart 2001), and many more. In this study, two objective functions have been used, which aim at i) reducing the amount of jobs with defects due to the material expiration, and ii) reducing the amount of jobs delivered tardy to the customer. As in Thürer, Silva, and Stevenson (2010 and 2011), the simulation software calculates the mean values of the objective functions from 100 replicates (Law and Kelton 2000). DEAP then evaluates this value and defines new parameters for the simulation which then repeats the calculation of the objective function within the newly defined parameters. This optimisation process can be repeated over a limited time period or until the optimum solution has been found. Results were collected over 10,000 time units following a warm-up period of 3,000 time units. These parameters allowed us to obtain stable results while keeping the simulation run time to a reasonable level. Below are listed the performance indicators measured in this study, which correspond to the most common performance indicators used in the studies of production control systems:  Percentage expired: the percentage of jobs completed after the maximum time allowed to remain uncured. This indicates the proportion of jobs with defects on its final degree of cure.  Percentage tardy: the percentage of jobs completed after the due date. This indicates the proportion of jobs that are delivered tardy to the customer.  Mean tardiness: the mean of the tardiness 𝑇𝑗=𝑚𝑎𝑥(0,𝐿𝑗), with 𝐿𝑗 being the lateness of job 𝑗 (i.e., its actual delivery time minus its due date). This indicates the extent to which jobs are tardy.  Gross throughput time: the mean of the completion time minus the arrival time across jobs. This measure reflects the time that a customer has to wait for the product.  Pre-shop time: the mean of the release time across jobs. This indicates the mean time that a job spends waiting in the pool before release. 5. Results and discussion First, this section analyses the obtained results related to the orders delivery, focusing on three indicators: the delivery of i) expired products, ii) delayed orders, and iii) the average of the delays duration. Secondly, we have studied the degree of utilisation of the shop by two indicators: i) the Pre-shop Time, consisting of the time that the orders remain in the pre-shop pool waiting to be released, and ii) the Gross Throughput Time, consisting of the total throughput time including pool waiting time. The first analysis consists of the study of the systems performance, which has been measured by 2 indicators, the delivery of expired products and the delivery of delayed orders. This analysis contains two opposing objectives: minimizing expired deliveries, and minimizing delayed deliveries. The performance achieved for each configuration of maximum permissible workload is represented by the coordinates of a point (𝑥,𝑦), where the first coordinate represents the ‘percentage of tardy deliveries’, and the second coordinate represents the ‘percentage of expired deliveries’. The Table 2 summarizes, for each combination of studied system (WLC and Kanban) and priority rule (FIFO, SRPT, EDD and CR), the efficient points that make up the efficiency frontier or Pareto frontier. Figures 2 to 5 show the percentage of expired deliveries over the percentage of tardy deliveries, obtained for both systems (WLC and Kanban), and applying the four priority rules studied in the present work. Each figure represents the results obtained from both the WLC system and the Kanban system, where each point corresponds to the average value obtained from all replicates which have been performed for a given maximum permissible workload. These figures also represent the points (or configurations of maximum permissible workload) that are simultaneously efficient to the two objectives of i) minimizing expired deliveries and ii) minimizing delayed deliveries. Thus, the group of efficient points composes the efficiency frontier or Pareto frontier. Table 2. Summary of efficient points for each combination of system and priority rule. Pareto Frontier of the Kanban system Pareto Frontier of the WLC system Total number of points of the frontier Endpoints of the frontier Total number of points of the frontier Endpoints of the frontier (𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑇𝑎𝑟𝑑𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠) (𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑇𝑎𝑟𝑑𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠) (𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑇𝑎𝑟𝑑𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠) (𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝐸𝑥𝑝𝑖𝑟𝑒𝑑 𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑠 ; 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑇𝑎𝑟𝑑𝑦 𝐷𝑒𝑙𝑖𝑣𝑒𝑟𝑖𝑒𝑠) Priority rule FIFO 2 (1.535%, 8.583%) (1.585%, 8.526%) 25 (0.829%, 6.344%) (2.916%, 2.335%) SRPT 2 (8.370%, 4.927%) (8.409%, 4.906%) 2 (4.185%, 3.026%) (4.213%, 3.017%) EDD 4 (0.098%, 3.389%) (0.124%, 3.352%) 20 (0.176%, 3.462%) (1.938%, 2.076%) CR 1 (0.065%, 0.085%) 7 (0.159%, 0.087%) (0.282%, 0.073%) (a) (b) Figure 2. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses FIFO rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses FIFO rule. (a) (b) Figure 3. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses SRPT rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses SRPT rule. (a) (b) Figure 4. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses EDD rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses EDD rule. (a) (b) Figure 5. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses CR rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses CR rule. First, the degree of concentration of the efficient points forming the efficiency frontier is analysed. Table 2 details the number of efficient points that make up each efficiency frontier. In addition, this table contains the endpoints of each efficiency frontier. Regarding the simultaneous response towards the two objectives, it is necessary to emphasize that achieving a high degree of concentration of efficient points allows simultaneously the minimizing of the quantity of expired products and delayed deliveries. As for the Kanban system, Figures 2(b), 3(b), 4(b) and 5(b), and Table 2 show a high degree of concentration of the efficient points for all the priority rules studied, since there are few efficient points which are close to each other. As for the WLC system, Figures 2(a), 3(a), 4(a) and 5(a), and Table 2 show how the applied priority rule affects the degree of concentration of the efficient points. Thus, higher levels of concentration are achieved by two priority rules, corresponding to the SRPT and CR. Regarding the production of expired items, the WLC system exceeds the Kanban system in the scenarios studied, except in the case where the Kanban system applies the CR as priority rule in which both systems achieve very similar performance levels. With regard to the delayed deliveries, the system that performs best varies according to the priority rule that has been applied. Thus, the WLC system overcomes the Kanban system when the FIFO or SRPT priority rules are applied. However, in scenarios applying the EDD and CR, the Kanban system surpasses the WLC system. Table 3 and Figure 6 gather for each priority rule the results obtained by both systems (WLC and Kanban). The objective of this analysis is to construct the joint efficiency frontier based on the best results belonging to each system. The Table 3 details separately for each priority rule the experimental results corresponding to i) the processing of the most urgent works on its due date, since they are directly released to the shop and do not have to wait for the next release period. Contrary to what was established by Stevenson, Hendry, and Kingsman (2005), but in agreement with the findings of González-R and Calle (2017), it has been shown that the performance of the Kanban system is competitive to that obtained by the WLC system which is usually implemented in this kind of environment. The scenario introduced is, as far as we know, new in the field of production control. This effect is not only found in real practise in the aeronautical industry, but also in the manufacture of pharmaceuticals and, as has been reported in literature in the production of perishable products, subject to a fixed internal termination date and an external due date (see e.g. Billaut, Della Croce, and Grosso 2015 or Cai et al. 2008). Several lines of research can be derived from this work. In our opinion, we believe it is important to study the integration of the planning methods in the higher hierarchical levels with the short-term decisions at production control level, in the case of internal caducity products. Furthermore, in this case only inorganic products have been considered, so that their validity or results may differ in the case that products such as fresh foods are processed. In such cases, other types of environmental factors e.g. humidity, temperature, or micro-organisms may affect the performance of the systems. Therefore, more research is needed in this area. Besides, in many cases in the processing of perishable products, the human factor is of great importance, greatly affecting the final quality of the product, and intervening directly in the processing time. 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Appendix: List of notation and acronyms used The acronyms used in the text are the following: ALNS Adaptive Large Neighbourhood Search CR Critical Ratio DD Due Date DEAP Distributed Evolutionary Algorithms in Python ED Expiration Date EDD Earliest Due Date FD Finish Date FIFO First in First Out ILDN Integrated Logistic Distribution Network IPDS Integrated Production and Distribution Scheduling Problem IRP Inventory Routing Problem JIT Just in Time LS Lifespan LT Lead time LUMS COR Lancaster University Management School Order Release MILP Mixed Integer Linear Programming MRP Materials Requirement Planning MTO Made to Order SRPT Shortest-Remaining-Processing-Time ST Slack Time VRP Vehicle Routing Problem WIP Work in Process WLC Workload Control Next are shown the WLC and Kanban operating parameters: 𝐷𝐷𝑗 Due date of job 𝑗 𝐽 List of jobs 𝐿𝑗 lateness of job 𝑗 𝑁𝑠𝐶. Workload norm at station 𝑠 𝑁𝐶𝑠 Number of cards available in the control panel of station 𝑠 𝑁𝐶𝑆𝑗0′ Number of cards available in the control panel of station 𝑠𝑗0′. 𝑝𝑗𝑠 Processing time of job j at station 𝑠 𝑆𝑗 Set of stations in the route of the job 𝑗 𝑡𝑗𝑅 Planned release date of job 𝑗 𝑡𝑜 Lefespan starting instant 𝑇 Release period 𝑇𝑗 Tardiness of job 𝑗 𝑇𝑗𝑠 Planned throughput time of job 𝑗 in station 𝑠 𝑊𝑠 Current workload at station 𝑠 Figure captions Figure 1. (a) External caducity timeline (b) Internal caducity timeline Figure 2. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses FIFO rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses FIFO rule. Figure 3. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses SRPT rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses SRPT rule. Figure 4. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses EDD rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses EDD rule. Figure 5. (a) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by WLC system when uses CR rule. (b) Percentage of expired deliveries over the percentage of tardy deliveries, obtained by Kanban system when uses CR rule. Figure 6. (a) Joint Efficiency Frontier when both systems use the FIFO rule. (b) Joint Efficiency Frontier when both systems use the SRPT rule. (c) Joint Efficiency Frontier when both systems use the EDD rule. (d) Joint Efficiency Frontier when both systems use the CR rule.