The integrated control of production-inventory systems

In this thesis, we investigate a multi-product, multi-machine production-inventory (PI) system that is characterized by: ? relatively high and stable demand; ? uncertainty in the precise timing of demand; ? variability in the production process; ? job shop routings; ? considerable setup times and costs. This type of PI system can be found in the supply chain of capital goods. Typically, it represents a manufacturer of parts that are assembled in later stages of the supply chain. Our exploratory research aims at identifying promising control approaches for this type of PI systems and the conditions in which they are applicable. The control approaches developed in this thesis are based on an integrated view of the PI system. The objective of the control approaches is to minimize the sum of setup costs, work-in-process holding costs and ? nal inventory holding costs, while target customer service levels are satis? ed. The research reveals that the exact analysis and optimization of this type of PI systems is impossible. Therefore, we are restricted to the development of heuristic control approaches. We propose two control strategies that are based on distinct control principles. For each of the control strategies, we develop and test decision-support systems that can be used to determine cost-e¢ cient (but not necessarily optimal) control decisions. Part I of this thesis deals with the ? rst approach, called Coordinated Batch Control (CBC). This strategy uses a periodic review, order-up-to inventory pol- icy to control the stock points. The replenishment orders generated by this inventory policy are manufactured by the production system. The CBC strat- egy integrates production and inventory control decisions by determining cost- e¢ cient review periods. There is no further integration of control decisions. At the shop ? oor, a myopic rule is used to sequence the orders, which ensures a certain degree of ? exibility for responding to unexpected circumstances. We develop three decision-support systems for the CBC approach. The ? rst decision-support system is based on an approximate analytical model of the PI system. In the approximate analytical model, we apply standard results from inventory theory, queueing theory and renewal theory. The second and third decision-support system use simulation optimization techniques to determine the near-optimal review periods. The three heuristic decision-support systems for CBC are tested in an exten- sive simulation study. The test bed consists of ? ve basic problem con? gurations, which de? ne a routing structure, processing times, etc. We vary four factors over several levels: setup costs, setup times, net utilization and target ? ll rates. In this way, we obtain 48 instances based on the same basic problem con? guration, leading to 5 x 48 = 240 problem instances. The simulation study shows that the use of simulation optimization resulted in relatively small improvements over the solution obtained from the approximate analytical model. Since simulation optimization requires large amounts of computation e¤ort, we decide that the use of the decision-support system based on the approximate analytical model is justi? ed. Part II is concerned with the Cyclical Production Planning (CPP) strategy. This strategy approaches the control of the PI system from a totally di¤erent angle. In this strategy, a detailed production schedule is used to control the production system. The schedule prescribes the sequence in which the orders are produced on the work centers and this schedule is repeated at regular time intervals. The time that elapses between the start of two schedules is called the ? cycle time? The schedule is determined such that the total costs are minimized. The stock points are controlled with periodic review, order-up-to policies. The main advantage of the use of a production schedule is that ? ow of the orders through the production system is controlled better, which results in more re- liable throughput times. A drawback of this approach is that the production frequencies of the di¤erent products need to be matched in order to make a cyclic production schedule. Hence, there is less ? exibility in setting the lot sizes, which may result in higher costs. Another drawback of the CPP approach is that production capacity may be wasted by strictly following the prespeci? ed processing sequences. We propose a decision-support system for the CPP strategy which is based on a deterministic model of the PI system. The decision-support system is used to determine cost-e¢ cient production plans. We present a heuristic method to approximately minimize the total costs of the deterministic model. When the solution of the deterministic model is used in a stochastic environment, the solution may be instable or nearly instable. Therefore, we use a simulation procedure to check whether the proposed solution is stable. If not, slack-time is added to the schedule and deterministic model is solved again. We test the decision-support system for CPP in an extensive simulation study. The test bed is identical to the one used in Part I. We test wether the Summary 273 decision-support system responds soundly to changes in the factors. Further- more, we investigate the estimation quality of the deterministic model that is embedded in the decision-support system. Finally, we test the optimization quality of the decision-support system. Based on the results of these tests, we decide that it is acceptable to use the proposed decision-support system to determine the control variables of the CPP strategy. Part III compares the performance of the CBC and the CPP strategy. Both strategies are compared in a simulation study consisting of the same instances as in Part I and II. We compare the strategies in terms of realized total costs. In about 62% of the instances, the CPP strategy outperforms the CBC strategy. In the remaining 38% of the instances, the CBC strategy realizes lower costs than the CPP strategy. An analysis of variance reveals that the following factors have a signi? cant impact on the performance di¤erence between CPP and CBC: ? net utilization; ? setup costs; ? interaction between setup costs and net utilization; ? basic problem con? guration. Based on our investigations, we can provide an explanation for these obser- vations. The simulation results show that the performance di¤erence is pro- portional to the di¤erence between the average review periods (CBC) and the common cycle length (CPP), denoted as dR. The factors mentioned above have an in? uence on dR through their impact on capacity utilization. At low lev- els of capacity utilization, we observe that dR is low, which indicates that the CPP and CBC strategy operate with comparable review periods and common cycle lengths. In situations where the CBC strategy operates at higher levels of capacity utilization (because net utilization increases and/or setup costs de- crease), it becomes more di¢ cult for the CPP strategy to ? nd a feasible cyclical production schedule, mainly because production capacity is wasted by strictly following a prespeci? ed processing sequence. In these cases, the CPP strategy needs to increase the common cycle length to free up production capacity that is used to compensate for the loss of capacity. This leads to increases in dR and to higher costs. The speci? c characteristics of a problem instance have a strong in? uence on the magnitude of this e¤ect. Based on the insights obtained from our research, we formulate some guidelines for the application of CPP and CBC.