تنظیم به روز اقتصادی در تولید کارگاهی بر اساس مسیر یابی و عملکرد توزیع زمان جریان وابسته حجم کار

The trade-off between the length of the lead times quoted to the customers and the delivery reliability has been investigated by many authors. However, only a few studies do this in an economic setting. In this study, the setting of cost optimal due dates taking into account lead-time related and tardiness related costs is investigated. More specifically, in setting the internal due dates, which are used for determining the priorities on the shop floor, and in determining the expected order flow time probability density functions which are used for setting the external due dates, the work load is taken into account. From this study, it follows that this approach leads to (much) lower costs as compared to the situation with workload independent order flow time p.d.f.'s.

For many firms it is crucial to have short lead times and a good due date performance [1], [2] and [3]. With the latter it is meant that orders are delivered as close as possible to their due dates. Two decision functions play an important role in this respect: the order acceptance function where, amongst others, a lead time is promised to the customers and the order realisation function which influences the order completion time. In quoting lead times to the customers a trade-off has to be made between the length of the lead times and the reliability of the lead-time. Promising a short lead time might lead to an impossible task for the order realisation function with regard to delivering the order close to the order due date. On the other hand long lead times make it easy for the order realisation function to obtain a good due date performance but these lead times are, in general, not acceptable for the customers. Many authors (e.g. Cheng [4]; Vig and Dooley [5]; Lawrence [6]; Enns [7]) have studied this trade-off between the length of the lead times quoted to the customer and the delivery reliability (or due date performance). In these studies, lead times are determined such that a certain delivery reliability (in terms of lateness or tardiness) is obtained. However, a number of production situations are characterised by the fact that customers are willing to pay more for short lead times while, at the same time, there are penalties for the manufacturer for late deliveries. Short lead times lead to high prices but also to high penalties. Long lead times lead to lower prices paid by the customers but also to (very) low penalties to be paid by the manufacturer. In these situations the question is not which lead times lead to a certain delivery reliability but which lead times lead to the highest profit. Up to now only a small number of studies have taken this into account in determining optimal lead times ( [8], [9], [10] and [11]). Gong et al. use the equivalence between the production lead-time model and the inventory model (‘newsboy’ problem) for a serial production line where all orders have the same number of operations. This paper concentrates on job-shop like production systems where orders might have quite different routings and routing lengths and on the effect of using (operation) due date sequencing. Enns uses the overall lateness distribution function in setting economically optimal due dates. Bertrand and Van Ooijen [12] show that the flow time distribution functions might have quite different shapes for orders with different numbers of operations. The order flow time p.d.f.'s they use in setting the cost optimal external due dates, which determine the delivery performance, are the long term p.d.f.'s that are correct for the average utilisation. However, on the short term the utilisation (workload), in general, will deviate from the average utilisation (workload). In this study the approach of Bertrand and Van Ooijen [12] is followed. Their research is extended by taking into account the work load in setting the internal due dates, that are used for determining the priorities on the shop floor, and in determining the external due dates, that are quoted to the customer. The latter are based on different flow time p.d.f.'s for orders with different numbers of operations. The rest of this paper is organised as follows. In Section 2, a detailed description of the economic lead times determination problem is given. Next, in Section 3, it is discussed how order flow time probability density functions can be used to determine the economically optimal lead times. Section 4 discusses in more detail the production situation that is considered and the simulation study that has been used to investigate the effects of the policies discussed in Section 3 after which in Section 5 the results of this simulation study are presented and discussed. Finally, Section 6, summarizes the findings of this study.

In this study, cost optimal lead-times have been determined by using workload dependent internal due dates and order flow time p.d.f. for each type of order instead of the aggregate overall flow time p.d.f. as used up to now in research on determining optimal lead times. It has been investigated whether taking into account the fact that flow time p.d.f.'s should be determined for each level of work-in-process, by normalising the observed work load independent flow time p.d.f.'s, leads to lower costs. It can be concluded that to obtain the lowest cost per order the XDD's should be set on the basis of the normalised flow time p.d.f. per order type and the IDD's should be based on the workload. For low tardiness costs the method using normalised flow time p.d.f.'s (in setting the XDD) in combination with work load dependent IDD's and the MOD priority rule leads to about the same costs as Enns’ method. For moderate tardiness costs the cost optimal method in combination with the ODD rule leads to about the same costs as Enns’ method, whereas for high tardiness costs the cost optimal method leads to lower costs. Although compared to Enns’ method the cost optimal method does not lead to a (much) lower costs per order, the advantage of the cost optimal method is that, for each order category, the percentage of tardy deliveries is controlled. This in contrast to the percentage of tardy deliveries that is obtained with Enns’ method, where even the overall percentage tardy is not controlled.