ترخیص محصول بهینه برای تولید کارگاهی ساخت سفارشی مشتری همراه با هزینه های زمان انتظار تا رسیدن محموله سفارش داده شده، هزینه های تاخیر و هزینه های کالای در جریان ساخت

Work order release mainly has been studied with regard to its impact on throughput, throughput time and work-in-process. In this research, we investigate work order release from an economic perspective. We study the situations where there are costs associated with the length of the customer order lead-time, the order tardiness and the work-in-process on the shop floor. Our research aims at minimizing the sum of these three costs. We derive expressions for the optimal value for the maximum number of orders that is allowed to be in process. Numerical analysis of a job shop model is used to investigate the reduction in total costs that results from optimally controlling the work-in-process as compared to the total costs under immediate release of arriving orders. The results show that cost reductions can be substantial for small shops, and for high ratios of work-in-process costs to lead-time costs.

Controlled work order release has been widely advocated as an approach to control production order throughput times at a predetermined level (Bertrand and Wortmann, 1981; Bechte, 1988; Spearman et al., 1989; Kingsman, 2000). For an overview of research of work order release we refer to Cigolini et al. (1998). Theoretical studies of queuing models of production systems reveal that for the same throughput under workload control, modeled with a closed network queueing system, the average and the standard deviation of the production order throughput times are smaller than under uncontrolled workload, modeled with an open network queueing system (Spearman et al., 1989). For instance, at a utilization rate of about 90% the average shop throughput time decreases with about 20%. A general assumption in these analyses is that the order-processing rate is independent of the workload in the system. For workload-dependent processing rates, controlled work order release can be a necessary condition for having a stable production system (Bertrand and van Ooijen, 2002). In this paper, we consider systems with workload independent processing rates. For such systems the above-mentioned benefits of workload control can only be fully realized if the production system is embedded in a market that can generate a new customer order each time a production order is completed. It will be clear that this is a rather strong assumption that will not be valid for many production situations. Generally, customer orders are placed under long-term contracts, or after a negotiation process where the customer can choose from a number of suppliers, making the customer order arrival process stochastic on the short term. As a result, the production system best can be modeled as an open queueing network with a stochastic order arrival process. Applying workload control in an open queueing network leads to a shop floor throughput time that is stochastically smaller than without workload control. However, the total order throughput time, including the time after arrival and before release to the shop, is stochastically larger than without workload control (Van Ooijen, 1996). Only if work order release also takes into account detailed information about the shop status, making it not just a workload control system but also providing detailed scheduling, the total order throughput time using controlled work order release can be shorter than without workload control (Van Ooijen, 1996; Land and Gaalman, 1998; Kingsman and Hendry, 2002; Land, 2004; Henrich et al., 2004a and Henrich et al., 2004b). In this paper, we study work order release based on the total number of orders in the job shop. We consider make-to-order job shop production systems that use a constant customer order lead-time in their market and that experience a linear penalty on customer order lead-time, a linear penalty on customer order tardiness and a linear penalty on work-in-process. Penalties on customer order lead-times may be due to the sales effort needed to attract orders being dependent on lead-times, or to sales prices being dependent on lead-time. Penalties on customer order tardiness may be due to contracts implying a reduction in sales price as function of order tardiness. Penalties on work-in-process may be related to cost of capital needed to finance work-in-process (raw materials and value added) and costs of storage of work-in-process. In this paper, we investigate the cost effectiveness of controlled work order release for this type of production situation. The problem setting and the model that we use to analyze the problem are presented in Section 2. In Section 3, we show that there exists a finite optimal value for the maximum number of orders on the shop floor and we use numerical analysis to determine the optimal values of the maximum number of orders on the shop floor, for different shop sizes, different shop utilizations and different ratios of work-in-process costs to lead-time-related costs. We also calculate for each of these settings the decrease in average total costs as compared to the average total costs under immediate release and give a discussion of the results. Conclusions are given in Section 4.

In this paper, we have studied the effects of controlled work order release on the sum of costs of work-in-process, lead-time costs and tardiness costs for job shops that can be characterized by Poisson order arrivals, random routings and stationary exponential processing times. We have derived explicit relationships for the average number of orders on the shop floor and the average number of orders in the release queue as a function of the maximum number of orders that is allowed to be on the shop floor. We have modeled the order flow time distribution function as an exponential with a parameter derived from the average number of orders in the release queue and the average number of orders on the shop floor. From these expressions it can be derived that the optimal value for the maximum number of orders on the shop floor is finite and is a function of the shop size, the utilization of the shop and the ratio of work-in-process costs to lead-time-related costs and tardiness costs. For a selected set of shop configurations we have used numerical analysis to determine for each shop the optimal value of the maximum number of orders on the shop floor, and the percentages decrease in the sum of work-in-process carrying costs, lead-time costs, and tardiness costs under controlled work order release as compared to these costs under immediate release. Inspection of the results of this numerical analysis suggests that controlled work order release should be considered if the shop size is small or if work-in-process costs are high relative to the lead-time costs. For large shops or for low relative low work-in-process costs, the cost benefits to be obtained from controlled work order release are small and unlikely to be sufficient to compensate for the costs of operation of controlled work order release. Real-life production systems face all kinds of perturbations like machine breakdowns, product rejects and varying demand. We investigated our research question at the hand of a job shop model, which captures the existence of all kinds of perturbations and variability via geometrical distributed number of operations per order, exponential processing times and exponential order interarrival times. We therefore may conclude that our conclusion is robust for the existence of perturbations of the production system. Moreover, production systems over time will operate under different shop utilization rates. We therefore have investigated our research question under two utilization rates, 90% and 95%, representing the production systems capacity utilization during the low demand period of the business cycle, and the production systems capacity utilization during the high demand period of the business cycle. The results show that the conditions for which controlled work order release is beneficial is robust to changes in the capacity utilization. Robustness to perturbations that cause the system to have non-exponential processing times or non-exponential order interarrival times cannot be investigated using analytical and numerical models and techniques. This would be a next research project requiring systematic computer simulation.