MRP در یک محیط تولید کارگاهی با استفاده از مدل برنامه ریزی محدود شده پروژه منابع

One of the most difficult tasks in a job shop manufacturing environment is to balance schedule and capacity in an ongoing basis. MRP systems are commonly used for scheduling, although their inability to deal with capacity constraints adequately is a severe drawback. In this study, we show that material requirements planning can be done more effectively in a job shop environment using a resource constrained project scheduling model. The proposed model augments MRP models by incorporating capacity constraints and using variable lead time lengths. The efficacy of this approach is tested on MRP systems by comparing the inventory carrying costs and resource allocation of the solutions obtained by the proposed model to those obtained by using a traditional MRP model. In general, it is concluded that the proposed model provides improved schedules with considerable reductions in inventory carrying costs.

Material requirements planning (MRP) is extensively used in manufacturing to schedule dependent demand items based on the production schedule for the independent demand items (end items). Despite its wide spread use, several difficulties with the implementation of MRP systems have been reported, see, for example [1], [2], [3] and [4]. The main shortcoming generally mentioned is the lack of integration of capacity requirements into an MRP schedule. Typically an MRP schedule is followed by rough cut capacity planning and if a capacity problem exists the master production schedule (MPS) is modified. The MRP schedule is then re-run and this procedure is repeated until all capacity requirements are within acceptable limits. Many of the studies in the literature indicate that lead times are often extended to make it easier to satisfy capacity requirements [4], [5] and [6]. This, however, will also lead to an increase in the amount of work-in-process. The use of discrete time periods (time buckets) in MRP systems further aggravates these problems. Often short lead times are rounded up to reach the length of a time bucket, and then doubled or tripled to ease capacity constraints, as well as provide for unanticipated occurrences such as maintenance downtime, supplier problems, and the like. This can then possibly lead to failures in meeting customer deadlines. Handling capacity limitations in this manner can greatly affect the quality of the MRP schedules, especially in a job shop, where customer orders cannot be satisfied through inventory when capacity is inadequate as scheduled. In this study, we offer a model using an optimization approach to solving capacity constrained, continuous-time, multi-stage production scheduling problems, based on resource constrained project scheduling (RCPS) concepts. This model addresses capacity and material requirements planning in a job shop environment. It develops a production schedule by determining the latest possible times for all the activities, or by leveling resource usages, while taking capacity constraints into account. The paper is organized as follows: In the next section, we review the literature on incorporating capacity into MRP systems and on using resource constrained project scheduling for material requirements planning. Then we discuss the relationship between RCPS and MRP systems using an example from the literature. The fourth section is devoted to the formulation and the description of the RCPS/MRP model, followed by the computational considerations and results. The last section is devoted to conclusions.

In this paper we investigate the applicability of resource constrained project scheduling models in solving capacitated MRP problems. The proposed model (RCPS/MRP) can be solved with a general purpose optimization package, such as OSL, and is more realistic in that time is treated as a continuous variable and the lead times for activities depend on the size of an order. A variety of objectives can be used in addition to the traditional late start, such as minimizing over/under utilization of labor. The model is developed for a deterministic environment although it can also be used as a planning tool in the presence of uncertainty. As indicated in [11], a good starting schedule is required as a pre-condition in many stochastic approaches to scheduling and RCPS/MRP can be used to provide one. Extensive computational testing of the model with various objectives was done using product structures from literature as well as from local manufacturers. The largest instances we solved had almost 2000 activities, 30 time intervals, and 10 work centers. These limitations are a consequence of the fact that RCPS/MRP model is formulated as a mixed integer program, and while improvements in algorithms and computer hardware will allow larger problems to be solved, the number of activities will always be a limiting factor. In general computational results indicate that material requirements planning can be done effectively using resource constrained project scheduling models. The assumptions underlying the RCPS/MRP model and the size limitations make this approach more applicable as a planning tool for job shops. With the use of this model rough cut capacity planning is no longer needed, multiple iterations of capacity plans are eliminated, and the schedule obtained minimizes carrying cost of inventories while meeting capacity requirements.