شکل گیری ساولی چند دوره ای یکپارچه و عقد قرارداد برنامه ریزی تولید در سیستم تولید سلولی پویا

In this paper, an integrated mathematical model of the multi-period cell formation and production planning in a dynamic cellular manufacturing system (DCMS) is proposed with the aim of minimizing machine, inter/intra-cell movement, reconfiguration, partial subcontracting, and inventory carrying costs. This paper puts emphasis on the effect of the trade-off between production and outsourcing costs on the re-configuration of the cells in cellular manufacturing systems (CMSs) under a dynamic environment, in which the product mix is different from a period to another resulting in the operational dynamism in the cells. The proposed model is verified by a number of numerical examples and related sensitivity analysis.

Most production environments involve the changes in operating parameters, such as the product demand over time. In such a case, managing the production resources and balancing them between successive time periods with the aim of minimizing the production costs is known as “production planning (PP)”. Cellular manufacturing systems (CMSs) are one of the well-known and efficient alternatives for the production environment with high variety and high volume of products. The main goal of CMSs is to minimize the throughput time, setup cost and also the material handling costs in the shop floor. However, for more reality, some of the PP alternatives, such as facility capacity, machine cost, inventories holding, backorders and subcontracting, have been considered to form the manufacturing cells in the recent researches. In general, integrating the concepts of the CMS design and PP is to be a fundamental requirement for modelling and simulating the real production environments. Actually, fluctuations in product mix, volume and introduction of new products are the key aspects that justify the integration of the CMS and PP. Despite the fact that the design of production systems depends on how planning the production resources, it is rare to find previous work integrating the concepts of the CMSs design and PP from the operational point of view. The objective of a typical PP problem is to minimize the total production-related costs, such as variable production costs, inventory costs, and shortage costs, over the fixed planning horizon. The main constraints of the PP problem are as follows: (1) inventory balance equation for making the inventory and/or shortages balanced with those from the previous period, production quantity, and demand quantity and (2) capacity constraints which ensure that the total workload for each resource (labour, machine, etc.) does not exceed the capacity in each period (Kim and Kim, 2001). Because of the dynamic nature of PP problems, the integration of the CMS and PP makes the problem very complex and computationally hard. The reason is that the cell reconfiguration is the most important operational aspect of the CMS design in the dynamic environment that must be considered in a real integrated model. The concept of the dynamic cellular manufacturing system (DCMS) is first introduced by Rheault et al. (1995). In the traditional CMS any changes in the product demand over time is ignored from product redesign and other factors. It assumes that the product mix and part demand is constant for the entire planning horizon. The product mix refers to a set of part types to be produced at each period. In the dynamic environment, a planning horizon can be divided into smaller periods where each period has different product mix and demand requirements. Consequently, the formed cells in the current period may not be optimal and efficient for the next period. To overcome disadvantages of the traditional CMS, the concept of the DCMS is introduced. In DCMS, The length of the planning horizon directly depends on the natural of the product. For example, if we encounter the season products, like clothing or heater/cooler equipments, the planning horizon may consist of two six-month periods or four three-month periods. The DCMS is related to reconfiguration of manufacturing cells including part families and machine groups at each period. Reconfiguration involves swapping the existing machines between each pair of cells, called machine relocation, adding new machines to cells including machine replication, and removing the existing machines from cells. A schema of the cell reconfiguration in the DCMS for two consecutive periods is schematically shown in Fig. 1. The system contains of two manufacturing cells for each period. Because of the processing requirements, machine 3 must be relocated from cell 1 to 2 and machine 7 from cell 2 to 1 at the beginning of period 2. Also, machine 8 must be added to cell 2 at the beginning of period 2 while machine 1 will not be used during period 2. In this case, either machine 1 keeps in the same cell or moves to another cell because of the cell size limitation. Considering the maximum cell size is equal to 4, machine 1 moves to the outside of cell 2 and machine 8 is replaced by that. Thus, the above reconfiguration requires three machine relocations. Full-size image (48 K) Fig. 1. A schema of the cell re-confirmation in DCMS. Figure options In a DCMS, the decision maker (DM) wants to know how big the changes of the cell configuration from a period to another are. As it is pointed out earlier, these changes are caused by the fluctuations in the production and outsourcing requirements. In this case, the DM must make an appropriate decision between the available alternatives, such as adding a new machine, relocating the machines between current cells, subcontracting some parts and hiring/firing the workers, to keep a balance between production and outsourcing costs. Making such a decision can be critical and risky in the cost-intensive production systems, such as DCMS, because it can significantly affect the cell configuration during the given horizon planning. Hence, the current paper is developed to put emphasis on the effect of the trade-off between production and outsourcing costs on the re-configuration of the cells in DCMSs. Material handling is the most important operational aspect of the CMS. In practical, the material handling cost in the CMS is divided to two main groups: inter and intra-cell movements. It is rare to find any previous work considering both inter and intra-cell movements in the DCMS simultaneously, especially, considering the operation sequence. Among the researches related to the DCMS, only Wicks and Reasor (1999), Defersha and Chen (2006a), Safaei et al. (2006) and Safaei et al. (2008) considered the operation sequence for inter-cell movements. Additional advantage of the research by Safaei et al. (2008) considered both intra-cell and inter-cell movements by assuming the operation sequence. Among the previous studies, Sankaran and Kasilingam (1993) formulated an integer programming model which uses a stepwise linear function to represent the cost of intra-cell moves. Ranges of cell sizes, in terms of the number of machines contained in a cell, are defined. As cells become larger and fall into the next range, there is a stepwise increase in the cost of an intra-cell move. However, their model does not consider the effect on which demand variability may have on the system. Fig. 2 shows the direct effects of the operation sequence on the material handling. For example, operations 1 and 3 of part 11 must be done on machine 7 in cell 1. Also operation 2 must be done on machine 5 in cell 2. Thus, to observe the operating sequence, the processing route for part 11 requires two inter-call movements from cell 1 to 2 and vice versa. By the same reason, the processing route for part 3 in cell 2 requires two intra-cell movements. From the efficiency point of view, considering both inter and intra-cell material handling simultaneously causes a balance in the size of the formed cells. The reason is that very large cells involve high intra-cell and low inter-cell material handling costs. On the other hand, very small cells involve high inter-cell and low intra-cell material handling costs. Full-size image (20 K) Fig. 2. Effect of the operation sequence on inter/intra-cell material handling. Figure options To simplify, as shown in Fig. 3, it is supposed that the part types are shifted within cells by a robot or manpower and between cells by a conveyor, crane, truck, or automated guided vehicle (AGV). In this figure, inter-cell movements are handled by manpower in cell 1 and by a robot in cell 2. Obviously, in this case, the capacity and unit cost of the intra-cell movement are less than the related cost incurred by inter-cell movement. In this paper, we extend the original model proposed by Safaei et al. (2008) with a new contribution on the outsourcing by considering the carrying inventory, backorder, and partial subcontracting. The proposed model is able to form the optimal cells and to determine the optimal alternate plan (i.e., production or partial/full subcontracting) for each part type at each period during the given horizon planning. Four objectives are considered to minimize in the proposed model as follows: (1) Machine costs consist of the constant and variable costs. (2) Material handling costs consist of inter and intra-cell movement costs by considering the operation sequence. (3) Cell reconfiguration cost consists of the machine relocation costs. (4) Outsourcing costs consist of the inventory carrying, backorder and subcontracting costs. Full-size image (18 K) Fig. 3. Hypothetical layout with nearly same distance between each pair of machines and cell locations. Figure options The rest of this paper is organized as follows. The literature related to the integrated CMS and PP is reviewed in Section 2. A new integrated model of the CMS and PP is proposed in Section 3. The performance of the proposed model is verified in Section 4, and the conclusion is given in Section 5

In this paper, a novel mathematical and integrated model of the multi-period cell formation and production planning (PP) in dynamic cellular manufacturing system (DCMS) has been introduced focusing on the operational aspects of the cell formation. This model is extended based on a basis DCMS model proposed in the literature (Safaei et al., 2008). Our proposed model minimizes the constant and variable costs of machine, inter and intra-cell material handling costs by assuming the operation sequence, machine relocation costs, and PP costs including inventory, backorder, and partial subcontracting costs. The main constraints are the machine time-capacity and maximal cell size. This model is able to determine the optimal cell configuration and production plan for each part type at each period over the planning horizon. The outstanding advantages of the proposed model are as follows: inter and intra-cell material handling by assuming the operation sequence, and also partial subcontracting by assuming a lead time for ordered items. The performance of the model is verified by two numerical examples. The obtained results show that the outsourcing requirements, such as inventory, backorder and subcontracting, can significantly affect the cell configuration during the horizon planning by frequent relocating/adding or removing of the machines. This is because that the outsourcing provides the condition in which a large portion of the total demand of the horizon may be satisfied by only a few numbers of periods while we have no production in other periods. In general, the obtained results show that the outsourcing can lead to a vacillation or convulsive behaviour in the cell reconfiguration in the DCMS. Obtaining an exact solution for such a hard problem in a reasonable time is computationally intractable. Thus, it is necessary to use a heuristic or meta-heuristic approach to solve the proposed model for real-sized problems. Most of the related studies use a multi-stage heuristic approach to first form the cells and then to plan production aspect of the manufacturing system and vice versa. However, the basis DCMS model is itself complex enough to be solved optimally in a reasonable time. Thus, computational intelligent methods are proper alternatives to solve the proposed problem.