رویکرد جدید نسبت به شکل گیری سلول های یکپارچه و تعیین اندازه دسته تولید موجودی در سیستم تولید سلولی غیر قابل اعتماد

This paper presents a comprehensive mathematical model for integrated cell formation and inventory lot sizing problem. The proposed model seeks to minimize cell formation costs as well as the costs associated with production, while dynamic conditions, alternative routings, machine capacity limitation, operations sequences, cell size constraints, process deterioration, and machine breakdowns are also taken into account. The total cost consists of machine procurement, cell reconfiguration, preventive and corrective repairs, material handling (intra-cell and inter-cell), machine operation, part subcontracting, finished and unfinished parts inventory cost, and defective parts replacement costs. With respect to the multiple products, multiple process plans for each product and multiple routing alternatives for each process plan which are assumed in the proposed model, the model is combinatorial. Moreover, unreliability conditions are considered, because moving from “in-control” state to “out-of-control” state (process deterioration) and machine breakdowns make the model more practical and applicable. To conquer the breakdowns, preventive and corrective actions are adopted. Finally, a Particle Swarm Optimization (PSO)-based meta-heuristic is developed to overcome NP-completeness of the proposed model.

In today’s global competitive environment, companies have to deliver low-cost, high quality products to cope with the challenges. Cellular manufacturing system (CMS) is an application of Group Technology (GT) which helps firms to achieve this goal. In spite of CMS, job shop and flow shop manufacturing systems are not able to respond all market requirements, thus CMS is applied as an alternative to overcome today ever growing issues. In designing a CMS, four major decisions are made; 1-cell formation: grouping parts with the closest features into part families, and subsequently, allocating machines to the formed cells, 2-group layout: determining layouts of cells themselves and machines within each cells (intra-cell and inter-cell layouts), 3-group scheduling: planning and managing cell operations, and 4-resource allocation: allocating resources, such as material, workforce and tools to the cells. Some advantages of CMS implementation include production efficiency and system flexibility improvements, simplified material flow, faster throughput, reduced setup times and costs, reduced work-in-process inventory level, reduced intercellular moves, lower cycle times, lower material-handling times and costs, lower product defect rates, lower machine idle times, smaller space requirements, etc. [1] and [2]. Additionally, many researches have been conducted to point out CMS disadvantages [3], [4], [5], [6] and [7], among which some can be noted: reduced flexibility compared to a job shop, lower level of machine utilization by dedicating machines to cells, and the effect of machine breakdowns on due date adherence. There are a few researches that considered main features of a CMS simultaneously. One of these features is production planning in CMSs [8] and [9] and the other is job sequencing and scheduling alternative process plans in such systems [10] and [11]. From another point of view, in most research articles, cell formation has been considered under static conditions in which cells are formed for a single-time period with known and constant product mix and demand. In contrast, in a more realistic dynamic situation, a multi-period planning horizon is considered, where the product mix and demand are different in different periods. This occurs in seasonally or monthly production contexts. As a result, the cell configuration in one period may not be optimal in another period, therefore the main focus is nowadays dedicated to dynamic cell formation models [12]. To address this problem, several authors have recently proposed models and solution procedures by considering dynamic cell reconfigurations over multiple time-periods [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23] and [24]. In the mentioned research articles, it is assumed that the demand is equal to production quantity, however, it might not be held for many circumstances and the demand is compensated from inventory or by subcontraction. Hence, production quantity should be calculated from production planning viewpoints and consequently, the calculated production quantities are critical for the cell sizes and number of required machines (cell capacity). Moreover, there is a relation between quantities of sub-assemblies and parts and the quantity of end products based up their Bill Of Materials (BOMs), therefore, product structures are also considered while production planning issues are integrated with cell formation. Thus, dynamic cell formation and production planning are correlative and should be addressed simultaneously [12]. In addition to the above-mentioned research facts, there is another important point which has been neglected. In past decades, it has been assumed that the production facilities work in a reliable state, however, it is not a realistic assumption. Due to technological innovations and scientific developments around the world, manufacturing infrastructure is also changing rapidly. Even though the production facilities are becoming sophisticated day by day, the modern facilities are not free from deterioration due to aging. As a result, machines shift from “in-control” state to “out-of-control” state frequently and machine breakdowns occur during planning horizon. Another related aspect to the considered problem in this paper is production planning and inventory lot sizing. Many researches have been widely conducted in different manufacturing production planning and inventory control problems. These instances developed various methods and models to solve these problems, which can be found in well-known textbooks of production engineering or manufacturing systems [25] and [26]. Lots of inventory control models from simple Economic Order Quantity (EOQ) to more complicated Material Requirements Planning (MRP), Kanban and CONstant Work-In-Process (CONWIP) models have been utilized in the relative literature. To review mathematical programming models on Kanban and MRP systems, readers are referred to Price et al. [27]. Also, as stated by Chakraborty et al. [28], the basic Economic Manufacturing Quantity (EMQ) model fits unreliable manufacturing systems well. Therefore, from theoretical and practical viewpoints, the study of EMQ problem for unreliable manufacturing systems is quite significant and meaningful [28]. In order to study system breakdowns, two parallel research paradigms have been carried out in unreliable production systems. In one stream, the production process is assumed to shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time where it starts producing non-conforming items. Then, the process continues to produce defective items until the end of the production run. Rosenblatt and Lee [29] and Porteus [30] carried out the seminal works in this direction. On the other hand, Groenevelt et al. [31] initiated another research direction to cope with the unreliable production processes. In this regard, corrective and preventive repair times are all assumed to follow arbitrary probability distributions. However, considerable amount of research has been done focusing separately on the issue of either process deterioration or machine breakdowns and less attention has been paid to the joint effect of these two issues on the optimal lot-sizing decisions. Boone et al. [32] considered an EMQ model to determine the optimal production run time to buffer against both the production of defective items and stoppage occurrence due to machine breakdowns. They derived some analytical results based on specific shifting and breakdown distributions. For simplicity, they assumed that upon a machine breakdown, the corrective repair cost is constant and the repair time is negligible. Nevertheless, in true sense, the assumption of negligible corrective repair time is somewhat restrictive. Another important feature to be noted is that if the machine does not break down during a production run, then preventive maintenance should be carried out before the start of the next production run in order to improve the system reliability or to return the machine to the ‘as good as new’ condition. In this paper, we consider the joint effects of process deterioration, machine breakdown, and repairs (corrective and preventive) on the optimal lot-sizing and dynamic cell formation decisions [28]. Based on the above discussion, a mathematical programming model is developed which is an extension of Defersha and Chen [12] model for an integrated dynamic cell formation and a multi-item, multi-level, capacitated lot-sizing problem, while process deterioration and machine breakdowns are also considered. Since the proposed model is an integrated one, computational complexities are burdensome. Therefore, it is impossible to solve the problem with optimization softwares in an acceptable time. To overcome the mentioned complexity, a developed meta-heuristic based on PSO is proposed with some modifications in comparison with the original PSO. The structure of this paper is follows. Next section describes the proposed mathematical model. Next, general PSO is reviewed in Section 3. Section 4 validates the proposed model through some numerical experiments. Finally, conclusions and future research directions are provided in Section 5.

his paper addressed the integrated cell formation and inventory lot sizing problem under the condition of dynamic planning and machine breakdown possibility. The integrated approach was adopted to analyze the cellular manufacturing system better, since different aspects of the manufacturing system are interrelated. The proposed model incorporates production planning lot sizing and dynamic cellular reconfiguration decisions. In this regard, the model seeks economic multi-item, multi-level lot sizes to produce, optimal subcontracted lot sizes and optimal numbers of machine types in each cell, whilst random process deterioration and machine breakdowns are considered as well. The proposed minimization objective function consists of machine procurement cost, reconfiguration (installing and removing) cost, process routes setup cost, operational cost, intra-cell moves, inter-cell moves, sub-contracting cost, holding cost, corrective repair cost, and preventive maintenance cost. On the other hand, the developed model is NP-complete and not solvable in an acceptable amount of time by means of any exact solution procedure and commercial optimization softwares. Therefore, a modified PSO meta-heuristic is developed to cope with computational complexity of the developed model. Finally, a numerical sample validates the feasibility and applicability of the developed model and the developed meta-heuristic. To continue the research direction outlined in this paper, two major directions are suggested. First, assessment of other intelligent search procedures, especially those hybrid ones with exact solution methodologies can be outstanding. As the second suggestion, the authors attract readers’ attention to different aspects of dynamic cellular manufacturing systems which have been studied in the literature during past years. Taking into account such aspects might lead to multi-objective mathematical models which not only model the practice better, but also provide challenging issues about solution methodologies required.