حل مشکل تشکیل سلول مجازی پویا توسط الگوریتم ازدحام ذرات بهینه سازی برنامه ریزی خطی تعبیه شده

In this paper, a new mathematical model for virtual cell formation problem (VCFP) under condition of multi-period planning horizon is presented where the product mix and demand are different in each period, but they are deterministic moreover production planning decisions are incorporated. The advantages of the proposed model are as follows: considering operation sequence, alternative process plans for part types, machine time-capacity, lot splitting, maximal virtual cell size and balanced workload for virtual cells. The objective of the model is to determine the optimal number of virtual cells while minimizing the manufacturing, material handling, subcontracting, inventory holding and internal production costs in each period. The proposed model for real-world instances cannot be solved optimally within a reasonable amount of computational time. Thus, an efficient linear programming embedded particle swarm optimization algorithm with a simulated annealing-based local search engine (LPEPSO-SA) is proposed for solving it. This model is solved optimally by the LINGO software then the optimal solution is compared with the proposed algorithm.

A competitive global market is compelling manufacturing firms to increase quality, customer responsibility and reduce production costs. Therefore, there have been major shifts in the design of manufacturing systems from traditional configurations such as job shop and flow shop to new configurations such as cellular manufacturing system (CMS). Cellular manufacturing (CM) is described as a manufacturing procedure which produces part families within a cell of machines serviced by operators and/or robots that function only within the cell. However, CMSs have some advantages such as reduction in lead times, work-in-process inventories, setup times, etc., there also exist some disadvantages. The performance of CMS, though, depends significantly on the stability of demand with respect to volume and mix. In the cell formation phase of CMS design, it is assumed that the demand pattern is relatively stable over a long product life cycle. It is well known that the performance advantages of CMS deteriorate rapidly with demand instability. Dynamic cellular manufacturing system (DCMS) is one of the methods which have been proposed for increasing the applicability of CMS in instable demand conditions. In DCMS, to match the demand of each period, configuration of cells can be changed from one period to another. To address this problem, several authors recently proposed models and solution procedures by considering dynamic cell reconfigurations over multiple time periods (e.g. Chen [4]; Mungwattana [13]; Tavakkoli-Moghaddam et al. [31]; Balakrishnan and Cheng [2]; Defersha and Chen [5]; Safaei et al. [22]). Reconfiguration of the cells to meet the unstable demand conditions, however, may be time-consuming and costly. Further, if these changes occur very frequently or machines are immobile, implementation of these systems is impossible [33]. In recent years, several researchers developed the new concept of virtual cellular manufacturing system (VCMS) in order to overcome the disadvantages of traditional CMSs. VCMS belongs to a family of modern production methods, which many industrial sectors have used beneficially. Retaining the functional layout, virtual manufacturing cells have been defined as “a temporary grouping of machines and jobs to realize the benefits normally associated with CM.” A virtual cell is a logical grouping of workstations that are not necessarily transposed into physical proximity. The logical grouping of jobs and machines is based on a predefined logic, and it is only resident in the production control system. In other words, Machines are not physically relocated into cells. Virtual manufacturing cells are created periodically, for instance every week or every month, depending on changes in volumes and mix of demand as new jobs accumulates during a planning period. This paper is focused on the design of VCMS where there are existing multiple part types. All part types have different processing routes. To process these part types, multiple machine types and workers are available. Every machine type has more than one individual machine. Every worker has more than an ability to work on multiple machines. Meanwhile, they have ability to train on some new machines. The machines are located in different locations in shop floor. The design decision that is the manufacturing cell formation and the production planning problems for dynamic virtual cellular manufacturing system (DVCMS) to minimize total sum of the manufacturing, material handling, subcontracting, inventory holding and internal production costs over the planning horizon. This paper, unlike previous research on design of VCMS, considers a dual resource constrained (DRC) system is considered. The cell formation problem is known to be an NP-hard optimization problem [31]. Therefore, effective approaches for the VCMS are necessary to find optimal or near optimal solutions in reasonable amount of time. This paper proposes a linear programming embedded particle swarm optimization algorithm with a simulated annealing based local search engine for the problem under consideration. The advantage of proposed approach is that part of the optimal solution is obtained through the particle swarm optimization algorithm, which is extended by Rezazadeh et al. [20] and the remaining solution is obtained by solving the LP sub-problem. The remainder of this paper is organized as follows: In Section 2, we review relevant literature on the VCMS. Section 3 presents the Problem description and mathematical formulation for the VCMS. In Section 4, we introduce a brief review of particle swarm optimization. Section 5 presents implementation of linear programming embedded particle swarm optimization is described. In Section 7, computational results are reported and in Section 6 the conclusion is given.

In this paper a new mathematical model of dynamic virtual cellular manufacturing system (DVCMS) was introduced. The advantages of the proposed model are as follows: simultaneous considering of dynamic system configuration, operation sequence, alternative process plans for part types, machine capacity, workload balancing, cell size limit and lot splitting. The objective is to minimize the total sum of the manufacturing cost, material handling cost, subcontracting cost, inventory holding cost and internal production cost over the planning horizon. The formulated mathematical is still open for considering other issues such as developing integrated method in designing manufacturing systems and supply chain networks, considering learning curves, product quality and the like which one suggested for future research. The proposed model is NP-hard and may not be solved to optimality or near optimality using of-the-shelf optimization packages. To this end, we developed an algorithm based on Particle swarm optimization algorithm so-called LPEPSO-SA to solve the proposed model. The performance of LPEPSO–SA is evaluated and compared to the performance of LINGO software by 20 test problems, with respect to the some of defined measures. The main difference between the classical methods such as branch and bound (B&B) and the proposed method (LPEPSO-SA) is generating a high quality solution in a negligible time. The obtained results show that the average gap between the quality of the solution found by proposed method and the best solution found by branch and bound (B&B) method is nearly 0.6%. Especially, as the size of problem increases, the superiority of the proposed method to B&B is more tangible. Thus the proposed method can be replaced by the traditional methods (B&B) in more difficult problems. However, the availability of feasible space is an open question in implementation of PSO.