Academic journal article Iranian Journal of Management Studies

# A New Mathematical Model in Cell Formation Problem with Consideration of Inventory and Backorder: Genetic and Particle Swarm Optimization Algorithms

Academic journal article Iranian Journal of Management Studies

# A New Mathematical Model in Cell Formation Problem with Consideration of Inventory and Backorder: Genetic and Particle Swarm Optimization Algorithms

## Article excerpt

(ProQuest: ... denotes formulae omitted.)

Introduction

Due to today's competitive conditions, companies should produce various types of products in small lot sizes. Group Technology (GT) is a manufacturing philosophy trying to produce efficiently by taking advantage of similarity of manufacturing processes. Cellular Manufacturing System (CMS) is a creative manufacturing strategy based on the GT concept. This method is employed to increase flexibility and efficiency of the manufacturing system, simultaneously. The advantages of using CMS include reduction of setup time, reduction of work-in-process and inventory, material movement reduction, improvement of quality, reduction in production lead time, and better supervisory control.

Most production environments have to deal with variations in the operating parameters along the planning horizon, such as in the product demand. Manufacturers are also confronted with constraints, conditions, and costs, such as facility capacity limits (i.e., time), machine costs (i.e., purchase and maintenance), inventory holdings, backorder, and subcontracting. In this condition, the act of managing and controlling resources and balancing them among subsequent periods to minimize cost is known as Production Planning (PP). The main goal of production planning is to minimize the costs of production over the planning horizon, which include fixed and variable production costs, inventory, shortage, and subcontracting costs. The main restraints of the production planning problem include: (1) The inventory balance at each given time period, which is moderated by the inventory or shortage from a prior period, production, subcontracting, and demand; and (2) capacity limits.

Majority of recent studies consider CMS and PP sequentially or independently (Chattopadhyay et al., 2013). However, considering the CMS and PP simultaneously is critical for manufacturers in real competitive production environments (Sakhaii et al., 2016). Variations in the production volume and mixture of products and introduction of new products lead to the necessity of integration of the CMS and PP (Hassan Zadeh et al., 2014). In a CMS, the sequence of operations has a critical effect on material handling and the inter-cell and intra-cell movement costs. As an example, consider Figure 1 which demonstrates the effect of the operation succession on the material movements. Operations 1 and 3 of part 10 (P10) are processed on Machine 5 (M5) in Cell 1, and Operation 2 of P10 is processed on Machine 7 (M7) in Cell 2. Therefore, the processing route of Part 10 includes two inter-cell movements. Processing Part 4 in Cell 2 needs two intra-cell movements. Therefore, the design of the production system depends on the operational planning of the resources (Hassan Zadeh et al., 2014).

This paper addresses the Cell Formation Problem (CFP) which is extended by considering aspects of production planning such as inventory, backorder, and subcontracting. The proposed model determines the optimal inter-cell and intra-cell formation layout and the production planning simultaneously. The rest of this paper is organized as follows. A review of the CFP literature is provided in Section 2. Problem formulation is presented in Section 3. Section 4 describes the proposed solution approaches. The parameters of the algorithms are tuned in Section 5. Verification of the proposed model and the performance of the developed solution algorithms are presented in Section 6. Finally, the concluding remarks and directions for future research are provided in Section 7.

Literature Review

In this section, the literature related to cell formation problem is reviewed. Defersha and Chen (2006) addressed a comprehensive model and proposed a two-stage Genetic Algorithm (GA) to form the manufacturing cells. They attempt to minimize machine related costs, inter-cell material movement costs, subcontracting costs, and system reconfiguration costs. …

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