یکپارچگی تولید و مدل موجودی برای کل زنجیره تامین تولید شامل لجستیک معکوس با دوره افق محدود

This paper proposes a model and solution method for coordinating integrated production and inventory cycles in a whole manufacturing supply chain involving reverse logistics for multiple items with finite horizon period. A whole manufacturing supply chain involving reverse logistic consists of tier-2 suppliers supplying raw materials to tier-1 suppliers, tier-1 suppliers producing parts, a manufacturer which manufactures and assembles parts from tier-1 suppliers into finished products, distributors distributing finished products to retailers, retailers selling products to end customers and a third party which collects the used finished products from end customers, dissembles collected products into parts, and feed the parts back to the supply chain. In this system, we consider a finite horizon period. A mathematical model for representing the behaviors of the system is developed. Solution methods based on decentralized and a combination of decentralized and centralized decision making process, referred to as the semi-centralized decision making process, are proposed to solve the model while the centralized decision making process is solved by a mixed integer nonlinear programming method. A numerical example is used to demonstrate the model and the solutions based on the three types of the coordination.

In today's competitive market, the collaboration between players in the supply chain does not only consist of two-level or three-level supply chain. In addition, in a real problem the supply chain does not manage just a single product. It may consist of more than three-level supply chain and manages more than just a single product. One type of the complex supply chain is named as a whole manufacturing supply chain involving reverse logistics consisting of tier-2 suppliers which produce raw materials to be supplied to tier-1 suppliers, tier-1 suppliers which produce parts for a manufacturer, the manufacturer which manufactures and assembles parts into finished products, distributors which deliver finished products to retailers, retailers selling products to end customers and a third party which collects used finished products and feeds reusable parts to the manufacturer. Because there are many players having their own objectives whilst participating in this chain, a coordination mechanism is needed to manage the effective and efficient flow of raw materials, parts, finished products and returned used products among them ([16] and [17]). Integrating production and inventory models of players in a supply chain is therefore needed to achieve the chain objectives with a coordinated decision making process. Coordinating in multi-level production and inventory has been addressed well, not limited to, in Chen and Chen [4], Chung et al. [8], Ganeshan [12], Gou et al. [13], Jaber and Goyal [16], Khouja [17], Munson and Rosenblatt [21], Lee [19], Sarmah et al. [23], Ben-Daya et al. [1], Akanle and Zhang [9], Savaskan [25], and Wang and Hsu [27]. Based on a literature review which has been carried out, researches only considered parts of the whole system studied. Chen and Chen [4] developed joint replenishment and channel coordination between a manufacturer and retailers. For three-level supply chains, Jaber and Goyal [16], Khouja [17] and Munson and Rosenblatt [21] developed three-level supply chain with coordination. Rieksts and Ventura [22] developed two-level inventory model considering two modes of transportation system which are truckload and less than truckload. However, these papers assume that there is no returning of used finished products from end customers. Concerning returned used products, many papers have also been published (See Srivastava [24]). Choi et al. [5] developed ordering and recovery policy for reusable items. El Saadany and Jaber [11] developed remanufacturing model for subassemblies of used products which are managed differently. Chung et al. [8] developed a closed-loop supply chain inventory system with remanufacturing and Teunter [26] developed EOQ model for recoverable item inventory system similarly with work in Koh et al. [18]. These papers considered only a part of the supply chain such as one player in Choi et al. [5] and a two-level supply chain in Chung et al. [8]. Chung and Wee [6] developed integrated production inventory model for deteriorating item with short life-cycles between a supplier and a buyer considering green product design and remanufacturing with re-usage concept whilst Wee et al. [28] developed vendor managed inventory strategy between one supplier and one buyer for deteriorating product and conducted life cycle cost and benefits analysis. Chung and Wee [7] investigated the impact of green product design, deteriorating factor, and information technology application investment on business process with remanufacturing. Later, Mitra [20] developed a two level supply chain with returns considering both deterministic and stochastic demand and return rate. When constraints of some or all players are considered, few researches had been carried out. Haksever and Moussourakis [14] built a model for optimizing multi-products inventory system with multiple resources constraints. Ishii and Imori [15] developed production ordering system for a two-items (products), two-stages supply chain with production capacity constraints. Both works have a single player and single level (just in the manufacturer). This paper, therefore, proposes an integrated production and inventory control model in a whole manufacturing supply chain system involving reverse logistics for multiple products, which extends works in Chen and Chen [4] and Jaber and Goyal [16]. The system consists of multiple raw materials suppliers, multiple parts suppliers, a manufacturer, multiple distributors and multiple retailers. Due to limited production capacity of each supplier, it is possible for each type of parts and raw materials to be supplied by more than one supplier. This paper considers reuse option for collecting used finished products from end customers by a third party returning collected parts to a manufacturer to be used into new finished products. This paper also considers the finite horizon period as it is relevant to the real problem. The model developed in this paper can be generalized as integrated production inventory model in multi-level supply chain. The rest of this paper is organized as follows. Section 2 provides an illustration of the system studied, lists the notations, describes the coordinations used, the modeling of the cost functions and constraints and the solution methods proposed for solving the model. In Section 3, a numerical example is used to demonstrate the real problem and some results of analysis are discussed for all types of coordinated decision-making processes. Finally, the paper is summarized and concluded in the Section 4.

This paper makes a contribution to the areas of coordinating production and inventory model in multi-level supply chain by proposing a model and solution methods for determining integrated production and inventory cycles for multiple raw materials, parts, and finished products in a whole manufacturing supply chain involving reverse logistics which consists of multiple tier-2 suppliers, multiple tier-1 suppliers, a manufacturer, multiple distributors, multiple retailers and a third party collecting the used finished products from end customers to be returned to the system for reuse. This paper considers a finite horizon period in the model. A mathematical model with a finite horizon period for the system, and solution methods based on decentralized and centralized decision making process, were developed. We have proposed the combination of decentralized and centralized decision making process as an alternative solution method. A numerical example is provided to demonstrate the model. Some analysis of the computational results of the example have been reported regarding the comparison of three types of coordination, between infinite and finite horizon period and between different lengths of horizon period. The centralized decision making process is the best solution for all types of the coordination. However, because this type of coordination has limitations in practice, we suggest decentralized and semi-centralized methods for solving real problems. We also suggest some compensation schemes to compensate for the disadvantages experienced by some players when applying this coordination in the system. As the customers demand in this model is assumed as constant/average rate, we suggest that this model can be applied to real system with small variation of the demand. If there is bigger variation of the demand, this model can still be used in the real cases by adding safety stock to retailers. The main limiting factors in this paper are the basic assumption of a common cycle time and the use of different production facilities in producing different types of finished products, parts and raw materials. The future researches will be carried out to eliminate these limitations.