This paper addresses the single-item, dynamic lot-sizing problem for systems with remanufacturing and outsourcing. Therein, demand and return amounts are deterministic over a finite planning horizon. Demand may be satisfied by the manufacturing of new items, remanufactured items, or outsourcing, but it cannot be backlogged. The objective of this study is to determine the lot sizes for manufacturing, remanufacturing, and outsourcing that minimise the total cost, which consists of the holding costs for returns and manufactured/remanufactured products, setup costs, and outsourcing costs. The problems addressed in this paper are an extension of those addressed by Richter et al. (2000,and 2001), Teunter et al. (2006), and Aksen et al. (2003). In this paper, the separate setup costs scheme is considered, we propose a dynamic programming approach to derive the optimal solution in the case of large quantities of returned product. The complexity of this dynamic programming approach is O(T2), wherein T is the number of periods in the planning horizon.
Economic incentives, legal pressure, and societal pressure have motivated an increasing number of
companies to engage in the product recovery business, which refers to activities that aim to regain
materials and added value in used or returned products (Thorn and Rogerson 2002)[1]. A key component of product recovery is remanufacturing, which can be defined as the recovery of returned or used products and often involves disassembly, cleaning, testing, part replacement/repair and reassembly operations. The remanufactured items are as-good-as new items. Remanufacturing is of great social concern in many industries, such as single use cameras, machine tools, automobile engines, and computers. At the same and dismantling of cars, which have led to the generation of revenue. In ddition, Canon and Xerox remanufacture products that are worn out or obsolete, which is now more profitable than manufacturing new products (Stock et al. 2000)[2]. The Yuchai group is the first and largest conglomerate to remanufacture automobile engines in China. Remanufacturing development in the Yuchai group has not only secured significant economic benefits but has also resulted in good social and ecological benefits via the generation of 500 million Yuan in economic returns in 2006, reduced industrial pollutant emissions, and saved resources.
Our study is an extension of the problems that were addressed by Richter et al. (2000 and 2001)
[3][4]and Teunter et al. (2006)[5], which include single-item lot sizing with manufacturing but without
outsourcing. Our model differs from those that investigate lot sizing with outsourcing, because our model considers remanufacturing. This paper addresses the single-item, dynamic lot-sizing problem for systems with remanufacturing and outsourcing. Demand and return amounts are deterministic over a finite planning horizon. Demand may be satisfied by the manufacture of new items, remanufactured items, or outsourcing but cannot be backlogged. The objective of this study is to determine the lot sizes for manufacturing, remanufacturing, and outsourcing that minimise the total costs, which consist of the holding costs for returns and manufactured/remanufactured products, setup costs, and outsourcing costs. For the lot-sizing problem with remanufacturing, Van den Heuvel[6] has demonstrated that the problem becomes NP-hard when variable (re)manufacturing costs are included, even under the condition that the variable cost for manufacturing is larger than that for emanufacturing (which will typically hold if remanufacturing is economically motivated). Therefore, problems that include remanufacturing and outsourcing will be more complex, and only some specific problems can be solved in polynomial time. In this paper, t separate setup costs scheme is considered, we propose a dynamic programming approach to derive the optimal solution in the case of large quantities of returned product. The complexity of the proposed approach is O(T 2 , wherein T is the number of periods in the planning horizon. This paper contributes by: (1) developing an optimisation model in order to simultaneously address several critical issues in production planning, including single-item, multi-period, remanufacturing, and outsourcing and (2) establishing the characteristics of single-item lot sizing with remanufacturing and outsourcing and developing a polynomial algorithm for the model. The rest of this paper is organised as follows. In section 2, we develop an uncapacitated, production-planning model that includes remanufacturing and outsourcing for a multi-period, single-item problem with separate setup costs. In this case, there are dedicated production lines for manufacturing and remanufacturing. In section 3, we propose a dynamic programming approach to derive the optimal solution when there are large quantities of returned products. In section 4, we provide a short conclusion and suggest future research.
In conclusion, the cost of variable outsourcing was included into the framework of the lot-sizing
problem with remanufacturing (Richter et al. 2000 and 2001, and Teunter et al. 2006)[3][4][5]. In the
extended model, the demand and return amounts are deterministic over a finite planning horizon. The
demand may be satisfied by the manufacturing of new items, remanufactured items, or outsourcing. The backlogging of demand is prohibited. The objective is to determine the lot sizes for manufacturing,
remanufacturing, and outsourcing that minimise the total cost, which consists of holding costs (for
returns, manufactured products, and remanufactured products), setup costs, and outsourcing costs. The authors proposed a dynamic programming approach to derive an optimal solution with large quantities of a returned product. The complexity of this algorithm is . Possible future research consists of investigating models with limited inventory capacities and multiple items.
