Single Item Lot-sizing Problem With Outsourcing

Manufacturing is mainstay industry of a country. Its developing level is the standard which reflect comprehensive national power of a country. Recent years, science and technology have developed rapidly. Rapidly developing science and technology speed up the process of global economy integration. The market scale is expanding continually. The competition which manufacturing is in face of become more and more fierce. It is difficult for enterprise to satisfy the rapidly changing market demand without external resources. So enterprises seek cooperation with others. By combining outside resources, enterprises can strengthen their adaptability to market environment. As an efficient tool for combining inside and outside resources, outsourcing had been implemented by more and more business manages.Lot-sizing problem is one of core problems of Production /purchase planning. The object of studying lot-sizing problem is to optimize problem in middle-term or short-term production planning. The aim of studying is to make a production/purchase planning in limited horizon, with the varied constraints of production, which can minimize the overall cost of the production. Lot-sizing problem has been studied for several dozens years. However, with those new productions and management pattern appearing, some new theory of production planning come forth. On the basis of new studying result in lot-sizing problem from home and abroad, single-item problem with dynamic program is studied in this paper.There are two basic lot-sizing models investigated in this paper. (1) For uncapacitated single-item lot-sizing problem with outsourcing, we consider the case of allowing outsourcing and backlogging. Considering that there are so many durable products in real life, we built deteriorating item lot-sizing model with outsourcing and backlogging and derive an O(T~2) dynamic program. (2) For capacitated single-item lot-sizing problem, also we consider the case of allowing outsourcing. Two cases are been considered in this model. In one case, unit production cost and unit inventory cost are constant. We derive an O ( TN~2 ) dynamic program. In the other case, unit production cost and unit inventory cost are time vary. We search for feasible subplans firstly, then computer their costs. And now lot-sizing problem is transferred into shortest path problem. We can solve the problem with ready-made arithmetic.