۱- Introduction

۲- Problem description

۳- Heuristic algorithm

۴- Computational results

۵- Concluding remarks

References

Abstract

We consider a two-level supply chain that consists of multiple suppliers and a manufacturing plant. Each supplier produces semi-finished products needed for several types of (finished) products and delivers the semi-finished products to the manufacturing plant, where the products are produced to satisfy dynamic demands. In each supplier, production times of semi-finished products for different product types may be different, but processing should be started at the same time if they are in the same production batch although they may be completed at different times. The problem considered here is to determine production plans of the suppliers with the objective of minimizing the sum of raw material purchasing costs, production costs, setup costs of the suppliers, transportation costs, and costs for outsourcing semi-finished products. We present a mixed integer programming model and develop a two-step heuristic algorithm in which the problem is decomposed into two subproblems and these subproblems are solved sequentially. We also present solution-improvement procedures. Performance of the algorithm is evaluated by comparing its solutions with optimal solutions and good solutions obtained from a simulated annealing algorithm developed in this study, and results are reported.

Introduction

In this paper, we consider a production planning problem in a twolevel supply chain that consists of multiple suppliers and a manufacturing plant. Each supplier has a single processing line where can produce all types of semi-finished products to be used to produce finished products at the manufacturing plant. Before starting production at each supplier, a setup operation is needed. After being produced by the suppliers, the semi-finished products are delivered to the manufacturing plant, where finished products are produced. In this two-level supply chain, the decision maker makes a production plan to satisfy the demand for the finished products in each period. That is, decision maker determines suppliers to be used, quantities of each type of semifinished products produced in each selected supplier, and outsourcing quantities of semi-finished products (if necessary) in each period with the objective of minimizing total costs associated with the supply chain. This paper focuses on a case in which several semi-finished product types are produced through similar processes at the suppliers. Although the processes are not exactly the same, semi-finished products are produced in almost the same general processes except for the production times, which may be different for different types of semifinished products. In this paper, it is assumed that processing of these semi-finished products should be started at the same time if those semifinished products are to be produced simultaneously (in a batch) at some point of time. In other words, different semi-finished product types should be started at the same time, but they are completed at different times depending on their production times. Note that products with such characteristic are called production-time-dependent products. Examples of systems producing such products can be found in the poultry farming industry. There are a few types of chickens (semi-finished product types) produced in poultry farms and the chickens are distinguished by the weights. The weights of the chickens usually depend on the raising time (production time) in the farms. Therefore, the (semi-finished) product types are distinguished by the production time. We can also find the production-time-dependent products in other livestock industries such as hog-raising and cattle-raising industries. If we expand this problem into other areas, semiconductor manufacturing and steel industry have similar characteristics. In CMP process in semiconductor manufacturing, the depth of polishing depends on its processing time.