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In this section, we study the production planning problem in supply chain involving several enterprises whose final products are doors and windows made out of aluminum and compare two approaches to decision-making: decentralized versus centralized. The first enterprise is in charge of purchasing the raw materials and producing a partially competed product, whereas the second Patent Translation Service enterprise is in charge of designing the final form of the product which needs several adjustments before being released to the market. Some of those adjustments is the placement of several small parts, the addition of paint and the placement of glass pieces. We focus on investigating the way that the seasonal demand can differently affect the performances of our whole system, in the case, of both centralized and decentralized optimization. Our basic system consists of two production plants, for which we would like to obtain the optimal production plan, with two output stocks and two external production facilities called Subcontractor 1 and Subcontractor. We have also a finite horizon divided into periods. The production lead time of each plant is equal to one period (between the factories or the subcontractors). In Figure 1 we present our system which has the ability to produce a great variety of products. We will focus in one of these products, the one that appears to have the greatest demand in today’s market. This product is a type of door made from aluminum type A. We call this product DoorTypeA (DTA). The demand which has a seasonal pattern that hits its maximum value during spring and its minimum value during winter as well as the production capacities and all the certain costs that we will talk about in a later stage are real and correspond to the Greek enterprise ANALKO. finished components for F2 which produces the final product. The subcontractors have the ability to manufacture the entire product that is in demand or work on a specific part of the production, for example the placement of paint. Backorders are not allowed and all demand has to be satisfied without any delay. Each factory has a nominal production capacity and the role of the subcontractor is to provide additional external capacity if desirable. For simplicity, we assume that both initial stocks are zero and also that there is no demand for the final product during the first period. All factories have a large storage space which allows us to assume that the capacity of storing stocks is infinite.
