Scheduling N Products On A Single Facility With Back-Ordering And Eixed Terminal Inventory

AbstractThe problem of scheduling A' products oil a single facility has gained widespread attention. The model suggests that each product is demanded at a fixed rate, rj, per period over a planning horizon of length T periods and the initial inventory, ijo for product ji, as well as its terminal inventory, IJT, are both fixed. When the facility is assigned to product j , it will produce a prespecified lot of size pj (>rj) units per period. The primary objective of this paper is to identify the schedule that minimizes the total cost of inventory holding and back-ordering; therefore, it is desired to schedule the N products on the single facility optimally starting with ijQ and ending with ijr. In this paper theoretical results are proved which lead to the development of dominance relations between the products and the construction of a strong lower bound on the optimal cost. Both the dominance relations and the lovrer bound provide the basis for an implicit search procedure that seeks to generate the optim...