A two-stage heuristic approach for a multi-item inventory system with limited budgetary resource and all-units discount

Abstract

Abstract This paper deals with a multi-item inventory system with a discrete stochastic demand stream under continuous review in which a limited resource and all-units quantity discount in purchasing are available. The resource is sharable and price-dependent which can be investments or budgetary. Most existing models focus on the resource restriction as a hard constraint, which is not always the common case since in some inventory systems resource shortage could be provided by renting extra resource and incurs the resource shortage cost to the system. In this case, as one of the recent extensions of (r, Q) inventory models, the resource constraint is treated as a soft constraint. By considering the discount opportunity besides the soft price-dependent resource constraint, the resource shortage cost will be dependent directly on quantity discount parameters. So, in the multi-item case the discounted price of each item is involved in determining other optimal policies. The problem is formulated as an integer nonlinear programming model. A heuristic method is presented to solve the model. According to this method, during the stages of the algorithm, the problem is separated into sub-problems which are solved by an exact method. A local search is used to improve the solutions during the algorithm procedure. In order to evaluate the efficiency of the solution approach, a lower bound on the minimum cost of the problem is proposed. Numerical evaluations based on the lower bound show that the proposed method with an average relative error equal to 3.91% performs well.