عنوان مقاله [English]
One of the major responsibilities of the industrial units is inventory planning and control. Inventory system design has an important effect on cost reduction of firms in order to determine optimal or near-optimal value of order quantity and reorder point. Inventory systems have constraints as many other systems do. While the constraints make a model more practical, they increase the complexity of the model and limit the solution approaches of the model. This paper deals with an inventory system under continuous review with multiple items and budget constraint. This budget is consumed to purchase items. The budget constraint is considered as a soft constraint that is included in the objective function. If the budget consumption becomes greater than the available budget, resource shortage cost is incurred. Customer demand has discrete Poisson distribution and the ordered quantities are received after a fixed lead time. The purpose of this paper is to determine the order quantity and reorder point, such that the total system cost, including ordering cost, holding cost, penalty cost for customer backorders, and resource shortage cost, is minimized. A heuristic method has been presented to determine (r,Q) policy. This method consists of two stages. In the first stage, the relaxed version of the problem is solved; if the obtained solution does not meet the budget constraint, the inventory position of each item is reduced from an upper bound of optimal inventory position for the relaxed version of the problem. If the optimal inventory position is not found in the first stage, a local search is used in the second stage to obtain a near-optimal solution. The presented solution approach is compared with other existing methods via experimental tests. Numerical results demonstrate that the presented method reduces total cost more than othermethods.