This paper is concerned with the single-item inventory system with resource constraint and all-units quantity discount under continuous review where demand is stochastic and discrete. In most actual inventory systems, the resource available for inventory management is limited and the system is able to confront the resource shortage by charging more costs. Considering the resource constraint as a soft constraint beside a quantity discount opportunity makes the model more practical. An optimization problem is formulated for finding an optimal (r, Q) policy for the problem in which the per unit resource usage depends on unit purchasing price. The properties of the cost function are investigated and then an algorithm based on a one-dimensional search procedure is proposed for finding an optimal (r, Q) policy which minimizes the expected system costs and converges to a global optimum. Based on the properties of the partially conditioned cost functions, the presented algorithm is modified such that its search path to optimal policy is changed. Experimental results show that the performance of the modified version of the presented algorithm is much better than the original algorithm in various environments of test problems. 
An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource