One of the major responsibilities in industry is inventory planning and control. Design of an inventory control system has an important effect on cost reduction of firms. This thesis is concerned with the (r, Q) inventory systems under continuous review with resource constraint and quantity discount. Demand is stochastic and discrete with Poisson arrivals. Replenishment goods are received after a constant lead time and the demands that cannot be satisfied immediately are backordered. Resource constraint is applied as a soft constraint and the corresponding shortage cost is considered in the cost function. Both single-item and multi-item systems are investigated. In single-item model both price-dependent and price-independent resource are considered. For the model with price-dependent resource, the per unit resource usage depends on unit purchasing price and discount pricing structure which increases complexity of the model and its solution approach. By considering the budget as a price-dependent resource, the single-item system is formulated under both all-units and incremental discounts. For both models, the properties of the cost function are investigated and the solution approaches based on a one-dimensional search procedure are proposed to finding the optimal (r, Q) policy. Then based on the cost function properties, an improved algorithm is developed for the single-item model under all-units discount. The multi-item system is investigated with soft budget constraint under all-units discount and formulated as an integer nonlinear programming model. A heuristic method has been 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.
