As order quantity is increased, the ordering cost per item will be cheaper due to saving of transportation and material handling costs. In this paper, two realistic assumptions such as quantity discount and budget limit are considered. Quantity discount means that all units in the order will be discounted according to the predetermined order levels. Budget limit represents that the costs for inventory investments are bounded. This paper develops a Lagrangian relaxation approach for a continuous review inventory model with a budget constraint and quantity discounts. Computational results indicate that the proposed approach provides a good solution. Sensitivity analysis is done to get some insights on budget limit and quantity discount. As budget limit or the amount of discount according to order quantity is increased, order quantity is increased, whereas reorder point is not always increased.

The modular assembly system can make it possible for the variety of products to be assembled in a short lead time. In this system, necessary components are assembled to optional components tailor to customers’ orders. Budget for inventory investments composed of inventory and purchasing costs are practically limited and the purchasing cost is often paid when an order is arrived. Service cost is assumed to be proportional to service level and it is included in budget constraint. We develop a heuristic procedure to find a good solution for a continuous review inventory system of the modular assembly system with a budget constraint. A regression analysis using a quadratic function based on the exponential function is applied to the cumulative density function of a normal distribution. With the regression result, an efficient heuristics is proposed by using an approximation for some complex functions that are composed of exponential functions only. A simple problem is introduced to illustrate the proposed heuristics.