A Two-Warehouse Inventory Model with Quantity Discounts and Maintenance Actions under Imperfect Production Processes

Many earlier studies dealing with the two-warehouse inventory model assumed that the direct cost of the product was irrelevant and that production processes are perfect and stationary. However, in the real world, the purchase cost is some function of the quantity purchased and the production processes may deteriorate and thus defective items will occur. This paper, therefore, aims at developing a new inventory model under an imperfect production process. Three considerations are included in this new model: (1) The supplier may offer quantity discounts to stimulate the retailer into ordering greater lot sizes; (2) The maintenance actions are employed to restore the production process back to the in-control state when the process is out-of-control; (3) A two-warehouse policy is adopted to hold a large amount of stock when a single warehouse would not be sufficient. The unique optimal lot size property and the candidate optimal solution boundaries are derived. An efficient algorithm is developed to help the manager in accurately and quickly determining the order policy. Some numerical examples are given to illustrate the proposed model and algorithm. Some interesting behaviors are also observed.