Modeling and Analyzing Incremental Quantity Discounts in Transportation Costs for a Joint Economic Lot Sizing Problem

Joint economic lot sizing (JELS) addresses integrated inventory models in a supply chain. Most of the studies in this field either do not consider the role of the transportation cost in their analysis or consider transportation cost as a fixed part of the ordering costs. In this article, a model is developed to analyze an incremental quantity discount in transportation cost. Appropriate equations are derived to compute the costs related to the inventory systems in the buyer and vendor sites. Then, a procedure including five steps is proposed to optimize the model and determine the values of the decision variables. To analyze the performance of the incremental discount, the JELS problem is studied in two other states of transportation costs.  These states include fixed transportation cost and all-unit quantity discount.  Moreover, some numerical analyses are carried out to show the impact of transportation costs and inventory-related parameters on the system performance. According to the results of the sensitivity analyses, it is observed that all-unit quantity discount leads to a better performance of the system in comparison with the incremental quantity discount.