Modelling a Multi-Period Joint Replenishment Problem with Quantity Discounts - Haidula, Johannes (2020)
In a classic Joint Replenishment problem, a retailer faces the problem of ordering multiple products from a single supply source. The retailers are sometimes offered discounts, but these discount conditions might be of a different criterion of which they have to select one. Although there has been substantial research undertaken that developed unique solution approaches in the literature using techniques such as metaheuristics, constructive heuristic, and genetic algorithms, it is essential to cement the utilisation of quantitative decision models for managerial insights. Moreover, joint replenishment with quantity discount and complicating constraints of full truckload under exact optimisation has not been dealt with in literature. This study developed a non-linear integer programming model that groups items into optimal groups to exploit full discount. Firstly, a single item algorithm that gives the optimum purchasing policy based on Economic Order Quantity (EOQ) is developed. The results show that the ordering periods of items are not synchronised that results in more orders. A non-linear integer programming is then developed focusing on one product family and giving discount groups. Additional functions are also added to enable the model to accommodate different family groups as well as discount level. A computational experimental test was conducted to determine the performance of the policy under different input parameter like inventory size, setup cost and holding cost. Results show excellent performance that demonstrates the practicality of the designed model in solving complex purchasing decisions. This model should therefore be of value to buyers in their purchasing decision process. Keywords: Joint Replenishment Problem, Full truckload, Quantity Discount, Grouping, Multi-Period