Determining the optimal routes in the multi-product multi-site joint delivery problem

When planning the delivery in a supply chain, it is necessary to prepare a schedule of deliveries for different products at different sites during the planning horizon while satisfying demand and respecting material and financial resources constraints. In addition, to manage a supply chain, we need to solve problems such as the JRP (Joint Replenishment Problem) taking into account the problem of organizing delivery tours as in the IRP (Inventory Routing Problem) model. In this study, the conventional assumption of periodic deliveries for each pair (product, website) was lifted to better utilize the degrees of freedom in the delivery program over a common cycle used in the optimization as a planning horizon. Assuming that the planning horizon was previously determined, the proposed formulation for the joint delivery model (JDP) takes the form of a multi-site version of the classical multi-product IRP problem, but with major and minor set-up costs and with consideration of an indirect grouping strategy for deliveries for each This is a mixed integer linear programming problem (MILP) having real variables and binary variables. As such, it is known as a NP-hard problem.