a model and extended algorithm for solving an inventory control problem with transportation costs

in this paper, a supplier-retailer transportation system is investigated as a two-echelon environment. there is a single location in each echelon; the unique supplier at the first echelon has to replenish the retailer's warehouse at the second echelon. by the way, the shortage situation should be avoided. for this situation, a model is provided based on the traditional eoq model. the inventory costs, ordering costs, transportation cost, etc. are considered in this model. multistage shipment during each ordering period with a specific number of vehicles is allowed in the proposed model. the model's decisions involved in managing the system include design decision (i.e., optimized number of required vehicles), as well as operation decision (i.e., optimized order quantity and number of trips and transportation stages). a solution algorithm is proposed for the proposed model and implemented with c#.net which is available and applicable on the website, namely www.pedramsahba.com. a numerical example and sensitivity analysis are presented for exposing the model and algorithm capability and then verifying and validating the model.