A New Replenishment Policy Based on Mathematical Modeling of Inventory and Transportation Costs with Probabilistic Demand Image

The implementation of supply chain has to reduce the total cost of system, but generally each component of a supply chain tries to find the best policy for its company and consequently tries to find a local optimum. Knowing that the sum of local optimum cannot constitute the global optimum, it is necessary to consider all costs of system simultaneously to find the best replenishment policy for all the components of a supply chain. This paper presents a new approach based on mathematical modeling of total costs of system (transportation and inventory costs) in a supply network (multi-echelon multi-product structure). Moreover, the demand in real case is often probabilistic and it has to be taken into account. This reality justifies the necessity to consider all costs, generated by all products, in all links and all echelons. The first part of this paper presents an overall view of the approach adopted. Then, the mathematical model of the logistic costs is developed. In the next part, a new replenishment policy based on joint optimization is detailed. Finally, the numerical experimentation and an example illustrate proposed approach.