Evaluation of logistics related policies between two different levels of the supply chain network—a case study

This paper will discuss the case study conducted to evaluate a logistics related policy (time between successive collections of commodities) that optimizes the total shifting cost and minimizes the transportation cost by considering the problem as a Dynamic Multi Capacitated Vehicle Routing Problem (DMCVRP). The DMCVRP is formulated and solved for various policies using Mixed Integer Linear Programming (MILP) with an objective to minimize the cost associated with the distance traveled by the vehicles and the cost associated with unutilized capacity in the vehicles. Finally, we approximate the total shifting cost as a single variable function of transportation, inspection and inventory carrying cost, which possesses continuous derivatives at every order with the single variable as time between successive collections and derive the necessary and sufficient conditions in locating the optimum (minimum) total shifting cost.