The research considers the problem of determining vehicle routes and replenishment intervals in the system composed of two depots supplying an inventory item to multiple retailers. Each transportation vehicle leaving a depot can end its route at any depot and, therefore, the vehicle route can be either close loop or open loop. However, the number of vehicles leaving any depot must equal to the number of vehicles arriving the depot. The objective is to minimize the sum of inventory holding cost, delivery setup cost, transportation cost, and vehicle owning cost. A genetic algorithm is developed in order to determine a good solution to the problem when there exists at most one delivery route for each depot. The chromosome representation is designed in such a way that, after decoding, a chromosome can represent both types of vehicle route. To determine the optimal replenishment interval, the concept of economic order interval with joint replenishment is inserted in the genetic algorithm structure. Two numerical experiments are conducted for the performance evaluation. The first experiment is to compare the genetic algorithm solution with the optimal solution obtained from the enumerative search. The result shows that the proposed method can provide optimal solution for 27 out of 30 randomly generated problems. The maximum percentage deviation is 1.79 percent. The second experiment is to compare the genetic algorithm solution with the solution yielded from a three-step heuristic at different levels of number of retailers and vehicle owning costs. According to the experimental result, the proposed method can provide better solution for all 270 randomly generated problems with the average percentage deviation of 10.33 percent. As the number of retailers and the vehicle owning cost increase, the open vehicle route tends to yield better solution than the close vehicle route.
Keywords: Inventory Routing Problem, Open Vehicle Routing, Vehicle Sharing, Genetic Algorithm
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