We consider a multi-period vehicle scheduling problem (MPVSP) in a transportation system where a fleet of homogeneous vehicles delivers products of a single type from a central depot to multiple (N) retailers. The objective of the MPVSP is to minimize transportation costs for product delivery and inventory holding costs at retailers over the planning horizon. To solve an MPVSP of large size in a reasonable computation time, a two-phase heuristic algorithm is suggested based on a kth shortest path algorithm. In the first phase of the algorithm, the MPVSP is decomposed into N single-retailer problems by ignoring the number of vehicles available. The single-retailer problem is formulated as the shortest path problem and several good delivery schedules are generated for each retailer using the kth shortest path algorithm assuming the exact requirement policy is used in the system. In the exact requirement policy, replenishments occur only when the inventory level is zero. In the second phase, a set of vehicle schedules is selected from those generated in the first phase. The vehicle schedule selection problem is a generalized assignment problem and it is solved by a heuristic based on the kth shortest path algorithm. Computational experiments on randomly generated test problems showed that the suggested algorithm gave near optimal solutions in a reasonable amount of computation time.
