—This paper investigates the periodic delivery planning of vending machine problem (PDPVMP). The problem is a periodic vehicle routing problem (PVRP), which is also an extension of the typical vehicle routing problem (VRP). The considered PDPVMP contains multiple vending machines with periodic demands. For each vending machine, its replenishment frequency is either once per two days or twice per two days, i.e., once per day. In the PDPVMP, there are multiple vehicles to deliver goods for vending machines. The objective of the considered problem is to minimize the total length of routes for all vehicles during the time horizon such that all demands for vending machines are delivered. In this paper, based upon a new coding procedure, we apply an immune based algorithm to solve the PDPVMP. A case of Taoyuan county in Taiwan is considered and solved. Numerical results show that the studied immune algorithm can effectively solve this PDPVMP.
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