Optimal Resource Allocation Between Spot and Package Demands

This paper deals with the problem of allocating fixed resources between two types of demands; (a) spot demand; and (b) package (subscription) demand—demand that is satisfied by selling usage rights over a prespecified time period prior to actual consumption. In Model 1, a probabilistic spot demand for a single resource, stationary over time, is assumed together with externally determined spot and package pricing. It is shown that the optimal (profit maximizing) policy is to sell all the packages in the first period and the optimal number of packages to offer is derived. Model 1 is extended to the case when the package offers rights to any one of a number M of resources at a given time; similar conclusions are obtained. In Model 2, package price is considered to be a decision variable. It is shown that the optimal price should be monotonically nondecreasing over time, implying that the number of packages offered for sale each period will not increase over time. Finally, managerial uses of the proposed models for entertainment, leisure and tourist services are reviewed.