Managing capital intensive rental businesses

Sergei V Savin, University of Pennsylvania


In the proposed thesis, we analyze a business problem faced by rental companies serving a heterogeneous set of customers under conditions of stochastic demand for rentals and uncertain rental durations. Customer classes may differ in the volume of rental requests, durations of rentals, rental fees paid, service level expectations. We propose a modeling framework that incorporates a set of interacting managerial decisions including rental capacity adjustments, choice of pricing policies, and rationing of rental capacity. The proposed framework considers the multi-period decision environment in which the rental prices as well as the service quality constraints are set in the beginning of planning horizon. At the start of each period rental capacity can be adjusted, while within the period capacity rationing between competing customer classes may be used to improve generated revenues. Within each planning period, for a given size of the service fleet, rental system is modeled as an M/G/c/c queue. For the case of 2 customer classes, we derive structural properties of the optimal capacity rationing policies. In particular, we establish conditions under which a particular customer class is preferred, so that service requests from customers belonging to such class are always honored as long as there is service capacity available. We also derive sufficient conditions for the optimality of a complete sharing capacity rationing policy often observed in practice. As an alternative to often complex optimal capacity rationing policies, we analyze aggregate threshold, mutiple threshold, and fleet partitioning heuristic policies. We propose simple and effective aggregate threshold heuristic based on the fluid approximation to the original stochastic control problem. In a multiperiod decision environment, we analyze the effect of using tactical admission control policies on the structure of the strategic fleet sizing decisions. In particular, we show that simple “3-region” structure of the optimal fleet sizing decisions corresponding to the complete sharing capacity rationing policy is preserved by proposed aggregate threshold heuristic. Finally, we use a deterministic approximation to the original problem to solve the combined contract selection-capacity sizing-capacity rationing problem. In particular, we establish that under this approximation it is always optimal to use complete sharing rationing policy. For the general stochastic case of the problem we propose an efficient solution algorithm of the conjugate gradient type. Proposed algorithm iterates between the capacity sizing-capacity rationing and contract selection subproblems. We provide a solution to the contract selection subproblem in the case when complete sharing capacity rationing is used.

Subject Area

Operations research|Management

Recommended Citation

Savin, Sergei V, "Managing capital intensive rental businesses" (2001). Dissertations available from ProQuest. AAI3003691.