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Tuesday 16 Nov 2021Capacity Management for A Leasing System with Different Equipment and Batch Demands

Wendy Jiao - University of Exeter - Business School

Zoom 15:30-16:30

This work studies the admission and capacity allocation problem for a leasing system with two types of equipment and three kinds of batch demands: elementary-specified, premium-specified, and unspecified demands. The demands arrive following mutually independent Poisson distributions and their rental durations follow a negative exponential distribution. The lessor can admit partially the specified demands with the required type of equipment, and admit partially the unspecified demands with any type of equipment. The objective is to maximize the expected discounted revenue. We formulate this problem as a Markov Decision Process (MDP), prove the antimultimodularity of the value function and characterize the structure of the optimal policy. We show that the optimal policy has a simple structure and is characterized by state-dependent rationing and priority thresholds. Moreover, a solution algorithm is proposed to calculate the optimal policy. We study the impacts of the system state on the optimal policy and find that the optimal policy has limited sensitivity to the system state. Numerical studies are conducted to compare the performances of the optimal policy and two heuristic methods and to get some managerial insights by analysis. Several extensions are discussed further.

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