Analyses of optimal policies for dynamic inventory and maintenance systems

Abstract

<p>This thesis represents research in the combined areas of inventory and maintenance. It analyzes two independent inventory and maintenance problems under dynamic systems: (i) a production and maintenance problem and (ii) a repairable-item inventory problem. For each problem, the thesis develops a new control model and proposes a simultaneous determination of optimal inventory and maintenance policies. The first part of the thesis examines a production process where the process performance deteriorates over time in the absence of preventive maintenance. First, it develops a new finite-time control model for optimal production and maintenance decisions by combining a dynamic maintenance model with a production control model. Second, it derives the necessary conditions for optimal production and maintenance controls using the maximum principle. Finally, it proposes two optimization algorithms for numerically solving the necessary conditions already derived. The second part of the thesis considers the repairable-item inventory problem, which may be faced at each period by the inventory manager responsible for determining the optimum quantities to purchase new serviceable units, to repair and to junk returned repairable units in order to satisfy random demand for serviceable units. First, it proposes an inventory model for repairables, incorporating several important features. The model includes a periodic review policy, random demand, lost sales for unsatisfied demand, set-up costs for ordering and repair, and a dynamic return process. Second, it employs a quite different solution methodology from what the previous research has used. The approach employed here is a 'Markov decision process (MDP)'. With this approach, the inventory problem is remodelled as a discrete-time Markov decision problem with two-dimensional state and three-dimensional decision spaces and then solved for finite-time planning horizon using the backward induction algorithm and for infinite-time planning horizon using the method of successive approximations. Finally, it introduces and utilizes two acceleration techniques, the error bounds approach and State Decomposition by Dimension (SDD), for speeding up the convergence of the computational methods described above.</p>