Optimum ordering policies for an equipment with random lead times

Abstract

This thesis considers the optimum replacement (ordering) policy for a single equipment, for which lead times are explicitly involved. For the problem, two distinctive models are investigated. In Model I, an ordering policy allowing two kinds of random lead times (one for regular order and the other one for expedited order) is considered, where the operational condition of the equipment is monitored by the attached sensing device continuously. Both the equipment and the sensing device are subject to random failures. It is shown that there exists under certain conditions a finite and unique optimum ordering policy maximizing the cost effectiveness which is used as a criterion for optimality. In Model II, an ordering policy with a constant lead time is considered under the assumption that the equipment, at failure, is repairable and subject to random repair costs. In the model, the employed equipment can be either repaired minimally or replaced with a spare unit by a procurement ordering, whose decision depends on repair cost estimation. The expected cost per unit time is used as a criterion for optimality. For both models, illustrative numerical examples are presented.