Monotone optimal preventive maintenance policies for stochastically failing equipment

This paper examines various models for maintenance of a machine operating subject to stochastic deterioration. Three alternative models are presented for the deterioration process. For each model, in addition to the replacement decision, the option exists of performing preventive maintenance. The effect of this maintenance is to “slow” the deterioration process. With an appropriate reward structure imposed on the processes, the models are formulated as continuous time Markov decision processes. the optimality criterion being the maximization of expected discounted reward earned over an infinite time horizon. For each model conditions are presented under which the optimal maintenance policy exhibits the following monotonic structure. First, there exists a control limit rule for replacement. That is, there exists a number i* such that if the state of machine deterioration exceeds i* the optimal policy replaces the machine by a new machine. Secondly, prior to replacement the optimal level of preventive maintenance is a nonincreasing function of the state of machine deterioration. The conditions which guarantee this result have a cost/benefit interpretation.     

A dynamic inventory system with recycling

This paper deals with a periodic review inventory system in which a constant proportion of stock issued to meet demand each period feeds back into the inventory after a fixed number of periods. Various applications of the model are discussed, including blood bank management and the control of reparable item inventories. We assume that on hand inventory is subject to proportional decay. Demands in successive periods are assumed to be independent identically distributed random variables. The functional equation defining an optimal policy is formulated and a myopic base stock approximation is developed. This myopic policy is shown to be optimal for the case where the feedback delay is equal to one period. Both cost and ordering decision comparisons for optimal and myopic policies are carried out numerically for a delay time of two periods over a wide range of input parameter values.     

Statistical analysis of a conventional fuze timer

In this paper, a statistical analytic model for evaluation of the performance of a standard electric bomb fuze timer is presented. The model is based on what is called a selective design assembly, where one item, namely, a resistor, is used to time the circuit. In such an assembly, the remaining components are chosen a priori from predetermined distributions. Based on the analysis, a general numerical integration scheme is utilized for assessing performance of the timer. The results of a computer simulation are also given. In the last section of the paper, a theory for evaluation of the yield of two or more timers designed to operate in sequence is derived. To appraise such a scheme, a numerical quadrature routine is developed.     

A note on the sensitivity of navy first term reenlistment to bonuses,unemployment and relative wages

Multiple regression analysis of first term reenlistment rates over the period 1968–1977 confirms previous findings that reenlistment is highly sensitive to unemployment at the time of reenlistment and shortly after enlistment, almost four years earlier. Bonuses, particularly lump sum bonuses, were also shown to be a significant determinant of reenlistment.     

Storage problems when demand is “all or nothing”

An inventory of physical goods or storage space (in a communications system buffer, for instance) often experiences “all or nothing” demand: if a demand of random size D can be immediately and entirely filled from stock it is satisfied, but otherwise it vanishes. Probabilistic properties of the resulting inventory level are discussed analytically, both for the single buffer and for multiple buffer problems. Numerical results are presented.     

Nonadjacent extreme point methods for solving linear programs

In this article we present some advanced basis or block-pivoting, relaxation, and feasible direction methods for solving linear programming problems. Preliminary computational results appear to indicate that the former two types of simplex-based procedures may hold promise for solving linear programming problems, unlike the third type of scheme which is shown to be computationally unattractive.