The scheduling of maintenance service

Abstract

We study a discrete problem of scheduling activities of several types under the constraint that at most a single activity can be scheduled to any one period. Applications of such a model are the scheduling of maintenance service to machines and multi-item replenishment of stock. In this paper we assume that the cost associated with any given type of activity increases linearly with the number of periods since the last execution of this type. The problem is to find an optimal schedule specifying at which periods to execute each of the activity types in order to minimize the long-run average cost per period. We investigate properties of an optimal solution and show that there is always a cyclic optimal policy. We propose a greedy algorithm and report on computational comparison with the optimal. We also provide a heuristic, based on regular cycles for all but one activity type, with a guaranteed worse case bound.

General perfectly periodic scheduling

“…Partition it into three parts (see Figure 2): the start of j i until t; t until the start of the job following j t ; and the start of the job following j t until the start of j i . Denote the lengths of these subintervals by t i,1 , t i,2 , and t i, 3 , respectively. By definition, we have…”

Windows scheduling of arbitrary-length jobs on multiple machines

“…Closely related problems from the operation research and the communication networks areas include the machine maintenance problem (Wei and Liu 1983;Anily et al 1998), the multi-item replenishment and other inventory problems (Hadley and Whitin 1963;Roundy 1985;Hassin and Megiddo 1991), and the sensor resource management problem (Feinberg et al 2002).…”

Maintenance Scheduling: Description, Status and Future Directions

“…Anily et al [1] studied a discrete problem of scheduling in machines, M,…, M m , in an infinite time horizon discrete time. The cost of operating a machine at any given period, C(t,p), is a linear cost structure where each machine i is associated with a constraint a i and the cost of operating the machine in the j th period after the last maintenance of that machine is ja i for j ≥ 0.…”

“…However, simulation appears to be the most significant [45,57,75,83]. Furthermore, among the general MS studies is the work of Anily [1,2], Dillon [24], Contaxis et al [17], and others [26,30,62,65,68,80,88]. There are also numerous studies on simultaneous scheduling [40,44,66].…”