A discrete‐time order‐replacement model with time discounting and spare part provisioning

Abstract

PurposeTo determine the optimal spare part order‐replacement policy for any high cost single unit complex system in a discrete‐time circumstance.Design/methodology/approachThe expected total discounted cost over an infinite planning horizon is taken as a criterion of optimality as it allows us to put emphasis on the present behavior of the system.FindingsThe problem under consideration is a two‐dimensional discrete optimization problem (regular ordering time and inventory time limit for the spare are decision variables) which is difficult to handle, in general. However, it is explored that the problem can be reduced to a simple one‐dimensional one and the optimal ordering time is to be determined under the two extreme situations: no replacement of the spare until the original unit fails and replacement of the spare as soon as it is delivered.Research limitations/implicationsFor modeling simplicity, deterministic lead time is considered for both regular and expedited orders. A more appropriate assumption would be to consider randomized lead time for both the orders.Practical implicationsThe research provides a useful order‐replacement strategy for a single‐unit system where the failure of the unit is better measured by the number of cycles completed before failure rather than the instant of failure.Originality/valueThe work done in this paper carries certain values as any continuous time model for the problem under consideration can be regarded as only an approximate model.