Production-Inventory System for Deteriorating Items with Machine Breakdown, Inspection, and Partial Backordering

This study considers the effects of a machine breakdown, inspection, and partial backordering for deteriorating items. Most industries try to reduce facility unavailability by implementing a regular inspection and preventive maintenance since there is a possibility that some machines will breakdown during the production process. Moreover, an emergency purchase policy can be provided for quick response to customer’s backorder. The system also produces imperfect items with different rates before and after the inspection. Rework process and post-sales warranty are launched for the defective items. Unlike previous studies, we applied a fixed-point approach and renewal reward theorem to solve the deteriorating production-inventory model while considering machine breakdown, inspection, and partial backordering. A case example and sensitivity analysis are provided. The sensitivity analysis shows the important parameters that should be considered in designing the inspection plan and the replenishment policy when facility unavailability and imperfect items exist.

Scheduling Preventive Maintenance for a Nonperiodically Inspected Deteriorating System

We consider the problem of scheduling maintenance activities for a stochastically deteriorating manufacturing system inspected aperiodically. The state of the system (which can only be revealed at inspection epochs) is characterized jointly by the system’s physical state (the level of damage or remaining capacity) and its virtual age. Assuming a threshold-type policy, the paper aims at minimizing the long-run average maintenance cost per unit time by determining appropriate inspection intervals and maintenance thresholds. Using the renewal reward theorem, the expected cost per cycle and expected cycle length emerge as solutions of an integral equation, and a recursive scheme is devised to solve them. We illustrate the procedure for the case when the physical state evolves as a Gamma process.

RENEWAL PROCESS WITH FUZZY INTERARRIVAL TIMES AND REWARDS

This paper considers a renewal process in which the interarrival times and rewards are characterized as fuzzy variables. A fuzzy elementary renewal theorem shows that the expected number of renewals per unit time is just the expected reciprocal of the interarrival time. Furthermore, the expected reward per unit time is provided by a fuzzy renewal reward theorem. Finally, a numerical example is presented for illustrating the theorems introduced in the paper.