Procurement policy of vulnerable parts with jointly distributed lifespan

Abstract

Vulnerable parts exist in most machines or equipment. Failure of those vulnerable parts may result in damage of the machine or the product, and may sometimes cause unnecessary down-time within a production cycle, all of which increases the production costs. Therefore, such failures should be minimized and the parts should be replaced at a point before the end of their expected lifespan, which usually follow some kind of distributions and can be known due to its mass usage attributes. On the other hand, too early replacement of the parts also means increased maintenance costs, increased inventory, and increased parts purchasing cost. This study developed a mathematical model to deal with the issue of determining the optimal stopping time of vulnerable tools. Under the preemption situation, a periodic procurement policy is investigated simultaneously to find the optimal order cycle and eventually minimize the total cost. A case study is given to show the feasibility of the model and several parameters are analyzed to show the impact on the total cost and decision variables.