Optimal Machine Stopping Time and Ordering Cycle for Parts to Minimize the Total Cost of a Supply Chain

Many parts or components in a facility are sometime vulnerable to failure causing downtime and production loss. So, in order to decrease the downtime, parts of the same type that follow the same lifespan distribution need to be replaced at least once to minimize the cost of unscheduled labor and the damages to the products. A decision on replacing all such vulnerable parts decreases the total cost including penalty cost, purchasing cost and holding cost. Different preempt times of a machine result in different purchasing quantity, procurement cost and carrying costs. So, a rational decision of allowable stopping time of a machine and order cycle for vulnerable parts jointly minimizes the total cost of supply chain. This study proposes a novel model to minimize the total cost for the vulnerable parts which have joint influence on machine performance. An integrated nonlinear cost model developed here is optimally solved and tested with several different distributions. Strong results are propounded to support the proposed model in terms of manufacturing time and system cost.