Planned Leadtimes For A Two-stage Manufacturing System With Unreliable Machines

In a manufacturing system, we assume that every order has an accurate due date; therefore we need to set planned leadtimes for each stage to minimize the manufacturing system’s cost. For a two-stage manufacturing system, we assume there is a probability for the machine in each stage to get broken and it will take some time to repair the machine. The probability of machine will naturally lead to the uncertainty of production time. Because of the uncertainty, there will be the holding cost for early finishing item and the penalty cost for tardiness. Under two occasions, deterministic fixing time and random fixing time, we study how to set planned leadtimes for each stage to minimize the system’s expected cost. We find that, for the deterministic fixing time occasion, the problem is a simple linear program and it is easy to find the optimal solution. However, under the random fixing time occasion, the problem becomes far more complex and is no longer a linear program. By analyzing the cost function, we develop an algorism of finding optimal solution. Based on the numerical simulation, we find that the system’s minimum expected cost first increases and then decreases with the increasing of machines’ disruptions probability under the condition of deterministic fixing time; however, the system’s minimum expected cost increases all the time with the increasing of machines’ disruptions probability under the condition of random fixing time.