Risk-averse scheduling-location (ScheLoc) problem

Scheduling-Location (ScheLoc) problem is a new and hot topic. It is difficult to make production planning in ScheLoc problem considering job sequencing and machine assignment concurrently, especially when taking uncertainty into account. However, most existing works focus on the deterministic ScheLoc problem, which is unpractical in actual life. This paper addresses a stochastic parallel machine ScheLoc problem with the consideration of uncertain processing time, which may be caused by efficiency of workers, job damage and so on, to minimize the weighted sum of the location cost and the expectation of the total completion time. A two-stage stochastic programming formulation based on scenarios is developed and sample average approximation (SAA) method is applied to solve the model. The formulation above is risk-neutral model, which may provide solutions that perform poorly while considering uncertainty and conservity. Therefore, a risk-averse measure called Conditional Value-at-Risk (CVaR), which is rarely used in the ScheLoc problem, is introduced in this paper to incorporate decision makers' perspectives. Finally, computational experiments are conducted and give the impacts by testing different risk levels and confidence levels.