Profit-oriented distributionally robust chance constrained flowshop scheduling considering credit risk

Customer credit risk or payment probability, influenced by factors such as financial conditions and bank policies, has hindered fast Asia-Pacific economic growth. Besides, the working time is usually limited due to regulations and limited resources. Driven by profit, some jobs may be rejected on tactical level and the accepted jobs are scheduled on operational level, respecting the allowed working time. This paper studies a stochastic flowshop scheduling problem, assuming that only the mean and covariance matrix of uncertain payment probabilities and processing times are known. The objective is to maximise the profit level, i.e. the probability of the profit no less than the planned one, while controlling the risk of surpassing the limited working time. A new distributionally robust chance constrained model is proposed. The sample average approximation (SAA) method, the robust SAA method and a hierarchical approach, based on an approximated mixed integer second-order conic program, are developed. Numerical experiments show that the hierarchical approach is more efficient. Moreover, some managerial insights are drawn.