Distributionally robust resource constrained single machine scheduling

Realistic production process usually involves various resources, such as raw materials. Most existing works assume that the quantities of resources required for processing each job are deterministic and fixed. However, in practice, such quantities are usually uncertain, due to various factors, such as product failure rates, damage to resources and perishable materials. Besides, the given historical data may be inadequate or not representative enough, thus the probability distributions of such uncertain parameters cannot always be exactly estimated. This work investigates a single machine scheduling problem with resource limitation, in which the required resource quantities for processing jobs are stochastic. The problem is to determine the job rejection in the tactical level, and schedule the accepted jobs in the operational level. The objective is to minimize the weighted sum of the job rejection penalty cost and the total tardiness, and the probability of violating the resource limitation is controlled. For the problem, a novel distributionally robust chance constrained formulation is first proposed. To solve the problem, an approximated mixed integer second-order cone programming (MI-SOCP) model is then developed. A case study is conducted to evaluate the applicability of the proposed solution method.