Integrating Ant Colony System and Ordinal Optimization for Solving Stochastic Job Shop Scheduling Problem

The stochastic job shop scheduling problem (SJSSP) is a kind of stochastic programming problem which transformed from job shop scheduling problem. The SJSSP is an NP-hard problem. Current methods to solve the SJSSP ignored characteristics of SJSSP, which lead to large computation times and inefficient solutions. In order to efficiently solve the SJSSP, a method that integrates the ant colony system (ACS) and ordinal optimization (OO), abbreviated as ACSOO, is proposed to find a good enough schedule in a reasonable computation time. The proposed ACSOO utilizes the advantage of multi-directional search in ACS and goal softening in OO. The SJSSP is firstly formulated as a constraint stochastic simulation optimization problem. Next, the ACSOO is proposed to find a good enough schedule of the SJSSP with the objective of minimizing the makespan using limited computation time. The proposed approach is applied to a SJSSP comprising 6 jobs on 6 machines with random processing time in truncated normal, uniform, and exponential distributions and compared with five dispatching rules. Test results demonstrate that the obtaining good enough schedule is successful in the aspects of solution quality and computational efficiency.