Stochastic optimization of two-machine flow shop robotic cells with controllable inspection times: From theory toward practice

This paper considers the stochastic scheduling of a two-machine flow shop robotic cell with controllable inspection times. The inspection here is performed by a multi-function robot which can inspect identical parts with two alternatives for the inspection strategy: either at the back of the upstream machine or in transit between upstream and downstream machines. A characteristic of the inspection process is that its time is changed by altering the inspection cost. If the inspection time is reduced, more failures in parts may result regardless of when failures are identified. The challenge is therefore to find a suitable trade-off between inspection time and internal and external quality costs to increase reliability benefits. Initially, we complete a structural analysis of costs of quality and partial cycles, and then consider a simultaneous analysis of them. Then, through a sensitivity analysis, an epsilon-constraint method is used to find useful upper bounds on costs of quality and partial cycle times. The outcomes of the research are (i) an integrated framework for designing robotic cells with different levels of quality: low (e.g., disassembly industries), medium (e.g., automotive industries), and high (e.g., aerospace industries); and (ii) a sensitivity analysis for studying the impact of inspection strategies to assist production and quality managers with decision-making processes in stochastic environments. Finally, we extend the analysis to show that the given framework can be generalized for subtle variations found in practical applications with regard to (i) the quality of the part and (ii) accuracy of the inspection process. Robotic cells with scrap consideration and robotic cells with decreasing failure rates of the inspection process are studied as examples of the former, and robotic cells with either convex cost function or discrete cost function are studied for the latter.