Toward Robust Manufacturing Scheduling: Stochastic Job-Shop Scheduling

Abstract

Motivated by the presence of uncertainties as well as combinatorial complexity within the links of supply chains, this paper addresses the outstanding and timely challenge illustrated through a case study of stochastic job-shop scheduling problems arising within low-volume high-variety manufacturing. These problems have been classically formulated as integer linear programs (ILPs), which are known to be NP-hard, and are computationally intractable. Yet, optimal or near-optimal solutions must be obtained within strict computational time requirements. While the deterministic cases have been efficiently solved by state-of-the-art methods such as branch-and-cut (B&C), uncertainties may compromise the entire schedule thereby potentially affecting the entire supply chain downstream, thus, uncertainties must be explicitly captured to ensure the feasibility of operations. The stochastic nature of the resulting problem adds a layer of computational difficulty on top of an already intractable problem, as evidenced by the presented case studies with some cases taking hours without being able to find a "near-optimal" schedule. To efficiently solve the stochastic JSS problem, a recent Surrogate "Level-Based" Lagrangian Relaxation is used to reduce computational effort while efficiently exploiting geometric convergence potential inherent to Polyak's step-sizing formula thereby leading to fast convergence. Computational results demonstrate that the new method is more than two orders of magnitude faster compared to B&C. Moreover, insights based on a small intuitive example are provided through simulations demonstrating an advantage of scholastic scheduling.