Scheduling an Industrial Production Facility

Managing an industrial production facility requires carefully allocating limited resources, and gives rise to large, potentially complicated scheduling problems. In this paper we consider a specific instance of such a problem: planning efficient utilization of the facilities and technicians that maintain the United States nuclear stockpile. A detailed study of this problem yields a complicated mixed-integer programming (MIP) model with upward of hundreds of thousands of variables and even more constraints. Consistently and quickly solving such a model exactly is impossible using today’s algorithms and computers, and, in addition to branch-and-bound, requires good heuristics and approximation algorithms. In an effort to design such algorithms, we study several different methods of generating good solutions given the solution to the LP relaxation. We design a suite of sample data and test the algorithms. The goals of this project were twofold. First, we wanted to develop a program that could efficiently and accurately help with the Pantex planning problem. Second, we wanted to experimentally test various ideas, designed originally for “cleaner” problems, in this more challenging context. In summary, we demonstrate the value of using α-points as a way to quickly and cheaply generate, from one solution of an LP relaxation, many feasible solutions to an integer program. In this particular environment, the use of α-points, combined with other heuristics, outperforms local search. We also see the value of finding combinatorially-structured subproblems as opposed to using simple greedy approaches. ⋆ Research partially supported by NSF Grant DMI-9970063 and an AmericanScandinavian Foundation Thor Thors Memorial Fund Grant. [email protected]. ⋆⋆ Some of this work done while this author visited the third author at Sandia National Labs. [email protected]. ⋆ ⋆ ⋆ Sandia is a multipurpose laboratory operated by Sandia Corporation, a LockheedMartin Company, for the United States Department of Energy under contract DEAC04-94AL85000. [email protected]. † Research partially supported by NSF Grants DGE-0086390 and DMI-9970063. [email protected]. ‡ Research partially supported by NSF Grant DMI-9970063 and an Alfred P. Sloan Foundation Fellowship. [email protected]. § Research partially supported by NSF Grant DMI-9970063. [email protected] .