Capacity-oriented planning and scheduling in production and distribution systems

Choonho Ryu, University of Pennsylvania


This research considers four capacity-oriented planning and scheduling problems in production/distribution systems: the Capacitated Plant Location Problem (CPLP), the Multi-Item Capacitated Lot-Sizing Problem (MCLP), the Dynamic Production Scheduling Problem (DPSP), and the Multilayer Plant Location Problem (MPLP). All of them are mixed 0-1 integer programming problems and have two common basic constraints: (1) all customer demands must be satisfied, and (2) facility utilization may not exceed its capacity and is associated with a 0-1 integer variable (a decision to open/operate the facility or not). CPLP is the simplest model that has constraints (1) and (2). CPLP is often embedded in production planning and scheduling problems (such as MPLP, MCLP, and DPSP) and thus may be a good starting point for tackling these problems. While CPLP is interesting in its own right, it is especially important because of its extension to more complicated scheduling problems. We consider branch-and-bound algorithms based on three Lagrangean schemes and discuss preprocessing, reordering, and correlation of the dual multipliers between consecutive nodes. The other three problems are more complicated than CPLP. Since optimal solutions to the problems are very difficult to obtain, our main concern is to find good feasible solutions and tight bounds in a reasonable time. Various Lagrangean schemes are considered to obtain bounds on the optimal objective value, and Lagrangean heuristics are designed to generate feasible solutions from Lagrangean solutions which are usually infeasible. For MCLP, we consider Lagrangean relaxation (LR) and Lagrangean heuristics and test them on eight problems from Thizy and Van Wassenhove (1985). We found better feasible solutions than the best known ones for all the large problems and their gaps were less than one percent. We consider Lagrangean decomposition (LD) for DPSP and improved bounds compared to the LR bounds of De Matta and Guignard (1989). For MPLP, we consider LR with LD structure and Lagrangean heuristics. Computational results showed that the gap percentages were less than one percent for all test problems.

Subject Area

Business community|Operations research

Recommended Citation

Ryu, Choonho, "Capacity-oriented planning and scheduling in production and distribution systems" (1993). Dissertations available from ProQuest. AAI9331835.