A Branch and Bound Approach for Machine Load Balancing in Flexible Manufacturing Systems

Abstract

A flexible manufacturing system (FMS) is an integrated system of computer numerically controlled machine tools connected with automated material handling. A set of production planning problems for FMSs has been defined (Stecke [Stecke, Kathryn E. 1983. Formulation and solution of nonlinear integer production planning problems for flexible manufacturing systems. Management Sci. 29 (3, March) 273--288.]), and this paper considers one called the loading problem. This problem involves assigning to the machine tools, operations and associated cutting tools required for part types that have been selected to be produced simultaneously. The part types will be machined during the upcoming production period (say, of one to three weeks duration on average) and according to a prespecified part mix. This assignment is constrained by the capacity of each machine's tool magazine as well as by the production capacities of both the system, and each machine type. There are several loading objectives that are applicable in a flexible manufacturing situation. This paper considers the most commonly applied one, that of balancing the workload on all machines. This paper first discusses a nonlinear integer mathematical programming formulation of the loading problem. The problem is formulated in all detail. Then an efficient solution procedure is proposed and illustrated with an example. Computational results are provided to demonstrate the efficiency of the suggested special-purpose procedures.production/scheduling: flexible manufacturing, production/scheduling: line balancing, programming: integer, algorithms: branch and bound

An iterative approach to system setup problems in flexible manufacturing systems

“…Computational results reported in Kim and Yano (1990) indicate that this composite algorithm provides better solutions than the e-optimal algorithm developed in Berrada and Stecke (1986), in some test problems in a fraction of the computation time (refer to these papers for additional details).…”

“…Later, Stecke (1983) formulates the FMS loading problem as a nonlinear mixed-integer program and solves it through linearization techniques. A branch-and-bound algorithm is developed by Berrada and Stecke (1986) for this formulation with the objective of balancing the workloads. This algorithm is modified to accommodate the objective of finding the best (unbalanced) workloads for machines groups of unequal sizes in Kim and Yano (1987).…”

Meta-hierarchical-heuristic-mathematical- model of loading problems in flexible manufacturing system for development of an intelligent approach

“…Table 1 is review of literature on mathematical modelling of loading problem of FMS. Stecke (1983b) Grouping and loading Need to decrease computational time Ammons et al (1985) General loading problem for discrete optimization Heuristics improves computational efficiency & effectiveness Berrada & Stecke (1986) Minimize Stecke (1983a) Maximize throughput and machine utilizations Future need to develop efficient heuristic algorithms for more real life solution Stecke (1986) Optimal allocation ratios Developed queueing network model where information is suppressed Greene & Sadowski (1986) Minimize make span, flow time and lateness Identified variables and constraints necessary to solve real world program Sarin & Chen (1987) Minimize machining cost Lagrangian relaxation is proposed Ventura et al (1988) Minimize make-span Heuristic algorithms are proposed Henery et al (1990) Balancing of workload and maximize flexibility Mathematical solution was found impractical Rajamani & Adil (1996) Routeing flexibility Routing flexibility is required for rigid loading schedules Nayak & Acharya (1998) Minimize number of batches heuristic has been proposed Ozdamarl & Barbarosoglu (1999) Minimize the holding cost GA-SA hybrid heuristics were developed Lee & Kim (2000) Minimize maximum workload Better performance with partial grouping than total grouping, solved by heuristics Kumar & Shanker (2000) Genetic algorithms for constrained optimization GA shows near-optimum performance and need of modern heuristic techniques Kumar & Shanker (2001) Balancing of workloads Results are in agreement with previous findings Yang & Wu (2002) Balancing of workloads Tested for small size test problems only Gamila & Motavalli (2003) Minimize total processing time Used computer generated data for validation Tadeusz (2004) Minimize inter-station transfer time Very high computational effort is required for realistic problems Chan et al (2004) Minimize system unbalance and maximize throughput Validated only for small set of test problems Require further extension of research Chen & Ho (2005) Minimize flow time & tool cost and workload unbalancing multi-objective genetic algorithm (GA) is proposed Bilgin & Azizoglu (2006) Optimization of total processing time near-optimal solution in reasonable time Nagarjuna et al (2006) Minimize system u...…”

“…Researchers also felt the need of real-time FMS control (Stecke & Brian, 1995) and to develop planning software that can be actually implemented in real systems (Lee et al, 1997). Ammons et al (1985) stated that the use of heuristics in model development improves computational efficiency & effectiveness and provides more optimal solution (Berrada & Stecke, 1986;Ammons et al, 1985;Dobson & Nambimadom, 2001). Heuristic based methods are more robust in practicality .…”

Tool sharing in parallel part production

“…In the literature the FMS loading problem has been extensively discussed; [9][10][11] to name a few. This typical short range planning problem involves the assignment of operations and tools of selected part types to machine groups, taking into account technological and capacity constraints.…”