An Integer Programming Procedure for Assembly System Design Problems

Abstract

Recent advances in robot technology have revolutionized the concept of manufacturing and assembly systems. These advances have created the need for new mathematical models to reflect the capabilities of the new technologies. In this paper, we focus on the system design problem by defining a work station selection and task assignment problem for automated assembly systems. We formulate this problem as a zero-one integer program and describe a procedure for seeking lower and upper bounds to the optimal value of the integer program. The upper bound provides a feasible solution to the integer formulation and the lower bound is tighter than the standard linear programming relaxation of the integer formulation. Computational results indicate that the proposed bounds are extremely tight. In fact, in each of the 42 test problems evaluated, the lower and upper bound coincided, indicating that the optimal solution to the integer program had been obtained.