A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements

•We consider U-shaped assembly lines with equipment assignment decisions and fixed number of workstations.•We aim to assign the tasks and equipments to the workstations so as to minimize the total equipment cost.•We present a mathematical model and a branch and bound procedure.•Our computational study has revealed the satisfactory behavior of our branch and bound procedure.

In this study we consider a U-shaped assembly line balancing problem where each task uses a specified set of equipments and each type of equipment has a specified cost. Our problem is to assign the tasks together with their equipments to the workstations so as to minimize the total equipment cost. We formulate the problem as a mixed integer linear programming model that is capable of solving small sized instances. We propose a branch and bound algorithm that uses efficient precedence relations and lower bounds. We find that the algorithm is able to solve moderate sized problem instances in reasonable times.