On a Multiproduct Assembly Line-Balancing Problem

Shortest-route formulation of mixed-model assembly line balancing problem

“…Common tasks between the models are assumed to exist and these tasks are assigned to the same stations. The resulting network is considerably smaller than the one of the shortest-route formulation of Roberts and Villa (1970); this is partly due to the constraint of assigning the common tasks to the same stations.…”

“…The size of the network grows as x increases; however, assigning common tasks of dierent models to the same stations and the constraints that can be imposed by the designers limit the increase. Thus, it is more ecient than the shortest-route formulation of Roberts and Villa (1970) in which the nodes of the network consists of the Cartesian product of the nodes of each model. The model proposed in this note is a new shortest-route model of the mixed-model version in which a combined precedence diagram is utilized.…”

“…Note that task 6 which is a common task among the models is assigned to dierent stations; the assumption of assigning the common tasks to the same stations of our model results in a solution with one extra station. However, the number of nodes in the network of Roberts and Villa (1970) is considerably higher (more than 4.5 times). As the number of models in the problem increases, the dierence between the sizes of the networks will be signi®cantly larger, since the Cartesian product will increase the network size quite rapidly.…”

“…We have solved the same problem using the shortest-route formulation of Roberts and Villa (1970). In the formulation, feasible states are generated for each model and the set of states for the problem is obtained from the Cartesian product of these feasible states.…”

“…Mansoor (1967) presented an adjustment to the Gutjahr and Nemhauser (1964) algorithm to obtain the optimal solution after considering only a fraction of thè shortest-route' calculations. Roberts and Villa (1970) extended the Gutjahr and Nemhauser (1964) algorithm to solve the mixed-model version of the problem. Nodes were generated similarly for each model in the problem, and the nodes of the network consisted of the Cartesian product of the nodes of each model.…”