Changeover

Abstract: Production orders for a number of products must be scheduled on a number of similar production lines so as to minimize the sum of product-dependent changeover costs, production costs, and time-constraint penalties. We treat the problem by a quadratic assignment algorithm with a linear programming adjustment, and describe a successful practical application for chemical reactor scheduling.

Abstract: Certain manufacturing situations involve a small number of items produced sequentially on the same facility with high changeover cost. Production schedules are characterized by long runs, and individual items are produced infrequently. At the same time, seasonal demand patterns require that the items be maintained in inventory in the right mix. This paper presents alternative formulations of this problem. It uses a Lagrangean relaxation approach to decouple the problem and provide lower bounds used in a branch and bound algorithm. Some experimental computations on small problems are reported.

Abstract: The pigeon and the rat partition total response output between both schedules of a concurrent variable-interval pair. The quantitative nature of a partition seems critically dependent on the relative rates with which the two schedules provide reinforcements for responding, in addition to the changeover delay. The manner in which the changeover delay controls the partition was studied by varying the duration of the changeover delay from 0 to 20 sec with each of two pairs of concurrent variable-interval schedules, viz., Conc VI 1.5-min VI 1.5-min and Conc VI 1-min VI 3-min. Rats served as the subjects and brain stimulation was employed as the reinforcer. When the schedules were Conc VI 1.5-min VI 1.5-min, relative response rate approximated 0.50 at all values of the changeover delay. When the schedules were Conc VI 1-min VI 3-min, relative response rate, computed with respect to the VI 1-min schedule, increased when the duration of the changeover delay increased. Changeover rate decreased when the duration of the changeover delay increased. The decrease was the same for both VI schedules of the Conc VI 1.5-min VI 1.5-min pair but was more rapid for the VI 3-min schedule of the Conc VI 1-min VI 3-min pair.

Abstract: Without assuming any constraints on behavior, we derive the policy that maximizes overall reward rate on two variable-interval paradigms. The first paradigm is concurrent variable time-variable time with changeover delay. It is shown that for nearly all parameter values, a switch to the schedule with the longer interval should be followed immediately by a switch back to the schedule with the shorter interval. The matching law does not hold at the optimum and does not uniquely specify the obtained reward rate. The second paradigm is discrete trial concurrent variable interval-variable interval. For given schedule parameters, the optimal policy involves a cycle of a fixed number of choices of the schedule with the shorter interval followed by one choice of the schedule with the longer interval. Molecular maximization sometimes results in optimal behavior.