Developing an Upper Bound and Heuristic Solution Algorithm for Order Scheduling Problem with Machine's Idle Time Minimization: A Case Study in Printing Industry

In this paper, the problem of received order scheduling by a manufacturer, with the measure of maximum completion times of orders, has been formulated and then an analytical approach has been devised for its solution. At the beginning of a planning period, the manufacturer receives a number of orders from customers, each of which requires two different stages for processing. In order to minimize the work in process inventories, the no-wait condition between two operations of each order is regarded. Then, the equality of obtained schedules is proved by machine idle time minimization, as objective, with the schedules obtained by maximum completion time minimization. A concept entitled “Order pairing” has been defined and an algorithm for achieving optimal order pairs which is based on symmetric assignment problem has been presented. Using the established order pairs, an upper bound has been developed based on contribution of every order pair out of total machines idle time. Out of different states of improving upper bound, 12 potential situations of order pairs sequencing have been also evaluated and then the upper bound improvement has been proved in each situation, separately. Finally, a heuristic algorithm has been developed based on attained results of pair improvement and a case study in printing industry has been investigated and analyzed to approve its applicability.