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In many manufacturing or service industries, there exists maximum allowable tardiness for orders, according to purchase contracts between the customers and suppliers. Customers may cancel their orders and request compensation for damages, for breach of contract, when the delivery time is expected to exceed maximum allowable tardiness, whereas they may accept the delayed delivery of orders with a reasonable discount of price within maximum allowable tardiness. Although many research works have been produced on the job shop scheduling problem relating to minimizing total tardiness, none of them have yet considered problems with maximum allowable tardiness. In this study, we solve a job shop scheduling problem under maximum allowable tardiness, with the objective of minimizing tardiness penalty costs. Two kinds of penalty costs are considered, i.e., one for tardy jobs, and the other for canceled jobs. To deal with this problem within a reasonable time at actual production facilities, we propose several dispatching rules by extending well-known dispatching rules for the job shop scheduling problem, in cooperation with a probabilistic conception of those rules. To evaluate the proposed rules, computational experiments were carried out on 300 test instances. The test results show that the suggested probabilistic dispatching rules work better than the existing rules and the optimization solver CPLEX, with a time limit.

Minimizing Tardiness Penalty Costs in Job Shop Scheduling under Maximum Allowable Tardiness