Exact and heuristic algorithms for minimizing Tardy/Lost penalties on a single-machine scheduling problem

This paper addresses minimizing Tardy/Lost penalties with common due dates on a single machine. According to this penalty criterion, if tardiness of a job exceeds a predefined value, the job will be lost and penalized by a fixed value. The problem is formulated as an integer programming model, and a heuristic algorithm is constructed. Then, using the proposed dominance rules and lower bounds, we develop two dynamic programming algorithms as well as a branch and bound. Experimental results show that the heuristic algorithm has an average optimality gap less than 2 % in all problem sizes. Instances up to 250 jobs with low variety of process times are optimally solved and for high process time varieties, the algorithms solved all instances up to 75 jobs.