Bicriteria scheduling on a single batching machine with job transportation and deterioration considerations

Abstract

Abstract:We study a single batching machine scheduling problem with transportation and deterioration considerations arising from steel production. A set of jobs are transported, one at a time, by a vehicle from a holding area to the single batching machine. The machine can process several jobs simultaneously as a batch. The processing time of a job will increase if the duration from the time leaving the holding area to the start of its processing exceeds a given threshold. The time needed to process a batch is the longest of the job processing times in the batch. The problem is to determine the job sequence for transportation and the job batching for processing so as to minimize the makespan and the number of batches. We study four variations (P1, P2, P3, P4) of the problem with different treatments of the two criteria. We prove that all the four variations are strongly NP-hard and further develop polynomial time algorithms for their special cases. For each of the first three variations, we propose a heuristic algorithm and analyze its worst-case performance. For P4, which is to find the Pareto frontier, we provide a heuristic algorithm and an exact algorithm based on branch and bound. Computational experiments show that all the heuristic algorithms perform well on randomly generated problem instances, and the exact algorithm for P4 can obtain Pareto optimal schedules for small-scale instances.

New Results on the Coordination of Transportation and Batching Scheduling

“…Tang et al [2] study the problem TBS with deterioration considerations. In this model, they define the exposure time of a job as the length of the time interval from the departure from the holding area to the start of the processing on the machine.…”

“…From a practical perspective, Tang et al [2] observe that (again in steel ingot processing) the fuel cost is directly proportional to the number of batches, which explains the desire to balance a time-related and a cost-related objective. Tang and Gong [1] investigate TBS when F (C 1 , .…”

“…Below, we will discuss the complexity status of TBS for subproblems corresponding with specific choices for the objective function F . Tang et al [2] provide an elaborate description of the practical relevance of this type of scheduling problems in the context of ingot processing in the steel industry. Steel ingots are created by pouring molten steel into molds placed on a vehicle; the steel then solidifies.…”

“…Tang et al [2] investigate TBS with deterioration considerations to minimize the makespan and the processing cost in a bi-criteria setting when m = 1; the authors show that different variants of the problem are all strongly NP-hard and present heuristic algorithms. Tang and Gong [4] study scheduling with batch processing and two-stage transportation, including an extra transportation stage after the stages of TBS.…”

“…The molds are subsequently removed ("stripped") from the ingots and the ingots are transported to a soaking pit by the vehicles. The transportation time of the ingots in each trip (representing the transportation phase) includes solidifying, stripping and actual travelling, and Tang et al [2] describe how different jobs may have different transportation times because the time required for solidifying and stripping depends on the steel grade as well as on other attributes of the ingots. In the soaking pit, multiple ingots are reheated simultaneously to be prepared for rolling (this reheating is the batching phase).…”