Abstract
This paper deals with the 1|{p-text {batch}, s_jle b}|sum C_j scheduling problem, where jobs are scheduled in batches on a single machine in order to minimize the total completion time. A size is given for each job, such that the total size of each batch cannot exceed a fixed capacity b. A graph-based model is proposed for computing a very effective lower bound based on linear programming; the model, with an exponential number of variables, is solved by column generation and embedded into both a heuristic price and branch algorithm and an exact branch and price algorithm. The same model is able to handle parallel-machine problems like Pm|{p-text {batch}, s_jle b}|sum C_j very efficiently. Computational results show that the new lower bound strongly dominates the bounds currently available in the literature, and the proposed heuristic algorithm is able to achieve high-quality solutions on large problems in a reasonable computation time. For the single-machine case, the exact branch and price algorithm is able to solve all the tested instances with 30 jobs and a good amount of 40-job examples.
Highlights
In manufacturing system management, capacity is a key factor in matching supply with demand, i.e., having a system that is able to produce what is needed to satisfy customer demand.Several factors negatively impact system capacity
Batches induced by setup times are called serial batches, and they are very important in manufacturing systems, they are not the only type of batches that can be present on the shop floor
A fundamental work in the field of parallel-batch processor scheduling is that of Uzsoy (1994), where a singlebatch processing machine problem is studied with regard to makespan and total flow time criteria
Summary
Capacity is a key factor in matching supply with demand, i.e., having a system that is able to produce what is needed to satisfy customer demand. Serial batches are due to the presence of setup times, while parallel batches stem from the ability of machines to accommodate and manufacture several jobs at the same time They are less studied than serial and transfer batches because they are less frequent; they are no less important. Cj. A fundamental work in the field of parallel-batch processor scheduling is that of Uzsoy (1994), where a singlebatch processing machine problem is studied with regard to makespan and total flow time criteria. – A heuristic procedure of the so-called price and branch type—following the terminology of Desrosiers and Lübbecke (2011)—relying on the graph model is developed This procedure allows one to generate high-quality solutions (with certified optimality gaps) for fairly large instances in short computation times.
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