Batch sizing and job sequencing on a single machine
Annals of Operations Research
Economic lot sizing: an O(n log n) algorithm that runs in linear time in the Wagner-Whitin case
Operations Research - Supplement
Improved algorithms for economic lot size problems
Operations Research
The complexity of one-machine batching problems
Discrete Applied Mathematics - Special issue on new frontiers in the theory and practice of combinatorial optimization: applications in manufacturing and VLSI design
Batching in single operation manufacturing systems
Operations Research Letters
A STOCHASTIC BATCHING AND SCHEDULING PROBLEM
Probability in the Engineering and Informational Sciences
Unbounded parallel-batching scheduling with two competitive agents
Journal of Scheduling
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We study four scheduling problems involving the maximum lateness criterion and an element of batching. For all the problems that we examine, algorithms appear in the literature that consist of a sorting step to determine an optimal job sequence, followed by a dynamic programming step that determines the optimal batches. In each case, the dynamic program is based on a backward recursion of which a straightforward implementation requires O(n^2) time, where n is the number of jobs. We present improved implementations of these dynamic programs that are based on monotonicity properties of the objective expressed as a function of the total processing time of the first batch. These properties and the use of efficient data structures enable optimal solutions to be found for each of the four problems in O(nlogn) time; in two cases, the batching step is actually performed in linear time and the overall complexity is determined by the sorting step.