Shallcross, David F. A polynomial algorithm for a one machine batching problem. (English) Zbl 0760.90059 Oper. Res. Lett. 11, No. 4, 213-218 (1992). Summary: A problem of batching identical jobs on a single machine is studied. Constant processing times and batch setup times are assumed. An algorithm if presented to minimize the sum over all jobs of the batched completion times, and shown to run in time polynomial in the logarithms of the problem parameters. Cited in 32 Documents MSC: 90B35 Deterministic scheduling theory in operations research 90C10 Integer programming 90C60 Abstract computational complexity for mathematical programming problems Keywords:lot-sizing; polynomial algorithms; identical jobs; single machine PDFBibTeX XMLCite \textit{D. F. Shallcross}, Oper. Res. Lett. 11, No. 4, 213--218 (1992; Zbl 0760.90059) Full Text: DOI References: [1] Coffman, E. G.; Nozari, A.; Yannakakis, M., Optimal Scheduling of products with two subassemblies on a single machine, Oper. Res., 37, 426-436 (1989) · Zbl 0672.90075 [2] Dobson, G.; Karmarkar, U. S.; Rummel, J. L., Batching to minimize flow times on one machine, Management Sci., 33, 784-799 (1987) · Zbl 0624.90047 [3] Hirschberg, D. S.; Wong, C. K., A polynomial algorithm for the knapsack problem in two variables, J. Assoc. Comput. Mach., 23, 147-154 (1976) · Zbl 0345.90048 [4] Kannan, R., Two variable integer programming, J. Assoc. Comput. Mach., 27, 118-122 (1980) · Zbl 0423.90052 [5] Naddef, D.; Santos, C., One-pass batching algorithms for the one-machine problem, Discrete Appl. Match., 21, 133-145 (1988) · Zbl 0661.90044 [6] Zamanskii, L. Ya; Cherkasskii, V. L., A formula for finding the number of integer points under a straight line and its application, Èkonom. i Mat. Metody, 20, 1132-1138 (1984), (in Russian) · Zbl 0569.90060 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.