Abstract
A fully polynomial approximation scheme for the problem of scheduling n deteriorating jobs on a single machine to minimize makespan is presented. Each algorithm of the scheme runs in O(n 5 L 4ɛ3) time, where L is the number of bits in the binary encoding of the largest numerical parameter in the input, and ɛ is required relative error. The idea behind the scheme is rather general and it can be used to develop fully polynomial approximation schemes for other combinatorial optimization problems. Main feature of the scheme is that it does not require any prior knowledge of lower and/or upper bounds on the value of optimal solutions.
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References
Browne, S. and U. Yechiali. (1989). "Dynamic Priority Rules for Cyclic Type Queues," Advances in Applied Probability 10, 432–450.
Browne, S. and U. Yechiali. (1990). "Scheduling Deteriorating Jobs on a Single Processor," Operations Research 38, 495–498.
Gens, G.V. and E.V. Levner. (1980). "Fast Approximation Algorithms for Knapsack Type Problems," Lecture Notes in Control and Information Science 23, 185–194.
Gupta, S.K., A.S. Kunnathur, and K. Dandapani. (1988). "Optimal Repayment Policies for Multiple Loans," OMEGA 15, 207–227.
Horowitz, E. and S. Sahni. (1976). "Exact and Approximate Algorithms for Scheduling Nonidentical Processors," Journal ACM 23, 317–327.
Ibarra, O.H. and C.E. Kim. (1975). "Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems," Journal ACM 22, 463–468.
Johnson, D.S. and K.A. Niemi. (1983). "On Knapsacks, Partitions, and a New Dynamic Programming Technique for Trees," Mathematics of Operations Research 8, 1–14.
Karp, R.M. (1975). "The Fast Approximate Solution of Hard Combinatorial Problems," Proc. 6th Southeastern Conference on Combinatorics; Graph Theory; and Computing. Winnipeg: Utilitas Mathematica Publishing, pp. 15–31.
Kovalyov, M.Y., Y.M. Shafransky, V.A. Strusevich, V.S. Tanaev, and A.V. Tuzikov. (1989). "Approximation Scheduling Algorithms: A Survey," Optimization 20, 859–878.
Kovalyov, M.Y., C.N. Potts, and L.N. van Wassenhove. (1994). "A Fully Polynomial Approximation Scheme for Scheduling a Single Machine to Minimize Total Weighted Late Work," Mathematics of Operations Research 19, 86–93.
Kubiak, W. and S. van de Velde. (1994). "Scheduling Deteriorating Jobs to Minimize Makespan,"Working Paper LOPM 94-12, University of Twente.
Kunnathur, A.S. and S.K. Gupta. (1990). "Minimizing the Makespan with Late Start Penalties Added to Processing Times in a Single Facility Scheduling Problem," European Journal of Operational Research 47, 56–64.
Lawler, E.L. (1979). "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research 4, 339–356.
Magazine, M.J. and O. Oguz. (1981). "A Fully Polynomial Approximation Algorithm for the 0-1 Knapsack Problem," European Journal of Operations Research 8, 270–273.
Mosheiov, G. (1991). "V-Shaped Policies for Scheduling Deteriorating Jobs," Operations Research 39, 979–991.
Sahni, S. (1976). "Algorithms for Scheduling Independent Tasks," Journal ACM 23, 116–127.
Sahni, S. (1977). "General Techniques for Combinatorial Approximation," Operations Research 25, 920–936.
Smith, W.E. (1956). "Various Optimizers for Single State Production," Naval Research Logistics Quarterly 3, 59–66.
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Kovalyov, M.Y., Kubiak, W. A Fully Polynomial Approximation Scheme for Minimizing Makespan of Deteriorating Jobs. Journal of Heuristics 3, 287–297 (1998). https://doi.org/10.1023/A:1009626427432
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DOI: https://doi.org/10.1023/A:1009626427432