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Single-machine scheduling with random machine breakdowns and randomly compressible processing times. (English) Zbl 0973.90035
Summary: This work presents a model of single-machine scheduling problem. The machine is failure-prone and subject to random breakdowns. The processing time is a deterministic sequence that is randomly compressible, which may be from the introduction of new technology or addition of new equipment. Taking into account the cost for the random break-downs and the random compressible processing time, our objective is to find the optimal scheduling policy to minimize an objective function. Under simple conditions, it is shown that the optimal sequence possesses a \(V\)-shape property.

90B35 Deterministic scheduling theory in operations research
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[1] DOI: 10.1016/0377-2217(93)90245-I · Zbl 0791.90028
[2] DOI: 10.1002/(SICI)1520-6750(199606)43:4<573::AID-NAV9>3.0.CO;2-4 · Zbl 0848.90067
[3] DOI: 10.1002/1520-6750(199010)37:5<661::AID-NAV3220370506>3.0.CO;2-3 · Zbl 0725.90038
[4] DOI: 10.1016/S0167-6377(97)00017-5 · Zbl 0888.90086
[5] Birge J.R., Introduction to Stochastic Programming (1997) · Zbl 0892.90142
[6] DOI: 10.1002/(SICI)1520-6750(199612)43:8<1127::AID-NAV5>3.0.CO;2-G · Zbl 0871.90043
[7] Cheng T.C.E., Parallel-Machine Scheduling with Controllable Processing Times (1994)
[8] DOI: 10.1002/(SICI)1520-6750(199802)45:1<67::AID-NAV4>3.0.CO;2-J · Zbl 0897.90125
[9] Cheng T.C.E., IEEE Trans. Automat. Control 45 (1994)
[10] DOI: 10.1016/0925-5273(96)00041-2
[11] DOI: 10.1287/opre.37.6.981 · Zbl 0686.90023
[12] DOI: 10.1287/opre.41.4.786 · Zbl 0782.90055
[13] DOI: 10.1016/0377-2217(88)90355-4 · Zbl 0647.90041
[14] DOI: 10.1016/0166-218X(90)90105-L · Zbl 0693.90056
[15] Parzen E., Stochastic processes (1962)
[16] DOI: 10.1016/0377-2217(92)90144-X · Zbl 0760.90058
[17] Ross S., Stochastic Processes (1983)
[18] DOI: 10.1016/S0377-2217(82)80008-8 · Zbl 0482.90043
[19] AIIE Transctions 12 pp 258– (1980)
[20] DOI: 10.1287/opre.28.5.1155 · Zbl 0449.90054
[21] Zhang, Q., ed. Mathematics of Stochastic Manufacturing Systems. Proc. 1996 AMS-SIAM Summer Seminar in Applied Mathematics. Providence, RI Lectures in Applied Mathematics, Amer. Math. Soc
[22] DOI: 10.1016/0167-6377(91)90071-V · Zbl 0744.90045
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