On the Single-Machine Scheduling Problem with Tardiness Penalties

One-Machine Sequencing to Minimize Total Tardiness: A Fourth Theorem for Emmons

“…The prominent role of Emmons's theorems is well established because in most all of these studies use of the theorems has been a key feature of any solution approach. Examples Fisher (1976), Baker and Schrage (1978), Van Wassenhove (1982, 1985), Sen andBorah (1991), Della Croce et al (1998), Szwarc et al (1999Szwarc et al ( , 2001, and Tansel et al (2001)-all of which make prominent use of Emmons's theorems. Emmons's theorems have justifiably generated considerable attention.…”

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“…These theorems are later generalized to non-decreasing cost functions (Rinnooy Kan et al, 1975). Exact methods rely either on 0740-817X © 2001 "lIE" branch and bound (Schwimer, 1972;Rinnooy Kan et al, 1975;Fisher, 1976;Picard and Queyranne, 1978;Sen et al, 1983;Potts and van Wassenhove, 1985;Sen and Borah, 1991;Szwarc and Mukhopadhyay, 1996) or on dynamic programming (Srinivasan, 1971;Lawler, 1977;Schrage and Baker, 1978;Potts andvan Wassenhove, 1982, 1987).…”

Single facility sequencing with variable processing times and costs

“…Gupta, Gupta and Bector [4] considered the problem of minimizing job flow time variance in the single machine sequencing problem. Sen and Borah [10] considered the one machine n job problem and developed a branch and bound algorithm for minimizing the total job tardiness. Alidae [l] developed a heuristic solution procedure to minimize makespan in a single facility environment where the job processing times are a non·decreasing and differentiable function of their starting (waiting) times.…”