Earliness-tardiness scheduling around almost equal due dates

The just-in-time concept in manufacturing has aroused interest in machine scheduling problems with earliness-tardiness penalties. In particular, common due date problems, which are structurally less complicated than problems with general due dates, have emerged as an interesting and prolific field of research

Earliness-tardiness scheduling around almost equal due dates

Discusses the existence of another class of problems that are structurally less complicated than the general earliness-tardiness problem. Details of common due date problems; Logic behind Emmons' matching algorithm; List of earliness-tardiness problems to which the optimality principle of the dynamic algorithm applies; Properties that apply to the variants of dynamic programming

Earliness-Tardiness Scheduling Around Almost Equal Due Dates

The just-in-time concept in manufacturing has aroused interest in machine scheduling problems with earliness-tardiness penalties. In particular, common due date problems, which are structurally less complicated than problems with general due dates, have emerged as an interesting and prolific field of research. We prove that so-called almost common due date problems, in which the due date d j and processing time p j of each job J j (j = 1; : : : ; n) are such that d j 2 [D; D+p j ] for some constant D, are structurally less complicated also. Our main contribution is an O(n 2 ) time dynamic programming algorithm for the almost common due date problem with large D. The dynamic programming algorithm is interesting in its own right, since the optimality principle behind it applies to other common due date and almost common due date problems as well. 1980 Mathematics Subject Classification (1991): 90B35. Key Words and Phrases: scheduling with earliness and tardiness penalties, almost eq..