Algorithms for Solving Production-Scheduling Problems

Abstract

Algorithms are developed for solving problems to minimize the length of production schedules. The algorithms generate anyone, or all, schedule(s) of a particular subset of all possible schedules, called the active schedules. This subset contains, in turn, a subset of the optimal schedules. It is further shown that every optimal schedule is equivalent to an active optimal schedule. Computational experience with the algorithms shows that it is practical, in problems of small size, to generate the complete set of all active schedules and to pick the optimal schedules directly from this set and, when this is not practical, to random sample from the bet of all active schedules and, thus, to produce schedules that are optimal with a probability as close to unity as is desired. The basic algorithm can also generate the particular schedules produced by well-known machine loading rules.

Particle Swarm Optimisation for Open Shop Problems with Fuzzy Durations

“…2: The pF G&T algorithm Decodification of a particle may be done in different ways. For the crisp job shop and by extension for the open shop, it is common to use the G&T algorithm [6], which is an active schedule builder. A schedule is active if one task must be delayed for any other one to start earlier.…”

Metaheuristics for the multi-objective FJSP with sequence-dependent set-up times, auxiliary resources and machine down time

“…In this paper, Giffler and Thompson's (1960) heuristic (initially developed in 1960 and since then successfully used by Sha and Hsu (2006) and Gao et al (2006)) was extended to include the unique problem characteristics of the Optimatix environment (Algorithm 3). Figure 5 provides an example of the procedure followed to obtain Q i , the set of possible starting times of operation i on resource d i .…”

“…6, the priorities can be converted into the job permutation: {1, 4, 3, 2}. However, Giffler and Thompson's (1960) heuristic ensures that the precedence constraints between operations are satisfied and subsequently, the schedule in Fig. 6 is obtained.…”

“…A sorting mechanism (which is given in Algorithm 4) is used to decode the real-valued n-dimensional vector into its corresponding resource indices and priorities. Giffler and Thompson's (1960) schedulebuilding heuristic (Algorithm 3) can then be applied directly. From the example in Fig.…”

“…However, the limitations of Giffler and Thompson's (1960) heuristic, as identified in the previous section, are still applicable. Furthermore, in most traditional optimization applications one dimension is used to denote one unique and separate concept.…”