Abstract
This chapter deals with the multi-mode project scheduling problem (MMPSP). As outlined in Chapter 2, the MMPSP is probably the most general and most difficult problem dealt with. A description of the model as well as a 0–1 programming formulation has been provided in Section 2.3. Furthermore, there it has been proven that even the feasibility problem of MMPSP, the so-called mode-assignment problem (MAP), is NP-complete. As a consequence, solution procedures proposed so far suffer from severe drawbacks: Exact procedures can only solve very small instances with roughly up to 16 activities to optimality, while heuristic solution approaches fail to generate feasible solutions quite often. Even when feasible solutions are produced, the quality of the latter in terms of the average deviation from the optimum objective function value is rather poor. This discrepancy between applicability of the MMPSP on the one side and the lack of good solution procedures for it on the other side has been the motivation to design a new heuristic capable to solve real-world instances close to optimality.
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References
The same set of instances will be employed in the computational study of Section 6.3.
A schedule which belongs to the set of active schedules is termed by Speranza / Vercellis (1993) a “tight” schedule.
Slowinski et al. do not mention the connection between their heuristic and the exact procedure of Patterson et al. (1989). Instead, they classify the heuristic as a parallel scheduling scheme by referring to the parallel algorithm as outlined by Kelley (1963). Although the formal description of the algorithm is rather vague and bears a lot of ambiguities, the following can be stated: Indeed, the procedure makes use of the schedule time, which is a significant feature of the parallel scheduling scheme. But at the same time the decision set is restricted to activities which are feasible w.r.t precedence constraints only. Hence, if an activity is selected for scheduling, it might have to be right-shifted in order to start after the current schedule time. Consequently, the solution procedure can neither be characterised as parallel nor as serial.
Throughout the project scheduling literature two synonymous expressions are used: slack (cf. e.g. Levy et al. (1963) and Wiest (1964)) and float (cf. e.g. Elmaghraby (1977, p. 145) and Moder et al. (1983, p.78)). In analogy to the well-known minimum slack (MSLK) priority rule (cf. formula 5.9), in here it is referred to slack. The different kinds of slack (float), e.g. total float, free float, interfering float etc., as a result of the time analysis only, are not treated in this study. For details refer to Moder et al. (1983, p. 78) and Ziegler (1985).
For the values actually employed in the probability mappings, cf. Table 5.15.
For details of the study refer to Kolisch et al. (1992).
E.g., the CPU time of the exact procedure of Sprecher increases with more than factor 100 when the number of non-dummy activities is increased form 10 to 16 (cf. Sprecher (1994)).
Where SPP (MPP) denotes the single-pass (multi-priority rule) procedure of Boctor (1994), TE the truncated enumeration of Talbot (1982), BSP/I (BSP/II) the original (improved) version of the regret-based biased random sampling procedure of Drexl / Grünewald (1993), and TBB the truncated branch and bound procedure of Sprecher (1994). TBB has been coded in C and implemented on an IBM PS2/70 model with 80486dx processor and 25 MHz clockpulse.
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© 1995 Springer-Verlag Berlin Heidelberg
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Kolisch, R. (1995). The Multi-Mode Project Scheduling Problem. In: Project Scheduling under Resource Constraints. Production and Logistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-50296-5_6
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DOI: https://doi.org/10.1007/978-3-642-50296-5_6
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0829-2
Online ISBN: 978-3-642-50296-5
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