Abstract
In this chapter we compare the BSP with the discrete lotsizing and scheduling problem (DLSP). We show that BSP and DLSP address the same planning problem, and we examine the question which solution procedures of the different models are better suited to solve it.
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References
The formulation in Salomon et al. [110] does not exclude undesired schedules and so we use an extended formulation.
Recall that in the CLSP only the lotsize per period is determined, but not the sequence of lots in a period.
In the ba case, additional variables for BA and BA2LV are needed to determine (i) the batch completion and (ii) the batch size (which both depend on Yi,t) to state the inventory balance constraints.
But note that σ a is not a regenerative schedule since job (1,3) starts a batch at d(1,2) = 20.
In [24], the slack in a production schedule for an item i corresponds to unsatisfied demand for this item.
This procedure is not further specified in [24]. In an earlier working paper a reference to the mathematical programming software LINDO [87] is given.
The solutions of DACGP are not known, hence we cannot calculate Aavg for DACGP.
For these parameters, average (maximal) CPU seconds vary between 3.1 (4.8) and 11.9 (24.9) on a 486/33 Mhz PC.
A similar observation has been made by Fleischmann who conjectures that “primarily the heuristics need to be improved”([50], p. 403).
Cf. e.g. Table 4.10 for problem class 88-92hard. The number of unsuccessful trials #UT is 29 (6) out of 10 15 trials for BRJSA2LV (GA[Foba,sti])
Objective function values can only be compared for an example given in [20], (Table 1 and Figures 3 to 5). In [20] a solution is given for the second level, which consists of a sequence of 10 batches. This solution can be improved interchanging the positions of the batch 2 with 3 and batch 6 with 7, which is the solution of GA[Foba,sti] on the second level for this instance. In [20] batches 2,3, and 6,7 are not ordered according to Theorem 2.10.
In the PLSP there is no unit capacity per period, and not more than two items can be produced per period. The construction of an equivalent BSP with these assumptions requires much more technical overhead and modification. However, for the models in Chapter 2 an equivalence can be stated for a special case: the PLSP with demands which are multiples of the (time invariant) period capacity is equivalent to [l/fam, if holding costs are equal.
In multi-level problems the constraints imposed by the product structure are also expressed in different ways in scheduling and in lotsizing models. On the one hand there are precedence constraints between jobs for the construction of a schedule, and planning is done for jobs. On the other hand there are inventory balance constraints in lotsizing, and planning is done for quantities.
As a consequence, the mathematical programming formulation in Table 4.3 becomes more difficult in this case. A much shorter formulation can be given for the (standard) DLSP with zero setup times and sequence independent setup costs (cf. e.g. Fleischmann [49]).
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© 1996 Springer-Verlag Berlin Heidelberg
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Jordan, C. (1996). Discrete Lotsizing and Scheduling by Batch Sequencing. In: Batching and Scheduling. Lecture Notes in Economics and Mathematical Systems, vol 437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-48403-2_4
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DOI: https://doi.org/10.1007/978-3-642-48403-2_4
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