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Jordan and Drexl (1998) showed the equivalence between the discrete lot sizing and scheduling and the continuous batch sequencing problem for the single-machine case with sequence-dependent setup times and cost.
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In contrast to discrete lot-sizing models, the timing of stock receipts is variable and not confined to period boundaries.
This in combination with the increased number of product variants makes it necessary to base discrete lot-sizing models on an accordingly shorter period length which in turn causes a significant increase in the number of variables and constraints.
This modelling approach was derived from the "General Lot Sizing and Scheduling Problem (GLSP)" due to Fleischmann and Meyr (1997) and can be regarded as more realistic compared to purely discrete lot-sizing models.
Thus statements about subsequent 10-year returns are a bit more meaningful than they can be when covering 30-40 years when there are, by necessity, only 3-4 discrete periods.A lot of people think that anything before the 1970s is irrelevant, citing world wars, accounting standards or so on.
This requirement is satisfied (within the class of deterministic models) by dynamic discrete time lot sizing models with deterministic non-stationary demand.
We present an algorithm for solving an infinite horizon discrete time lot sizing problem with deterministic non-stationary demand and discounting of future cost.
Qian et al [18] study, in a quasi-static framework, discrete parking lots treated as links between origin and destination nodes with exogenous time-dependent demand.
The block planning approach presented in the subsequent sections tries to overcome the difficulties associated with classic discrete time-based lot-sizing models and constitutes an attempt to integrate lot sizing and scheduling in a way that can easily be implemented in practice.
In the following decades, discrete time-based lot-sizing models were introduced to cope with dynamic demand conditions (Wagner and Whitin 1958).
The block planning approach proposed in this paper relies on a continuous representation of time which makes it unnecessary to use binary variables for the product-period assignments and the changeovers as in capacitated discrete time-based lot-sizing models.
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