Abstract
In this paper, a novel way of modeling uncertainty on demand in the single-item dynamic lot sizing problem is proposed and studied. The uncertainty is not related to the demand quantity, but rather to the demand timing, i.e., the demand fully occurs in a single period of a given time interval with a given probability and no partial delivery is allowed. The problem is first motivated and modeled. Our modeling naturally correlates uncertain demands in different periods contrary to most of the literature in lot sizing. Dynamic programs are then proposed for the general case of multiple demands with stochastic demand timing and for several special cases. We also show that the most general case where the backlog cost depends both on the time period and the stochastic demand is NP-hard.
Highlights
This paper tackles a single-item dynamic lot sizing problem, i.e., quantities to be produced or replenished on a finite planning horizon discretized in periods must be determined to satisfy timevarying demands
As it is common in lot sizing, we propose to formalize our problem with the variables in [0, 1] zlt, the fraction of the deterministic demand Dt produced in period l ≤ t, and zli, the fraction of the stochastic demand quantity di produced in period l ≤ ui
We extend our previous results to the more general case where each stochastic demand timing can be seen as an order with a specific backlog cost, i.e. bit depends both on period t and on stochastic demand quantity di
Summary
This paper tackles a single-item dynamic lot sizing problem, i.e., quantities to be produced or replenished on a finite planning horizon discretized in periods must be determined to satisfy timevarying demands. An alternative to expected cost is to use service levels, modeled through chance constraints, as in Tempelmeier (2007) In their survey, Brahimi et al (2017) show (see Table 2) that the vast majority of the research literature in single-item stochastic dynamic lot sizing investigate stochastic demands with a particular focus on volumes. The supplier company knows very well the quantity that will be either picked up by or delivered to a customer, but is not able to know exactly when, an interval of several days is known This is noticeable in operational or tactical production and inventory planning over several weeks with periods of a day, where demand and order quantities are well established, and is a typical context in process industries, which satisfy the demands of other industries.
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