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Abstract
The objective of this paper is to propose a lot-sizing methodology for an inventory system that faces time-dependent random demands and that seeks to minimize total cost as a function of order, purchase, holding and shortage costs. A two-stage stochastic programming framework is derived to optimize lot-sizing decisions over a time horizon. To this end, we simulate a demand time-series by using a generalized autoregressive moving average structure. The modeling includes covariates of the demand, which are used as predictors of this. We describe an algorithm that summarizes the methodology and we discuss its computational framework. A case study with unpublished real-world data is presented to illustrate the potential of this methodology. We report that the accuracy of the demand variance estimator improves when a temporal structure is considered, instead of assuming time-independent demand. The methodology is useful in decisions related to inventory logistics management when the demand shows patterns of temporal dependence.
Highlights
Introduction and bibliographical reviewThe use of inventory models is important when managing a logistically efficient organization [1,2,3]
To evaluate the purchase plan of the economic lot-sizing (ELS) obtained from stochastic programming (SP) models based on generation of scenarios, it is possible to apply the optimization to a realistic framework of the rolling horizon using out-of-sample scenarios
We can contrast the value of a solution in stochastic scenarios with respect to a solution obtained in a deterministic scenario, comparing the percentage increase of the total cost (TC) we pay for ignoring uncertainty [46]
Summary
Introduction and bibliographical reviewThe use of inventory models is important when managing a logistically efficient organization [1,2,3]. A typical objective for evaluating an inventory system is to minimize the total cost (TC), which is a function of purchase cost, ordering cost per lot (or setup), inventory holding cost, and shortage cost [4]. The inventory system should establish an economic order quantity (EOQ) or lot size to satisfy demand [5, 6]. The EOQ model often considers a single period of decision and assumes a constant rate of demand per unit time (DPUT). Note that this model can consider multiple periods with more than one level for the decision stages, but in that case the DPUT rate is frequently non-constant. The multi-period EOQ model may conduct to an inventory cost greater than that obtained with single-period EOQ model [4]
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