TÍTULO DE LA TESIS: “Un marco de referencia para el diseño de políticas de inventario en revisión periódica con demanda discreta y fill rate objetivo”

ABSTRACT

One of the most commonly customer service measure used to design the inventory control policies is the fill rate, which is defined as the fraction of demand that is immediately served from the on-hand stock. The main purpose of this thesis is to propose a reference framework to help managers to select the most efficient method to compute the order up to level, S, in periodic review inventory policies (R, S) when the fill rate is used as constrain and the demand process is considered stationary with a discrete, independent and identically distributed probability function considering either the backordering case and the lost sales case. Assuming a predefined review period R and a target fill rate, the problem consists of selecting the smaller order-up-to-level S that guarantees the achievement of the target fill rate. To reach this objective it is analyzed the performance of the available fill rate expressions in the literature (most of them approximations) to know when it is possible to use one of them and the risks associated with it.

In the literature we find quite a number works suggesting methods to estimate the fill rate in different context. However, few of those consider the periodic review systems, although these are arguably most realistic. In the backordering case, one limitation of the fill rate expressions is that they consider only continuous demand patterns despite of the discrete nature of demand is the most often in practical environments. Only in the lost sales case we find an approximation and an exact expression to compute the fill rate under discrete demand context. To achieve the aim of this thesis, the backordering fill rate expressions are reformulated basing on the same hypotheses assumed by each author and considering explicitly the discrete nature of the demand. Using these new expressions, we design two experiments which combines different demand distributions and an extensive range of values of the target fill rate and inventory policy parameters. The feasible combination of these parameters leads into 235,620 cases in the backordering case and 89,760 in the lost sales case. 

First, a descriptive analysis of the experimental results is carried out. Its purpose is to compare the performance of the approximated methods regarding the exact one. Second, an exploratory analysis is accomplished to identify under which circumstances the approximated methods show a similar behaviour in the estimation of the order up to level. It allows identifying a new space able to collect regions where approximated methods show that similar behaviour. For each of these regions it is qualified and quantified the risk incurred by each approximated method. Through this exhaustive analysis it is proposed the most efficient method to compute the order up to level according to the characteristics of the item and the inventory policy. Furthermore the thesis provides a framework to develop other practical approaches.

The reference framework presented in this thesis have a twofold practical use. On one hand, it can be used as predictive tool since provides information about the performance of the approximation. Then, a company can select the most suitable expression to establish the order-up-to-level being conscious of the risk of using it. On the other hand, it can be used as a corrective tool. In this sense, if a company is already using one of the fill rate approximations to determine the order-up-to-level, the reference framework provides information about the risk of using it.