ABSTRACT
The objective of the thesis is to propose a methodology for the efficient estimation of the order up to level (S) in periodic review inventory policies (R, S) when the cycle service level (CSL) is used as constrain and the demand process is considered stationary with a discrete, independent and identically distributed probability function. To reach this objective it is analysed the performance of four methods (one of them exact) used to compute S. The exact method involves a high computational effort which is not justified for any item and any circumstances. Therefore it is important to know when it is possible to use an approximated method and the risks associated with it.
The most widely method used to calculate the CSL, named classic in this thesis, is only an approximation of the exact one. Furthermore, this thesis shows that when this is use for determining the order up to level does not always ensure to achieve the CSL. The methods analyzed in the thesis are: (1) the exact method proposed by Cardós et al. (2006); (2) The approximation method, named PI, derived by Cardós and Babiloni (2008) to simplify the exact method, (3) The approximation method, named PII, derived by Cardós and Babiloni (2008) to simplify the exact and the PI method, and (4) the classic method [see p. ej. Silver et al. (1998)] which is a simplification of the exact, PI and PII method [Cardós and Babiloni (2008)].
The proposed methodology is based on a wide enough experiment (115.941 cases). 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 and to analyse the influence of some variables on the performance of the approximated methods. 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 thesis is organized as follow. The objective and the general outline are explained in the Chapter 1. Chapter 2 is devoted to review the literature about the design of periodic review policies (R, S) when the cycle service level is used as constrain and demand process is stationary with discrete, known and i.i.d probability function. It reviews the steps to design (R, S) policy including the classification and categorization of the item, the restriction of design, methods of calculating the order up to level and measurements of the performance of the policy. Chapter 3 shows the purpose and the assumptions used in the design of the experiment. Chapter 4 and 5 are devoted to the descriptive and exploratory analysis of the experimental results respectively. The exploratory analysis is done using the classification and regression trees, a data mining statistical technique which has a predictive and exploratory nature. This technique allows identifying the variables which define the performance of the approximated methods when in the order up to level calculation. In Chapter 6 it is discussed the classification errors incurred by the approximation methods and it is proposed a methodology for the efficient estimation of the order up to level based on traditional criteria of management and the classification ABC. Finally, Chapter 7 presents the conclusions and outlines the main lines of future research.


REFERENCES
Cardos, M.; Babiloni, M. E. (2008). Exact and approximated calculation of the cycle service level in periodic review policies. Fifteenth International Working Seminar on Production Economics.
Cardós, M.; Miralles, C.; Ros, L. (2006). An exact calculation of the cycle service level in a generalized periodic review system. Journal of the Operational Research Society, Vol.57, No 10, pp. 1252-1255.
Silver, E. A.; Pyke, D. F.; Peterson, R. (1998). Inventory Management and Production Planning and Scheduling. Third Edition. John Wiley & Sons.