Measures of bullwhip effect and inventory costs in supply chains

Abstract

The dissertation focuses on three main problems in measuring bullwhip effect and inventory cost in supply chains with the different demand processes such as first-order autoregressive, AR(1), and mixed first-order autoregressive-moving average, ARMA(1,1), models, as well as the deterministic and stochastic lead times. First, we consider a simple supply chain with one supplier and one retailer. The retailer faces an ARMA(1,1) demand process with a fixed order lead time, and employs a base stock inventory policy. We aim to develop an exact method for measuring a bullwhip effect on the supply chain by evaluating the ratio of the variance of order quantity experienced by the supplier to the actual variance of demand quantity. On the other hand, we quantify the impact of bullwhip effect on the supply chain as well as investigate the effect of autoregressive coefficient, moving average parameter, and lead time on the bullwhip effect. A series of numerical experiments is carried out to illustrate the model for the bullwhip effect measure and the model’s results. As a result, one of the most important findings in this problem is that the bullwhip effect does not always exist. In addition, the bullwhip effect also does not always increase when the order lead time increases. Secondly, the first problem is extended to the problem in which the order lead time is assumed to be stochastic and independent with the customer demand by the time while it is supposed to be deterministic in the previous problem. In fact, we develop the bullwhip effect measure in the two-stage supply chain with an AR(1) demand process. After that, a series of numerical studies is conducted to investigate behavior of a measure for the bullwhip effect with respect to autoregressive coefficient and stochastic order lead time in the case of AR(1) demand process. Moreover, the extension to an ARMA(1,1), demand process is also considered. As a result, in both cases of AR(1) and ARMA(1,1) demand proce...