Modeling of a Continuous Review Supply Chain in an Uncertain Environment

Although supply chain (SC) has gained increasing attention in the last two decades and numerous SC problems have been identified and solved, there is a lack of systematic approach to solve SC problems in an uncertain environment. Since past data are not always available or reliable due to market durbulance, the sources of uncertainty (e.g. lead time, demand rate, inventory costs and backorder costs) are modeled by fuzzy numbers rather than by probabilistic distributions. In this paper, a realistic supply chain model with imprecise demand, lead-time and inventory costs have been formulated and an optimal policy is proposed to minimize the cost using man-machine interaction. Here we consider a two-level supply chain with single warehouse at the upper echelon and many retailers at the lowerechelon. The unsatisfied customer demands at the retailers are partially backordered using the control parameter b. The replenishment policy at all installations is continuous review policy. The imprecise parameters of lead-time, inventory costs and demand are expressed through linear/non-linear membership functions. These are represented by different types of membership functions, linear or quadratic, depending upon the prevailing supply condition and marketing environment. The imprecise parameters are transformed into corresponding interval numbers and then following the interval analysis, the objective function for average cost is changed into respective multi-objective functions. These functions are minimized and solved for a Pareto-optimum solution by interactive fuzzy decision-making procedure. This process leads to man-machine interaction for optimum and appropriate decision acceptable to the decision makers firm. The model is illustrated numerically and the results are presented in tabular forms.