Development of an inventory model for two suppliers with random capacity considering supply disruption

Abstract

In today’s complex supply chain system supply disruptions due to occasional unavailability of raw materials or products pose serious consequences for firms and are thus of particular concern for strategic decision makers. Supply disruption occurs for diverse reasons including transportation problem, equipment failure, raw material shortages, natural calamities etc. If any of the above reasons occurs supplier may become unavailable at random times for random time length. The difficulty is that those who order do not know when supply shortages may start or end. Another important point to be noted is, from the beginning of the supply chain literature, it has been a common trend to assume that suppliers will always deliver the amount as ordered. But in reality in many cases suppliers may have random capacities which will lead to uncertain yield in orders. Again under random supplier capacities, the retailer should order from a number of suppliers in order to diversify the risk associated with shortages. The objective of this thesis is to develop an inventory model for two suppliers with random capacities considering supply disruption. A modified (Q, r) model is developed to tackle the problem of future supply uncertainty in response to the demand generated by Poisson process. The availability and unavailability of the suppliers is identified as respectively ON (0) and OFF (1) state whose lengths are treated as exponentially distributed and these states are modeled as four state CTMC (Continuous Time Markov Chain). Suppliers’ capacity is assumed to be exponentially distributed and diversification of order between them is considered when both of them are available. The transient probabilities of the four states CTMC is derived with the help of Kolmogorov forward equations and spectral theory. Concept from renewal reward process is used to identify the regenerative cycle and thereby develop average cost objective functions for two suppliers. Two suitable optimization algorithms are applied to search for the optimal values of the decision variables which are state dependent order quantities and reorder point to minimize the cost per unit time. A hypothetical example and its solution are then provided to have a better understanding about the demonstration of the proposed model. Finally sensitivity analysis is also carried out to have better insights about the model developed.