In this study an integrated model is proposed for the location inventory routing problem under uncertainty. This problem involves determining the location of distribution centers (DCs) in a three echelon supply chain. The DCs receive orders from the customer and according to a continuous review inventory replenishment policy place orders to the supplier. The products are directly shipped from the supplier to the DCs. The vehicles start from the DCs to fulfill the demands of the customers. Determining the routing of the vehicles is one of the decisions involved in this problem. The demands of customers are stochastically distributed and the capacity of DCs are limited. If one of the DCs undergo a disruption and is unable to fulfill the demands of the customers, shortage may occur. Moreover in the proposed model the shortage is considered as partial backlogging. This means that if shortage occurs, some of the orders result in lost sales and other orders are fulfilled in the next period. In order to optimally solve the proposed model a nonlinear integer programming (INLP) model is developed. However, since the problem is NP-hard, the mathematical formulation cannot be efficiently solved for large sized instances of the problem. Therefore an outer approximation method is developed to solve the problem more efficiently. The computational results show the efficiency of the proposed method.

Although supply chains disruptions rarely occur, their negative effects are prolonged and severe. In this paper, we propose a reliable capacitated supply chain network design (RSCND) model by considering random disruptions in both distribution centers and suppliers. The proposed model determines the optimal location of distribution centers (DC) with the highest reliability, the best plan to assign customers to opened DCs and assigns opened DCs to suitable suppliers with lowest transportation cost. In this study, random disruption occurs at the location, capacity of the distribution centers (DCs) and suppliers. It is assumed that a disrupted DC and a disrupted supplier may lose a portion of their capacities, and the rest of the disrupted DC & apos; s demand can be supplied by other DCs. In addition, we consider shortage in DCs, which can occur in either normal or disruption conditions and DCs, can support each other in such circumstances. Unlike other studies in the extent of literature, we use new approach to model the reliability of DCs; we consider a range of reliability instead of using binary variables. In order to solve the proposed model for real-world instances, a Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is applied. Preliminary results of testing the proposed model of this paper on several problems with different sizes provide seem to be promising.

One of the primary concerns on supply chain management is to handle risk components, properly. There are various reasons for having risk in supply chain such as natural disasters, unexpected incidents, etc. When a series of facilities are built and deployed, one or a number of them could probably fail at any time due to bad weather conditions, labor strikes, economic crises, sabotage or terrorist attacks and changes in ownership of the system. The objective of risk management is to reduce the effects of different domains to an acceptable level. To overcome the risk, we propose a reliable capacitated supply chain network design (RSCND) model by considering random disruptions risk in both distribution centers and suppliers. The proposed study of this paper considers three objective functions and the implementation is verified using some instance.