Vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. Previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. This paper presents a bi-objective mathematical model for single manufacture multi-retailer with multi-product in order to maximize their benefits. It is assumed that demand is a decreasing and convex function of the retail price. In this paper, common replenishment cycle is considered for the manufacturer and its retailers. Then, the proposed model converts to the single-objective optimization problem using a weighted sum method. A genetic algorithm (GA) is applied to solve it and response surface methodology is employed to tune the GA parameters. Finally, several numerical examples are investigated to demonstrate the applicability of the proposed model and solution approach.

The present study aimed to design a bi-objective bi-level mathematical model for multi-dimensional cellular manufacturing system. Minimizing the total number of voids and balancing the assigned workloads to cells are regarded as two objectives of the upper level of the model. However, the lower level attempts to maximize the workers' interest to work together in a special cell. To this aim, two nested bi-level metaheuristics including particle swarm optimization (NBL-PSO) and a population-based simulated annealing algorithm (NBL-PBSA) were implemented to solve the model. In addition, the goal programming approach was utilized in the upper level procedure of these algorithms. Further, nine numerical examples were applied to verify the suggested framework and the TOPSIS method was used to find the better algorithm. Furthermore, the best weights for upper level objectives were tuned by using a weight sensitivity analysis. Based on computational results, all three objectives were different from their ideal goals when decisions about inter and intra-cell layouts, and cell formation to balance the assigned workloads by considering voids and workers' interest were simultaneously madeby considering a wide assumption-made problem closer to the real world. Finally, NBL-PBSA could perform better than NBL-PSO, which confirmed the efficiency of the proposed framework.

One of the most important factors in a humanitarian supply chain during a disaster is a timely and e cient response. Delivering emergency commodities to the a ected areas is also of signi cance in reducing consequences. Moreover, transferring the injured people in the fastest and shortest time period using all available resources is quite important. To this end, a multi-echelon multi-objective forward and backward relief network is proposed that considers the location of hospitals, local warehouses, and hybrid centers which are hospital-warehouse centers in the pre-disaster phase. In the postdisaster phase, routing the relief commodities should be considered in the forward route. In the backward route, some vehicles that can transfer the injured people after delivering commodities, called hybrid transportation facilities, will take the injured to hospitals and hybrid centers. According to the degree of hardness, a hybrid Non-dominated Sorting Genetic Algorithm (NSGA-II) with Simulated Annealing (SA) and Variable Neighborhood Search (VNS) algorithms was proposed to solve the given problems. The results obtained from this hybrid algorithm were compared with those from NSGA-II and multi-objective SA-VNS using  ve metrics (i. e., the number of Pareto, mean ideal distance, spacing, diversity, and time), and it was concluded that the proposed hybrid algorithm outperformed the two foregoing algorithms.

In most past studies on Hub Location Problem (HLP), failure probability is limited to a constant value; however, in reality, it depends on various factors including natural disasters such as floods and earthquakes, commodity ow, institutional elements (strikes), etc. This paper looks into the problem of the hub network design through a new model. The problem is to maximize network reliability and minimize the total routing cost simultaneously. In order to provide a more realistic model, the hub's failure probabilities were considered as a function of the hub's incoming traffic. Reserve hub elements were also taken into account in the model with the aim of increasing network reliability. To solve the model, a Non-dominated Sorting Genetic Algorithm (NSGA-II) was presented. The parameters of the algorithm were tuned using Taguchi method. The proposed solution was then carried out in a case study where the results confirmed the acceptable performance of the model; moreover, sensitivity analysis was performed in order to describe the effects of critical parameters on objective functions.

Emergency blood distribution seeks to employ different means in order to optimize the amount of blood transported while timely provision. This paper addresses the concept of blood distribution management in disastrous conditions and develops a fuzzy scenario-based bi-objective model whereas blood compatibility concept is incorporated in the model, and the aim is to minimize the level of unsatisfied demand of Affected Areas (AAs) while minimizing the cost of the supply chain. The blood supply chain network under investigation consists of blood suppliers (hospitals or blood centers), Blood Distribution Centers (BDCs), and AAs. Demand and capacity, as well as cost, are the sources of uncertainty and in accordance with the nature of the problem, the fuzzy-stochastic programming method is applied to deal with these uncertainties. After removing nonlinear terms, Ɛ-constraint solves the bi-objective model as a single objective one. Finally, we apply a case from Iran to show the applicability of the model, results prove the role of blood distribution management in decreasing the unsatisfied demand about 38%.