---

The Shapley value, one of the most common solution concepts of cooperative game theory is defined and axiomatically characterized in different game-theoretic models. Certainly, the Shapley value can be used in interesting sharing cost/reward problems in the Operations Research area such as connection, routing, scheduling, production and inventory situations. In this paper, we focus on the Shapley value for cooperative games, where the set of players is finite and the coalition values are interval grey numbers. The central question in this paper is how to characterize the grey Shapley value. In this context, we present two alternative axiomatic characterizations. First, we characterize the grey Shapley value using the properties of efficiency, symmetry and strong monotonicity. Second, we characterize the grey Shapley value by using the grey dividends.

---

In this research author reviews references related to the topic of multi criterion (goal programming, multiple objective linear and nonlinear programming, bi-criterion programming, Multi Attribute Decision Making, Compromise Programming, Surrogate Worth Trade-off Method) and various versions of vehicle routing problem (VRP), Multi depot VRP (MDVRP), VRP with time windows (VRPWTW), Stochastic VRP (SVRP), Capacitated VRP (CVRP), Fuzzy VRP (FVRP), Location VRP (LVRP), Backhauling VRP(BHVRP), Facility Location VRP (FLVRP), and Inventory control VRP (ICVRP). Although, VRP is a research area with rich research works and powerful researchers there found only 81 articles that relates various vehicle routing type problems with various multiple objectives techniques. This author found that there is no research done in some areas of VRP (i.e., FVRP, ICVRP, LRP and CVRP). It is interesting to see that this research area was completely an unattractive to master students (with zero research reported) and a somewhat attractive area to doctoral students (with 6 researches reported). Among the many multi criterion programming techniques available only three of them (goal programming, bi-criterion programming, linear and nonlinear multi objective programming) are being employed to solve the problem.

---

Material selection is a challenging issue in manufacturing processes while the inappropriate selected material may lead to fail the manufacturing process or end user experience especially in high-tech industries such as aircraft and shipping. Every material has different quantitative and qualitative criteria which should be considered simultaneously when assessing and selecting the right material. A weighted linear optimization method (WLOM) in the class of data envelopment analysis which exists in literature is adopted to address material selection problem while accounting for both qualitative and quantitative criteria. However, it is demonstrated the adopted WLOM method is not able to produce a full ranking vector for the material selection problems borrowed from the literature. Thus, an augmented common weight data envelopment analysis model (ACWDEA) is developed in this paper with the aim of eliminating deficiencies of WLOM model. The proposed ACWDEA is able to produce full ranking vector in decision making problems with less computational complexities in superior to the WLOM. Two material selection problems are solved and results are compared with WLOM and previous methods. Finally, the robustness and effectiveness of the proposed ACWDEA method are evaluated through Spearman’s correlation tests.