In this paper, the issue of cooperative (co-op) promotion efforts is addressed in a two-stage supply chain (SC). The investigated SC includes one monopolistic manufacturer and two duopolistic retailers facing different market demands. The customers’ demand is affected by both advertising efforts of the manufacturer and two retailers. Moreover, the retailers compete with each other on local advertising investments within the market. In order to boost the retailers’ advertising level, it is assumed that the manufacturer pays a ratio of the retailers' advertising expenditures. We propose four non-cooperative game scenarios and one cooperative game. Non-cooperative models are established through both Stackelberg and Nash game between two echelons. Moreover, both Cournot and Collusion behaviors are assumed to be followed by two retailers. We develop a promotion cost sharing contract to achieve the channel coordination. Under cooperation model, all SC members seek to reach the highest profit for the entire SC by considering the bargaining power of the SC participants. In each game scenario the optimal solution and unique equilibrium are determined. In addition, a comparison on the advertising level of all SC members along with the value of participation rate are provided. In addition, the feasibility of the cooperative game is discussed and resulted.

This study is an inventory model with consideration of price, stock dependent demand, partially backlogged shortages, and two constant deterioration rates. In this model, demand function depends on price and stock while during the shortage time, demand depends only on price of the product. The deterioration is taken into account as a non-instantaneous, once the item is stocked in retailer’s house, any time deterioration can start with a constant rate for a certain period, then this deterioration rate increases. Shortages are allowed and it is partially backlogged. The corresponding inventory problem constitutes a non-linear constraint optimization problem. Here this problem has been solved using Lingo 15 software and also give 3D graph with the help of MATLAB2010a to show the convexity of the objective function. Finally, to illustrate and validate the inventory model, a numerical example is used considering fixed price. To study the effect of changes of different inventory parameters, a sensitivity analysis has been carried out changing one parameter at a time holding other parameters unchanged.

In this paper, a weighted transfer point location problem is developed in which demand points have probabilistic coordinates. The proposed model is formulated as a probabilistic unconstrained nonlinear programming and the optimum values of decision variables are obtained in the form of probability distribution functions. Because of the complexity in solving the developed model by using the traditional solution approaches, a new stochastic inference method called Probabilistic Role Base (PRB) is developed based on the derived optimum probability distribution functions of the decision variables. This method is used to infer the optimum or near optimum values of all decision variables without solving nonlinear programming model, directly. Finally, to demonstrate the efficiency of the developed algorithm, a numerical example is presented and the results are compared with the optimum solution.

In this paper, an imperfect production inventory system with multi-production run for single vendor and single buyer is studied where the defective items are reworked after several production processes and there is no break down during the rework process. The model is considered for deteriorating items under two delivery policies in order to determine the delivery policy leading to the minimum holding cost of system. The objective of this model is to determine the optimal production setup, number of deliveries and lot size by minimizing the total relevant cost of the proposed vendor-buyer integrated system. To minimize the manufacturer’s and buyer’s holding cost, the supply of finished products are made in small quantities. The total relevant cost of the vendor and the buyer is derived and a numerical example is presented to demonstrate the utility of the model.

This article presents a broad review of Hub location problem (HLP), and its applications. The goal of this article is to provide a review on the newest and most recent publications on Hub location and its application in real world practices since 2013. While, there are some articles which reviewed hub location problem literature but some models were not covered in those articles. In this paper, we try to include capacitated models. We survey advances in analysis and modeling of the hub location problem including its variants and solution algorithm of HLPs. We emphasize the most applicable areas for Marine Transpiration. We show that first, majority of the articles consider network domain, while there are some articles which execute HLP in discrete and continuous domain. Also, the capacitated case attracts more attention in recent years. Finally, the contribution of any type of HLP in the literature is shown schematically.