This paper studies the Retailer Stackelberg game in a supply chain consisting of two manufacturers and one retailer where they compete simultaneously under three factors including price, service and simple price discount contract. It is assumed that the second manufacturer provides service directly to his customers, and the retailer provides service for the first product’s customers, while the retailer buys the first product under price discount from the first manufacturer. The analysis of the optimal equilibrium solutions and the results of the numerical examples show that if a manufacturer chooses the appropriate range of discount rate, he will gain more profit than when there is no discount given to the retailer. This situation can be considered as an effective tool for the coordination of the first manufacturer and the retailer to offer discount by manufacturer and to provide the service by the retailer. We obtain equilibrium solution of Retailer Stackelberg game and analyze the numerical examples under two cases: a) the manufacturers sell their products to the retailer without price discount contract. b) The first manufacturer sells his products to the retailer with the simple price discount contract. The preliminary results show that the service and the price discount contract can improve the performance of supply chain.

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Customer satisfaction is an important goal in total quality management. In order to meet this goal, it is necessary to use an evaluation model to measure customer satisfaction. This paper proposes an evaluation model for measuring the customer satisfaction level in a water supply domain. Some important criteria such as water quality, water quantity, responsibility of the company, etc. are distinguished and used in the proposed model. To integrate all of these criteria in a unit index, the analytic hierarchy process technique is used. The proposed model integrates customer opinions in a unit index to measure the customer satisfaction level. To evaluate the effectiveness and efficiency of the proposed model, Hamedan Water Company is studied as a case study. The results show that the proposed model can be used as a useful tool for analyzing customer satisfaction levels in water supply domains for other companies. The proposed model also distinguishes company strengths and weaknesses in the field of customer satisfaction.

The paper examines the application of semi-Markov models to the phenomenon of earthquakes in Tehran province. Generally, earthquakes are not independent of each other, and time and place of earthquakes are related to previous earthquakes; moreover, the time between earthquakes affects the pattern of their occurrence; thus, this occurrence can be likened to semi-Markov models. In our work, we divided the province of Tehran into six regions and grouped the earthquakes regarding their magnitude into three classes. Using a semi-Markov model, it proceeds to predict the likelihood of the time and place of occurrence of earthquakes in the province.