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Vaccines and refrigerated trucks are critical resources for controlling the spread of epidemic diseases. This paper addresses a novel bi-objective vehicle routing problem to distribute vaccines among different regions to control the spread of communicable diseases in the aftermath of a disaster. The developed model aims to minimize the social cost incurred by considering different priority groups under the SIR epidemic model and the cost of vehicles used simultaneously. A hybrid solution procedure is developed using the weighted augmented -constraint method, optimal control theory, and dynamic programming. To evaluate the performance of the model and the solution approach, four small test problems and an illustrative example inspired by a real case are presented and their numerical results are discussed.

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Warranty as a kind of service contract plays a key role in business and legal transactions today. In this paper, we present for the first time a tri-partite service contract model including a manufacturer, an agent and a customer under risk parameter. We determine an optimal sale price, a warranty period and a warranty price for the manufacturer under quantity discount policies. The optimal maintenance cost or repair cost is obtained by the maximizing of an agent's profit according to the penalty cost incurred due to waiting time. Moreover, the customer maximizes his/her satisfaction by purchasing several products and choosing a portfolio of service contracts. Whereas the risk-aversion parameter on the customer side has an impact on their decision for choosing the type of service contract. On the other hand, the discount rate regime on the manufacturer side influences the number of purchased products. We present some numerical examples to illustrate the working logic of our model.

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