The nurse scheduling problem (NSP) has received a great amount of attention in recent years. In the NSP, the goal is to assign shifts to the nurses in order to satisfy the hospital's demand during the planning horizon by considering different objective functions. In this research, we focus on maximizing the nurses' preferences for working shifts and weekends off by considering several important factors such as hospital's policies, labor laws, governmental regulations, and the status of nurses at the end of the previous planning horizon in one of the largest hospitals in Iran i.e., Milad Hospital. Due to the shortage of available nurses, at first, the minimum total number of required nurses is determined. Then, a mathematical programming model is proposed to solve the problem optimally. Since the proposed research problem is NP-hard, a meta-heuristic algorithm based on simulated annealing (SA) is applied to heuristically solve the problem in a reasonable time. An initial feasible solution generator and several novel neighborhood structures are applied to enhance performance of the SA algorithm. Inspired from our observations in Milad hospital, random test problems are generated to evaluate the performance of the SA algorithm. The results of computational experiments indicate that the applied SA algorithm provides solutions with average percentage gap of 5.49 % compared to the upper bounds obtained from the mathematical model. Moreover, the applied SA algorithm provides significantly better solutions in a reasonable time than the schedules provided by the head nurses.
In this study, to price a product that can be simultaneously sold in the e-tail and retail channels, a dual-channel supply chain is considered containing one manufacturer and multiple retailers. In this setting, the game-theoretic approach is applied to obtain the equilibrium prices To our best knowledge, the game-theoretic frameworks proposed to price the products in the dual-channel supply chain have considered a single retailer in the retail channel, while multiple retailers can exist in the retail channel in practice. It is assumed that the manufacturer and retailers have the same decision powers. First, the Nash game model is established to set the prices in decentralized model A centralized model is presented to maximize the profit of the whole system. Then, a coordination mechanism based on the linear quantity discount schedule is applied to fully coordinate the supply chain. Finally, the Nash bargaining model is used to share the extra profit given by the whole system cooperation among the members Mathematics Subject Classification. 91A80, 91A40.
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