In this study, a mathematical programming model is proposed for scheduling problem of nurses' labor shifts. The developed mathematical programming model's aim is to minimize nurses' total idle waiting time during a week planning horizon. In this model, investigated constraints are as follows: (1) Maximum total working time a week for each nurse must not be exceeded. (2) After a nurse works a shift, the nurse can be assigned to another shift after two shifts at least. This constraints-set ensures resting of the nurse after the nurse works a shift. (3) Total number of nurses worked for each shift must be controlled with maximum and minimum bounds given for number of nurses for each shift. In this manner, total number of nurses worked for each shift is between maximum and minimum limit-values given for each shift. This constraint ensures flexibility to the user to determine number of nurses for each shift. (4) The decision variable that shows nurse-shift assignment pairs is 0 or 1. In this study, maximum total working time a week for a nurse, total number of nurses in a health service, maximum and minimum numbers of nurses worked a shift are user-specified parameters. In this way, this model can be adapted for the studies with different values of these parameters. In this study, the developed model is illustrated using a numerical example and then LINGO8.0 software is used to ensure the global optimum solution of the developed model. Results and also sensitivity analysis carried out for this example are presented in the study.

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In this article, an integer mathematical programming model for the design problem of flexible cellular manufacturing systems is proposed. The developed mathematical programming model whose objective function is to minimize total design cost including cost of operating parts on machines, cost of using tools on machines, and cost of assigning employees to cells, also contains the present value method. Thus, it is ensured that the operational costs that occur along a certain time period are also taken into account. LINGO 19.0 optimization program software is used for the optimum solution of the integer mathematical programming model with the present value method whose objective function is to minimize the total design cost. In this article, the application of the model and the analysis related to the model are shown using a developed example problem. In addition, by ensuring the optimum design of flexible cellular manufacturing systems, the results of which alternative routes are used for processing parts, which machines are located in which cells, and which employees are assigned to which cells, are obtained. Then, a sensitivity analysis is presented to show the importance of alternative routes of parts.