Time dependent vehicle routing problem with simultaneous pickup and delivery is considered A mixed integer programming formulation is developed for the problem Performance of the model is tested on test instances In this study, Time Dependent Vehicle Routing Problem with Simultaneous PickUp and Delivery (TD_VRP_SPD) which has not been considered in the literature, is described for the first time and a mathematical model is proposed for the solution of the problem. Experimental studies of the proposed mathematical model are performed on well-known test problems of the literature and the results are interpreted. Performance of the model evaluated computation time and percentage deviations to the optimal solutions. Figure A shows the average of C, R and RC type problems. The results of 112 problems were found to be optimal for 3 problems. All three of these problems are RC type problems. Despite the optimal result in the type of RC problems, the higher gap value indicates the difficulty of the problem.
In this study, two goal programming models are proposed for balancing resource dependent assembly lines with precise and fuzzy goals in order to provide flexibility for decision makers based on their decision environment and preferred priorities. Three conflicting goals, namely, total number of utilized workstations, cycle time and total cost of additional resources (equipment and assistant workers) are considered. The proposed models are validated on illustrative examples and scenario analyses are performed with different priority levels of the goals. The results show that the proposed goal programming formulations are valid and useful for balancing resource dependent assembly lines.
Approximately 24% of the world energy requirement is supplied by natural gas. A natural gas distribution system in a city consists of four main processes, i.e. construction, operating, internal installations, and customer services, which are connected to each other. In this study, customer services processes of the distribution system which are directly related to customers is considered. Mathematical formulations are presented for customer services processes such as district design, route planning and mobile team workload assignment, and applied on one of the authorized natural gas distribution company in Turkey. Performance of the proposed formulations is compared with the current system by means of the number of mobile teams and amount of workloads. The computational studies show that the number of mobile teams of the proposed system is 37% lower than the current system.
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