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Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully label graphs. In this paper, first a new approach based on the mathematical programming technique is presented to model the graceful labeling problem. Then a “branching method” is developed to solve the problem for special classes of graphs. Computational results show the efficiency of the proposed algorithm for different classes of graphs. One of the interesting results of our model is in the class of trees. The largest tree known to be graceful has at most 27 vertices but our model can easily solve the graceful labeling for trees with 40 vertices.

Abstract. An important problem in todays industries is the cost issue, due to the high level of competition in the global market. This fact obliges organizations to focus on improvement of their production-distribution routes, in order to nd the best. The Supply Chain Network (SCN) is one of the, so-called, production-distribution models that has many layers and/or echelons. In this paper, a new SCN, which is more compatible with real world problems is presented, and then, two novel hybrid algorithms have been developed to solve the model. Each hybrid algorithm integrates the simulation technique with two metaheuristic algorithms, including the Genetic Algorithm (GA) and the Simulated Annealing Algorithm (SAA), namely, HSIM-META. The output of the simulation model is inserted as the initial population in tuned-parameter metaheuristic algorithms to nd near optimum solutions, which is in fact a new approach in the literature. To analyze the performance of the proposed algorithms, di erent numerical examples are presented. The computational results of the proposed HSIM-META, including hybrid simulation-GA (HSIM-GA) and hybrid simulation-SAA (HSIM-SAA), are compared to the GA and the SAA. Computational results show that the proposed HSIM-META has suitable accuracy and speed for use in real world applications.

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Pick up-dispatching problem together with delivery-dispatching problem of a multiple-load automated guided vehicle (AGV) system have been studied. By mixing different pick up-dispatching rules, several control strategies (alternatives) have been generated and the best control strategy has been determined considering some important criteria such as System Throughput (ST), Mean Flow Time of Parts (MFTP), Mean Tardiness of Parts (MFTP), AGV Idle Time (AGVIT), AGV Travel Full (AGVTF), AGV Travel Empty (AGVTE), AGV Load Time (AGVLT), AGV Unload Time (AGVUT), Mean Queue Length (MQL) and Mean Queue Waiting (MQW). For ranking the control strategies, a new framework based on MADM methods including fuzzy MADM and TOPSIS method were developed. Then several simulation experiments which had been based on a flow path layout to find the results were conducted. Finally, by using TOPSIS method, the control strategies were ranked. Furthermore, a similar approach was used for determining the optimal fleet size. The main contribution of this paper is developing a new approach combining the top managers' views in selecting the best control strategy for AGV systems while trying to optimize the fleet size at the mean time by combining MADM, MCDM and simulation methods.