ahmad makoui

The vehicle routing problem (VRP) is one of the most well-known optimization problems. It has been the focus of extensive research on transportation systems planning in recent decades. The present aims to investigate the problem of routing vehicles from the pharmacy for the delivery of drugs at patients' homes. The problem of delivery of drugs required by patients is accompanied by a series of operational limitations. It is assumed that each patient receives drugs through a vehicle, and also drugs must reach the patients’ homes before a certain time. To balance the workload of drivers, the maximum number of homes that each vehicle can go to deliver medicines is predetermined. The presented model determines the number of vehicles, the routes of the vehicles and also the time at which drugs are delivered at each patient’ home. To solve the proposed model, in addition to GAMS optimization software, a genetic algorithm is proposed for large-scale instances. The computational results demonstrate that the proposed model can be used to make optimal decisions on the distribution of drugs from pharmacies to patients' homes.

The large number of heterogeneous players makes difficult to determine the equilibrium point in the game theory, so firstly the players are clustered and then the game theory is used in two stages. First, the clusters compete to determine the point of equilibrium. Then the players within each cluster compete to determine the share and the payoff for each player. In this paper, the results of the game theory in the competition between 47 Airlines at the Imam Khomeini Airport are evaluated by statistical tests. The payoff functions in this model are the cost of the stand and the share of the jet way stand for each airline. The results show that the players clustering can be useful when the number of the players is high. ANOVA and the T student test in paired observations was used For the validation of the proposed algorithm.The result of P-Value = 1 were obtained by ANOVA with α = 0.05 in Minitab software. The share of jet way stand for airlines in the number of clusters 11, 12, 13, 15 and 47 (without clustering mode) did not differ significantly. Also the T student test in paired observations was performed to compare the non-clustering (k = 47) with different clustering states in the number of 11, 12, 13 and 15 clusters. Respectively P-Value results were obtained 0.930. 0.947, 0.944, 0.964. These results shown that there is no significant difference in the contribution of Airlines from the jet stand without clustering and clustering. The results of this research show how to using clustering in game theory approach on a real world case. Also considering airlines as a member of transportation modes can be useful.