---

In this study, a two-echelon supplier-manufacturer system with finite production rate and lead time is proposed. It is assumed that shortage is not permitted and the lot size of manufacturer (second echelon) is m-factors of the lot size of supplier (first echelon) and supplier can supply the manufacturer’s lot size in several shipments in each cycle. So, the production rate of supplier is greater than manufacturer’s. The proposed model aims to determine the optimal lot-size of each echelon such that the total cost of system is minimized. First, the problem is studied regardless of lead time and the optimal value of the lot sizes and the number of shipments is determined through analytical relations. Then, an exact solution algorithm for the problem is presented for the case with non-zero lead time. Finally, the performance of the proposed algorithm is reviewed by solving some numerical instances of the problem.

---

Growing tendency for Urbanization and rapid development of the cities has resulted in urban neighborhoods obstructing the access of each other to the natural sources e.g. solar energy, natural ventilation. Sunlight as the main part of input energy in urban energy balance equation and natural lighting is of vital importance. This paper attempts to achieve an optimum morphology for residential blocks in urban area with the highest exposure to the sunlight. To reach this goal a pilot area in Tabriz’s downtown was selected and regarding solar angle, local street regulations and the width of surrounding streets 3 different scenarios for the buildings blocks were defined. Using a three-dimensional microclimate model, ENVI-met, solar access of defined scenarios was calculated for the longest and the shortest day of the year. Results showed that Type C2 (highest, more open spaces) is a more efficient style for winter times as it receives more of the sun’s energy and also the amount of sun it gets during a day and type B2 (medium open space and height) is the better for summer as it gets less energy from the sun and it is exposed to sunlight less than other types in a hot summer day.

---

The open vehicle routing problem (OVRP) is a variance of the vehicle routing problem (VRP) that has a unique character which is its open path form. This means that the vehicles are not required to return to the depot after completing service. Because this problem belongs to the NP-hard problems, many metaheuristic approaches like the ant colony optimization (ACO) have been used to solve OVRP in recent years. The versions of ACO have some shortcomings like its slow computing speed and local-convergence. Therefore, in this paper, we present an efficient hybrid elite ant system called EHEAS in which a new state transition rule, tabu search as an effective local search algorithm and a new pheromone updating rule are used for more improving solutions. These modifications avoid the premature convergence and make better solutions. Computational results on sixteen standard benchmark problem instances show that the proposed algorithm finds closely the best known solutions for most of the instances in which ten best known solutions are also found. In addition, EHEAS is comparable in terms of solution quality to the best performing published metaheuristics.