This paper proposes a mathematical model for the design of a two-echelon supply chain where a set of suppliers serve a set of terminal facilities that receive uncertain customer demands. This model integrates a number of system decisions in both the planning and operational stages, including facility location, multi-level service assignments, multi-modal transportation configuration, and inventory management. In particular, we consider probabilistic supplier disruptions that may halt product supply from certain suppliers from time to time. To mitigate the impact from supplier disruptions, a terminal facility may be assigned to multiple supplies that back up each other with different service priorities. With such multi-level service assignments, even when some suppliers are disrupted, a facility may still be supplied by the remaining functioning suppliers. Expensive expedited shipments yet with assured fast delivery may be used in complement to less expensive regular shipments yet with uncertain long lead times. Combining these two shipment modes can better leverage the inventory management against uncertain demands. We formulate this problem into a mix-integer nonlinear program that simultaneously determines all these interdependent system decisions to minimize the expected system cost under uncertainties from both suppliers and demands. A customized solution algorithm based on the Lagrangian relaxation is developed to efficiently solve this model. Several numerical examples are conduced to test the proposed model and draw managerial insights into how the key parameters affect the optimal system design.
We study the effect that installing sidewalks and crosswalks, as traffic calming facilities, has on the safety and usability of a transportation network with automobile, public transit and walking as modes of transportation. A mathematical programming model is proposed for this problem whose objective is to minimize the safety hazard for pedestrians and the total transportation cost of the network. We utilize a customized greedy heuristic and a simulated annealing algorithm for solving the problem. The computational results indicate that installing sidewalks and crosswalks at proper locations can reduce the overall transportation cost and improve pedestrians' safety.
Fuel truck dispatch between a bulk terminal and gas stations as distribution centers is vital in large cities. This dispatch is considered a vehicle routing problem (VRP), a well-known class of combinatorial optimization problems, and is difficult to solve. Instead of focusing on the VRP, this study provides a practical framework to find an optimal solution for the routing of a fuel delivery truck between a bulk terminal and a large number of stations supplied by it. First, six important criteria were proposed; they were believed to be necessary to consider for assessing safety and cost of different routes. Some ArcGIS tools were used to quantify these criteria—a difficult task, especially in large-scale transportation networks. Then a shortest path model based on a multicriteria objective was proposed to solve the routing problem and find the optimum routes between bulk terminal and fuel stations. The case study considered the Tehran, Iran, metropolitan area, with more than 12 million inhabitants, and solved the dispatching problem for two types of fuel: gasoline and liquefied petroleum gas. Scenarios were defined by considering different criteria for solving the routing problem. Then each scenario was evaluated on the basis of safety and economic indexes defined in this study. The findings show that using the proposed approach for solving the routing problem could improve the safety and economic indexes compared with the existing situation.
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