This thesis studies two topics related to distributionally robust optimization in the areas of transportation and supply chain management.

The first part investigates the problem of location of quick charging stations to support long-distance trips for Electric Vehicles. Electric Vehicles (EVs) are gaining popularity with surging fuel costs and concerns on the environment. With the limited technology on battery capacity, it is necessary to locate enough quick charging stations along highways to ensure long-distance travel. We consider a location problem for quick charging stations for EVs and focus on the attractiveness of the different charging locations for travelers. A traveler who chooses to stop en route to recharge the EV incurs monetary (for electricity and charging serv...[ Read more ]

This thesis studies two topics related to distributionally robust optimization in the areas of transportation and supply chain management.

The first part investigates the problem of location of quick charging stations to support long-distance trips for Electric Vehicles. Electric Vehicles (EVs) are gaining popularity with surging fuel costs and concerns on the environment. With the limited technology on battery capacity, it is necessary to locate enough quick charging stations along highways to ensure long-distance travel. We consider a location problem for quick charging stations for EVs and focus on the attractiveness of the different charging locations for travelers. A traveler who chooses to stop en route to recharge the EV incurs monetary (for electricity and charging service) and inconvenience costs, which vary by location and travelers’ preferences. A traveler chooses to use charging locations that minimize total trip cost while ensuring completion of the trip. We prove that this charging location selection problem is mathematically equivalent to a bounded inventory replenishment problem in the production planning literature, which can be reformulated as a shortest path problem on an augmented network. By doing so, we formulate the problem for the service provider as a linear problem with uncertain and ambiguous coefficients. The problem is equivalent to completely positive programming (CPP) and the travelers’ preferences can be reflected by the persistency value which is the optimal solution for the CPP problem. We also consider a two-stage stochastic model to identify the proper locations to minimize the total construction costs and the trip costs.

The second part investigates the problem of sourcing and supplier selection under yield uncertainty and ambiguity. Supplier selection is a typical problem for manufacturing. With a proper selection of the suppliers, companies can reduce the cost and thus improve the profit margin. Over the years, researchers and practitioners tend to focus on consolidated sourcing with the benefit of economies of scales and qualify inspection. Yet, due to the uncertainty of the sourcing, yield etc., risk pooling effect has been concerned for the main effect when referring to the sourcing problem. As the yield is an unknown factor to the manufacturer, selecting only one of the suppliers available seems not a good solution. Companies tend to diversify the sourcing portfolio. However, selecting too many number of suppliers will also have a downside on building long-run relationship with the suppliers and quality monitoring and controlling. In our work, we assume only the knowledge of the means and covariance matrix of yield for suppliers, and consider the worst-case bounds, out of all distributions with the given moments, on the expected costs. We consider to select suppliers to source a single product. To extend the model, we also consider the ordering strategy to source complimentary components to assemble a product where each component has one unreliable supplier available. In addition, we consider sourcing strategy for an assembling production line, with each component facing a number of unreliable suppliers.