Research

In transportation and logistics problems, such as the traveling salesman problem or the vehicle routing problem, the geographic distribution of nodes can significantly impact both the solutions obtained and the performance of solution approaches. Therefore, it is common for researchers to share test instances for meaningful comparisons. In some contexts, this is more challenging when data are protected and cannot be shared. This is particularly true for transportation and logistics problems found in public school operations. Despite growing literature, proposed models and solution approaches are rarely compared across papers because data protection regulations prohibit sharing data. At the same time, randomly generated data can miss critical patterns existing in reality that may impact equitable access to education. In this paper, we introduce an approach to create context-rich data sets for school operations models and methods based on publicly available data that reflect public school district characteristics in the United States.

Comprehensive community engagement in public school district design is essential to create equitable and effective enrollment policies reflective of community needs and values.  We revisit the school district design problem with a focus on co-designing with community partners. We introduce a new compact formulation that incorporates multiple decisions simultaneously by assigning students in each geographic unit to a set of schools (e.g., elementary, middle, high schools, and schools with specialized programming) with a single composite variable, referred to as a "stream." This formulation is computationally efficient and easily reconfigurable for evolving problem specifications that are endemic to community co-design.  These features were essential in the district redesign process described in this paper, allowing the community to iteratively develop proposals to address inequities in access to education and improve the student assignment process.

Deployment of drones in delivery operations has been attracting growing interest from the commercial sector due to its prospective advantages for a range of distribution systems. Motivated by the widespread adoption of drones in last-mile delivery, we introduce the minimum cost traveling salesman problem with multiple drones, where a truck and multiple drones work in synchronization to deliver parcels to customers. In this problem, we aim to find an optimal delivery plan for the truck and drones operating in tandem with the objective of minimizing the total operational cost including the vehicles’ operating and waiting costs. Unlike most studies in the literature where the objective is to minimize completion time, which means one needs to know only the arrival time of the latest arriving vehicle (truck or drone) at each synchronization point, we need to keep track of all the individual waiting times of the truck and the drones to properly account for waiting costs, which makes it more challenging to handle the synchronization. We provide a flow based and two cut based mixed integer linear programming formulations strengthened with valid inequalities. For non-compact models, we devise a variety of branch-and-cut schemes to solve our problem to optimality. To compare our formulations/algorithms and to demonstrate their competitiveness, we conduct computational experiments on a range of instances. The results indicate the superiority of utilizing branch-andcut methodology over a flow based formulation. We also use our model to conduct sensitivity analyses with several problem parameters and to explore the benefits of launch and retrieval at the same node, the tradeoff between the number of drones and the operational cost, and the special case with a minimize completion objective with one drone. We also document very low waiting times for drones in optimal solutions and show solutions from minimizing cost have much lower cost than those from minimizing makespan.

Motivated by the recent rise in need for refugee camps, we address one of the key infrastructural problems in the establishment process: The clean water network design problem. We formulate the problem as a biobjective integer programming problem and determine the locations of the water source, water distribution units and the overall network design (pipelines), considering the objectives of minimizing cost (total network length) and maximizing accessibility (total walking distance) simultaneously. We solve the resulting model using exact and heuristic approaches that find the set (or a subset) of Pareto solutions and a set of approximate Pareto solutions, respectively. We demonstrate the applicability of our approach on a real-life problem in Gaziantep refugee camp and provide a detailed comparison of the solution approaches. The novel biobjective approach we propose will help the decision makers to make more informed design decisions in refugee camps, considering the trade-off between the two key criteria of cost and accessibility.