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The test planning group within Ford׳s Product Development division develops schedules for building prototype vehicles and assigning them to departments in charge of different vehicle components, systems and aspects (e.g., powertrain, electrical, safety). These departments conduct tests at pre-production phases of each vehicle program (e.g., 2015 Ford Fusion, 2016 Ford Escape) to ensure the vehicles meet all requirements by the time they reach the production phase. Each prototype can cost in excess of $200 K because many of the parts and the prototypes themselves are hand-made and highly customized. Parts needed often require months of lead time, which constrains when vehicle builds can start. That, combined with inflexible deadlines for completing tests on those prototypes introduces significant time pressure, an unavoidable and challenging reality. One way to alleviate time pressure is to build more prototype vehicles; however, this would greatly increase the cost of each program. A more efficient way is to develop test plans with tight schedules that combine multiple tests on vehicles to fully utilize all available time. There are many challenges that need to be overcome in implementing this approach, including complex compatibility relationships between the tests and destructive nature of, e.g., crash tests. We introduce analytical approaches for obtaining efficient schedules to replace the tedious manual scheduling process engineers undertake for each program. Our models and algorithms save test planners׳ and engineers׳ time, increases their ability to quickly react to program changes, and save resources by ensuring maximal vehicle utilization.

We consider the problem of scheduling crash tests for new vehicle programs at Ford. We describe the development of a comprehensive web-based system that automates time-consuming scheduling analyses through mathematical optimization, while also institutionalizing expert knowledge about the engineering complexities of crash testing. We present a novel integer programming model and a corresponding solution algorithm that quickly generates efficient schedules. The system’s user interface enables engineers to specify key program data and consider multiple scheduling scenarios, while using the underlying optimization model and solution algorithms as a black box.

We developed an innovative technology that uses analytics to promote sustainability as a central purchase consideration for organizations with large fleets of vehicles. Working with Ford’s fleet customers over the past several years, we witnessed their strong and increasing desire to adopt greener vehicle technologies, and their unmet need to financially justify the higher initial investment costs associated with adopting those more fuel-efficient technologies. We responded by developing the Ford Fleet Purchase Planner™—a set of tools that begin with simple calculators and gradually transition to highly precise full-fleet optimization tools. These tools enable fleet customers to invest strategically in greener vehicles.

We study a class of mixed-integer programs for solving linear programs with joint probabilistic constraints from random right-hand side vectors with finite distributions. We present greedy and dual heuristic algorithms that construct and solve a sequence of linear programs. We provide optimality gaps for our heuristic solutions via the linear programming relaxation of the extended mixed-integer formulation of Luedtke et al. (2010) [13] as well as via lower bounds produced by their cutting plane method. While we demonstrate through an extensive computational study the effectiveness and scalability of our heuristics, we also prove that the theoretical worst-case solution quality for these algorithms is arbitrarily far from optimal. Our computational study compares our heuristics against both the extended mixed-integer programming formulation and the cutting plane method of Luedtke et al. (2010) [13]. Our heuristics efficiently and consistently produce solutions with small optimality gaps, while for larger instances the extended formulation becomes intractable and the optimality gaps from the cutting plane method increase to over 5%.

We consider the scenario approach for chance constrained programming problems. Building on existing theoretical results, effective and readily applicable methodologies to achieve suitable risk-return trade-offs are developed in this paper. Unlike other approaches, that require solving non-convex optimization problems, our methodology consists of solving multiple convex optimization problems obtained by sampling and removing some of the constraints. More specifically, two constraint removal schemes are introduced, one greedy and the other randomized, and a comparison between them is provided in a detailed computational study in portfolio selection. Other practical aspects of the procedures are also discussed. The removal schemes proposed in this paper are generalizable to a wide range of practical problems.