Facets of the knapsack polytope from non-minimal covers

We propose two new classes of valid inequalities (VIs) for the binary knapsack polytope, based on non-minimal covers. We also show that these VIs can be obtained through neither sequential nor simultaneous lifting of well-known cover inequalities. We further provide conditions under which they are facet-defining. The usefulness of these VIs is demonstrated using computational … Read more

Stochastic programming for an integrated assignment, routing, and scheduling problem

We study a two-stage stochastic combinatorial optimization problem that integrates fleet-sizing, assignment, routing, and scheduling problems. Although this problem has wide applicability, it arises in particular in the home healthcare industry where a service team of caregivers have to be assigned to patients and put in vehicle fleet that have to be routed amongst the … Read more

Fair and Risk-averse Urban Air Mobility Resource Allocation Under Uncertainties

Urban Air Mobility (UAM) is an emerging air transportation mode to alleviate the ground traffic burden and achieve zero direct aviation emissions. Due to the potential economic scaling effects, the UAM traffic flow is expected to increase dramatically once implemented, and its market can be substantially large. To be prepared for the era of UAM, … Read more

Theoretical Insights and a New Class of Valid Inequalities for the Temporal Bin Packing Problem with Fire-Ups

The temporal bin packing problem with fire-ups (TBPP-FU) is a two-dimensional packing problem where one geometric dimension is replaced by a time horizon. The given items (jobs) are characterized by a resource consumption, that occurs exclusively during an activity interval, and they have to be placed on servers so that the capacity constraint is respected … Read more

Sparse multi-term disjunctive cuts for the epigraph of a function of binary variables

We propose a new method for separating valid inequalities for the epigraph of a function of binary variables. The proposed inequalities are disjunctive cuts defined by disjunctive terms obtained by enumerating a subset $I$ of the binary variables. We show that by restricting the support of the cut to the same set of variables $I$, … Read more

Exact and Heuristic Solution Techniques for Mixed-Integer Quantile Minimization Problems

We consider mixed-integer linear quantile minimization problems that yield large-scale problems that are very hard to solve for real-world instances. We motivate the study of this problem class by two important real-world problems: a maintenance planning problem for electricity networks and a quantile-based variant of the classic portfolio optimization problem. For these problems, we develop … Read more

Multi-depot routing with split deliveries: Models and a branch-and-cut algorithm

We study the multi-depot split-delivery vehicle routing problem (MDSDVRP) which combines the advantages and potential cost-savings of multiple depots and split-deliveries and develop the first exact algorithm for this problem. We propose an integer programming formulation using a small number of decision variables and several sets of valid inequalities. These inequalities focus on ensuring the … Read more

Distributionally Robust Fair Transit Resource Allocation During a Pandemic

This paper studies Distributionally robust Fair transit Resource Allocation model (DrFRAM) under Wasserstein ambiguity set to optimize the public transit resource allocation during a pandemic. We show that the proposed DrFRAM is highly nonconvex and nonlinear and is, in general, NP-hard. Fortunately, we show that DrFRAM can be reformulated as a mixed-integer linear programming (MILP) … Read more

New Valid Inequalities and Formulation for the Static Chance-constrained Lot-Sizing Problem

We study the static chance-constrained lot sizing problem, in which production decisions over a planning horizon are made before knowing random future demands, and the backlog and inventory variables are then determined by the demand realizations. The chance constraint imposes a service level constraint requiring that the probability that any backlogging is required should be … Read more

Why there is no need to use a big-M in linear bilevel optimization: A computational study of two ready-to-use approaches

Linear bilevel optimization problems have gained increasing attention both in theory as well as in practical applications of Operations Research (OR) during the last years and decades. The latter is mainly due to the ability of this class of problems to model hierarchical decision processes. However, this ability makes bilevel problems also very hard to … Read more