valid inequalities

Skip or Insert? A Priori Optimization for the Vehicle Routing Problem with Time Windows and Stochastic Customers

  • Yulin Han
  • Hande Yaman
    • Categories Combinatorial Optimization, Production and Logistics, Stochastic Programming Tags , , , , , , ,

    We study an extension of the vehicle routing problem with time windows by incorporating stochastic customers, i.e., ad-hoc service requests. The uncertainty in stochastic customers is captured through scenarios. Two a priori optimization approaches, a classical and a new one lead to two different problems, both of which are modeled as scenario-based two-stage stochastic programs. … Read more

    Relief-based Anesthesiologist Scheduling with Stochastic Surgery Durations

  • Ankit Bansal
  • Osman Y. Ozaltin
    • Categories (Mixed) Integer Linear Programming, Scheduling, Stochastic Programming Tags , , ,

    We present a two-stage stochastic programming model for scheduling anesthesiologists to operating rooms under uncertainty in surgery durations. The proposed model takes a relief order to balance anesthesiologists’ workload as input and captures the trade-offs between anesthesiologist relief times, handoffs and under-staffing. To address the computational challenges of solving the proposed model, we derive supervalid … Read more

    On Multi-Disjunctive Valid Inequalities for Chance-Constrained Stochastic Problems with Finite Support

  • Diego Cattaruzza
  • Martine Labbé
  • Matteo Petris
  • Marius Roland
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

    We consider mixed-integer linear chance-constrained problems for which the random vector that parameterizes the feasible region has finite support. Our key objective is to improve branch-and-bound or -cut approaches by introducing new types of valid inequalities that improve the dual bound and, by this, the overall performance of such methods. We introduce so-called multi-disjunctive valid … Read more

    Strengthening Dual Bounds for Multicommodity Capacitated Network Design with Unsplittable Flow Constraints

  • Lacy M. Greening
  • Santanu S. Dey
  • Alan L. Erera
    • Categories Integer Programming, Network Optimization, Production and Logistics Tags , , ,

    Multicommodity capacitated network design (MCND) models can be used to optimize the consolidation of shipments within e-commerce fulfillment networks. In practice, fulfillment networks require that shipments with the same origin and destination follow the same transfer path. This unsplittable flow requirement complicates the MCND problem, requiring integer programming (IP) formulations with binary variables replacing continuous … Read more

    Polynomial-Time Algorithms for Setting Tight Big-M Coefficients in Transmission Expansion Planning with Disconnected Buses

  • Behnam Jabbari Marand
  • Adolfo Escobedo
    • Categories Combinatorial Optimization, Cutting Plane Approaches, Energy Tags , , ,

    The increasing penetration of renewable energy into power systems necessitates the development of effective methodologies to integrate initially disconnected generation sources into the grid. This paper introduces the Longest Shortest-Path-Connection (LSPC) algorithm, a graph-based method to enhance the mixed-integer linear programming disjunctive formulation of Transmission Expansion Planning (TEP) using valid inequalities (VIs). Traditional approaches for … Read more

    Cover-based inequalities for the single-source capacitated facility location problem with customer preferences

  • Christina Büsing
  • Markus Leitner
  • Sophia Wrede
    • Categories Combinatorial Optimization, Integer Programming Tags , , ,

    The single-source capacitated facility location problem with customer preferences (SSCFLPCP) is known to be strongly NP-hard. Computational tests imply that state-of-the-art solvers struggle with computing exact solutions. In this paper, we contribute two novel preprocessing methods which reduce the size of the considered integer programming formulation, and introduce sets of valid inequalities which decrease the … Read more

    Facets of the knapsack polytope from non-minimal covers

  • Guneshwar Anand
  • Sachin Jayaswal
  • B. Srirangacharyulu
    • Categories (Mixed) Integer Linear Programming, Polyhedra, Transportation Tags , , , , ,

    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

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

  • Luying Sun
  • Weijun Xie
    • Categories Applications - OR and Management Sciences Tags , , , ,

    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

  • John Martinovic
  • Nico Strasdat
    • Categories (Mixed) Integer Linear Programming, Scheduling Tags , , , ,

    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