scholarly journals Strengthened Formulations and Valid Inequalities for Single Delay Management in Public Transportation

2019 ◽  
Vol 53 (5) ◽  
pp. 1271-1286
Author(s):  
Veronica Dal Sasso ◽  
Luigi De Giovanni ◽  
Martine Labbé
Keyword(s):  
Linear Programming ◽  
Public Transportation ◽  
Mixed Integer Linear Programming ◽  
Transportation Networks ◽  
Valid Inequalities ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Management Problem ◽  
Delay Management ◽  
Initial Delay

The delay management problem arises in public transportation networks, often characterized by the necessity of connections between different vehicles. The attractiveness of public transportation networks is strongly related to the reliability of connections, which can be missed when delays or other unpredictable events occur. Given a single initial delay at one node of the network, the delay management problem is to determine which vehicles have to wait for the delayed ones, with the aim of minimizing the dissatisfaction of the passengers. In this paper, we present strengthened mixed integer linear programming formulations and new families of valid inequalities. The implementation of branch-and-cut methods and tests on a benchmark of instances taken from real networks show the potential of the proposed formulations and cuts.

scholarly journals A Hybrid IP/GA Approach to the Parallel Production Lines Scheduling Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Huizhi Ren ◽  
Shenshen Sun
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Time Window ◽  
Valid Inequalities ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Production Lines ◽  
Solution Approach ◽  
Cp Decomposition

A special parallel production lines scheduling problem is studied in this paper. Considering the time window and technical constraints, a mixed integer linear programming (MILP) model is formulated for the problem. A few valid inequalities are deduced and a hybrid mixed integer linear programming/constraint programming (MILP/CP) decomposition strategy is introduced. Based on them, a hybrid integer programming/genetic algorithm (IP/GA) approach is proposed to solve the problem. At last, the numerical experiments demonstrate that the proposed solution approach is effective and efficient.

scholarly journals Global solutions of nonconvex standard quadratic programs via mixed integer linear programming reformulations

2021 ◽  
Author(s):  
Jacek Gondzio ◽  
E. Alper Yıldırım
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Valid Inequalities ◽  
Global Minimizer ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Complementarity Constraints ◽  
Binary Variables ◽  
Standard Quadratic Program

AbstractA standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative formulations. Our first formulation is based on casting a standard quadratic program as a linear program with complementarity constraints. We then employ binary variables to linearize the complementarity constraints. For the second formulation, we first derive an overestimating function of the objective function and establish its tightness at any global minimizer. We then linearize the overestimating function using binary variables and obtain our second formulation. For both formulations, we propose a set of valid inequalities. Our extensive computational results illustrate that the proposed mixed integer linear programming reformulations significantly outperform other global solution approaches. On larger instances, we usually observe improvements of several orders of magnitude.

scholarly journals Discrete Optimization Model and Algorithm for Driver Planning in Periodic Driver Routing Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Lin Huang ◽  
Wenya Lv ◽  
Qian Sun ◽  
Chengle Ma
Keyword(s):  
Linear Programming ◽  
Integer Linear Programming ◽  
Mixed Integer Linear Programming ◽  
Programming Model ◽  
Workforce Planning ◽  
Service Level ◽  
Mixed Integer ◽  
Management Problem ◽  
Routing Problem ◽  
Total Workload

Workforce planning is an operation management problem in the delivery industry to improve service quality and reliability, and the working attitude and passion of drivers, as the direct implementors of delivery service, affect the service level. Consequently, assigning equal workload for drivers so as to improve drivers’ acceptance is a reasonable and efficient workforce plan for managers. This paper investigates a periodic driver routing problem to explore the relationship between workload differential among drivers and total workload; the objective of the optimization problem is to minimize the total workload. To tackle this problem, we first propose a mixed-integer linear programming model, which can be solved by an off-the-shelf mixed-integer linear programming solver, and use the local branching based method to solve larger instances of the problem. Numerical experiments are conducted to validate the effectiveness and efficiency of the proposed model and solution method, as well as the effect of small workload differential among drivers on the total workload.

scholarly journals Analysis of Mixed-Integer Linear Programming Formulations for a Fuel-Constrained Multiple Vehicle Routing Problem

2017 ◽  
Vol 05 (04) ◽  
pp. 197-207 ◽  
Author(s):  
Kaarthik Sundar ◽  
Saravanan Venkatachalam ◽  
Sivakumar Rathinam
Keyword(s):  
Linear Programming ◽  
Vehicle Routing ◽  
Integer Linear Programming ◽  
Vehicle Routing Problem ◽  
Mixed Integer Linear Programming ◽  
Optimal Solution ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Computational Results ◽  
Routing Problem

This paper addresses a fuel-constrained, multiple vehicle routing problem (FCMVRP) in the presence of multiple refueling stations. We are given a set of targets, a set of refueling stations, and a depot where [Formula: see text] vehicles are stationed. The vehicles are allowed to refuel at any refueling station, and the objective of the problem is to determine a route for each vehicle starting and terminating at the depot, such that each target is visited by at least one vehicle, the vehicles never run out of fuel while traversing their routes, and the total travel cost of all the routes is a minimum. We present four new mixed-integer linear programming (MILP) formulations for the problem. These formulations are compared both analytically and empirically, and a branch-and-cut algorithm is developed to compute an optimal solution. Extensive computational results on a large class of test instances that corroborate the effectiveness of the algorithm are also presented.

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