scholarly journals The Ring Spur Assignment Problem: New formulation, valid inequalities and a branch-and-cut approach

2017 ◽  
Vol 88 ◽  
pp. 91-102
Author(s):  
Rahimeh Neamatian Monemi ◽  
Shahin Gelareh
Keyword(s):  
Assignment Problem ◽  
Valid Inequalities ◽  
Branch And Cut ◽  
New Formulation

A New Formulation for the Dial-a-Ride Problem

2021 ◽  
Author(s):  
Yannik Rist ◽  
Michael A. Forbes
Keyword(s):  
Time Window ◽  
Valid Inequalities ◽  
Route Planning ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Planning Problem ◽  
Current State ◽  
New Formulation ◽  
First Time ◽  
Delivery Location

This paper proposes a new mixed integer programming formulation and branch and cut (BC) algorithm to solve the dial-a-ride problem (DARP). The DARP is a route-planning problem where several vehicles must serve a set of customers, each of which has a pickup and delivery location, and includes time window and ride time constraints. We develop “restricted fragments,” which are select segments of routes that can represent any DARP route. We show how to enumerate these restricted fragments and prove results on domination between them. The formulation we propose is solved with a BC algorithm, which includes new valid inequalities specific to our restricted fragment formulation. The algorithm is benchmarked on existing and new instances, solving nine existing instances to optimality for the first time. In comparison with current state-of-the-art methods, run times are reduced between one and two orders of magnitude on large instances.

scholarly journals Production, Replenishment and Inventory Policies for Perishable Products in a Two-Echelon Distribution Network

2020 ◽  
Vol 12 (11) ◽  
pp. 4735
Author(s):  
Mingyuan Wei ◽  
Hao Guan ◽  
Yunhan Liu ◽  
Benhe Gao ◽  
Canrong Zhang
Keyword(s):  
Inventory Management ◽  
Valid Inequalities ◽  
Distribution Network ◽  
Planning Horizon ◽  
Branch And Cut ◽  
Computational Time ◽  
Perishable Products ◽  
Inventory Cost ◽  
Routing Problem ◽  
Selection Of

The research on production, delivery and inventory strategies for perishable products in a two-echelon distribution network integrates the production routing problem (PRP) and two-echelon vehicle routing problem (2E-VRP), which mainly considers the inventory and delivery sustainability of perishable products. The problem investigated in this study is an extension of the basic problems, and it simultaneously optimizes production, replenishment, inventory, and routing decisions for perishable products that will deteriorate over the planning horizon. Additionally, the lead time has been considered in the replenishment echelon, and the unit inventory cost varying with the inventory time is considered in the inventory management. Based on a newly designed model, different inventory strategies are discussed in this study: old first (OF) and fresh first (FF) strategies both for the first echelon and second echelon, for which four propositions to model them are proposed. Then, four valid inequalities, including logical inequalities, a ( ℓ , S , W W ) inequality, and a replenishment-related inequality, are proposed to construct a branch-and-cut algorithm. The computational experiments are conducted to test the efficiency of valid inequalities, branch-and-cut, and policies. Experimental results show that the valid inequalities can effectively increase the relaxed lower bound by 4.80% on average and the branch-and-cut algorithm can significantly reduce the computational time by 58.18% on average when compared to CPLEX in small and medium-sized cases. For the selection of strategy combinations, OF–FF is suggested to be used in priority.

The two-edge connected hop-constrained network design problem: Valid inequalities and branch-and-cut

Networks ◽  
2006 ◽  
Vol 49 (1) ◽  
pp. 116-133 ◽  
Author(s):  
David Huygens ◽  
Martine Labbé ◽  
A. Ridha Mahjoub ◽  
Pierre Pesneau
Keyword(s):  
Network Design ◽  
Design Problem ◽  
Valid Inequalities ◽  
Branch And Cut ◽  
Network Design Problem

A branch-and-cut algorithm for the truck dock assignment problem with operational time constraints

2016 ◽  
Vol 249 (3) ◽  
pp. 1144-1152 ◽  
Author(s):  
Shahin Gelareh ◽  
Rahimeh Neamatian Monemi ◽  
Frédéric Semet ◽  
Gilles Goncalves
Keyword(s):  
Assignment Problem ◽  
Branch And Cut ◽  
Time Constraints ◽  
Operational Time

scholarly journals Integer Programming, Constraint Programming, and Hybrid Decomposition Approaches to Discretizable Distance Geometry Problems

2021 ◽  
Author(s):  
Moira MacNeil ◽  
Merve Bodur
Keyword(s):  
Integer Programming ◽  
Constraint Programming ◽  
State Of The Art ◽  
Valid Inequalities ◽  
Distance Geometry ◽  
The State ◽  
Bp Algorithm ◽  
Branch And Cut ◽  
Vertex Order ◽  
Hybrid Decomposition

Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in [Formula: see text] such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called discretization assumptions reduce the search space of the realization to a finite discrete one, which can be explored via the branch-and-prune (BP) algorithm. Given a discretization vertex order in G, the BP algorithm constructs a binary tree where the nodes at a layer provide all possible coordinates of the vertex corresponding to that layer. The focus of this paper is on finding optimal BP trees for a class of discretizable DGPs. More specifically, we aim to find a discretization vertex order in G that yields a BP tree with the least number of branches. We propose an integer programming formulation and three constraint programming formulations that all significantly outperform the state-of-the-art cutting-plane algorithm for this problem. Moreover, motivated by the difficulty in solving instances with a large and low-density input graph, we develop two hybrid decomposition algorithms, strengthened by a set of valid inequalities, which further improve the solvability of the problem. Summary of Contribution: We present a new model to solve a combinatorial optimization problem on graphs, MIN DOUBLE, which comes from the highly active area of distance geometry and has applications in a wide variety of fields. We use integer programming (IP) and present the first constraint programming (CP) models and hybrid decomposition methods, implemented as a branch-and-cut procedure, for MIN DOUBLE. Through an extensive computational study, we show that our approaches advance the state of the art for MIN DOUBLE. We accomplish this by not only combining generic techniques from IP and CP but also exploring the structure of the problem in developing valid inequalities and variable fixing rules. Our methods significantly improve the solvability of MIN DOUBLE, which we believe can also provide insights for tackling other problem classes and applications.

scholarly journals Last mile deliveries with lockers: formulations and algorithms

2021 ◽  
Author(s):  
Giovanni Buzzega ◽  
Stefano Novellani
Keyword(s):  
Valid Inequalities ◽  
Time Windows ◽  
Home Delivery ◽  
Branch And Cut ◽  
Routing Problems ◽  
Last Mile ◽  
Multiple Vehicles ◽  
Recent Method ◽  
The Difference

Abstract In this paper we consider the use of lockers in parcel delivery, a recent method used in the last mile logistics. Lockers are pick up points made of several cells that are located in several points of a city where customers can collect their parcels as an alternative to home delivery. We study routing problems in which one or multiple vehicles are used to deliver parcels directly to customers or to lockers. We also study the influence of the introduction of lockers when these problems include time windows. We propose a set of novel formulations for these problems, some valid inequalities, and a branch-and-cut algorithm. Moreover, we investigate the difference between the routing problems with lockers and the classical routing problems.

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