scholarly journals Polyhedral Results and Branch-and-Cut for the Resource Loading Problem

2020 ◽  
Author(s):  
Guopeng Song ◽  
Tamás Kis ◽  
Roel Leus
Keyword(s):  
Resource Use ◽  
Capacity Planning ◽  
Mixed Integer Linear Programming ◽  
Branch And Cut ◽  
Mixed Integer ◽  
The Novel ◽  
Due Dates ◽  
Capacity Limits ◽  
Resource Loading ◽  
Loading Problem

We study the resource loading problem, which arises in tactical capacity planning. In this problem, one has to plan the intensity of execution of a set of orders to minimize a cost function that penalizes the resource use above given capacity limits and the completion of the orders after their due dates. Our main contributions include a novel mixed-integer linear-programming (MIP)‐based formulation, the investigation of the polyhedra associated with the feasible intensity assignments of individual orders, and a comparison of our branch-and-cut algorithm based on the novel formulation and the related polyhedral results with other MIP formulations. The computational results demonstrate the superiority of our approach. In our formulation and in one of the proofs, we use fundamental results of Egon Balas on disjunctive programming.

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 Recent Advancements in Commercial Integer Optimization Solvers for Business Intelligence Applications

2021 ◽  
Author(s):  
Cheng Seong Khor
Keyword(s):  
Business Intelligence ◽  
Mixed Integer Linear Programming ◽  
Branch And Cut ◽  
Mixed Integer ◽  
Neighborhood Search ◽  
Integer Optimization ◽  
Computational Performance ◽  
Solution Methods ◽  
Future Work ◽  
Optimization Solvers

The chapter focuses on the recent advancements in commercial integer optimization solvers as exemplified by the CPLEX software package particularly but not limited to mixed-integer linear programming (MILP) models applied to business intelligence applications. We provide background on the main underlying algorithmic method of branch-and-cut, which is based on the established optimization solution methods of branch-and-bound and cutting planes. The chapter also covers heuristic-based algorithms, which include preprocessing and probing strategies as well as the more advanced methods of local or neighborhood search for polishing solutions toward enhanced use in practical settings. Emphasis is given to both theory and implementation of the methods available. Other considerations are offered on parallelization, solution pools, and tuning tools, culminating with some concluding remarks on computational performance vis-à-vis business intelligence applications with a view toward perspective for future work in this area.

scholarly journals A Comparison of Algorithms for Finding an Efficient Theme Park Tour

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Elizabeth L. Bouzarth ◽  
Richard J. Forrester ◽  
Kevin R. Hutson ◽  
Rahul Isaac ◽  
James Midkiff ◽  
...  
Keyword(s):  
Mixed Integer Linear Programming ◽  
Search Algorithm ◽  
Computational Study ◽  
Branch And Cut ◽  
Time Dependent ◽  
Mixed Integer ◽  
Theme Park ◽  
Linear Programming Formulation ◽  
The Traveling Salesman Problem ◽  
Integer Linear Programming Formulation

The problem of efficiently touring a theme park so as to minimize the amount of time spent in queues is an instance of the Traveling Salesman Problem with Time-Dependent Service Times (TSP-TS). In this paper, we present a mixed-integer linear programming formulation of the TSP-TS and describe a branch-and-cut algorithm based on this model. In addition, we develop a lower bound for the TSP-TS and describe two metaheuristic approaches for obtaining good quality solutions: a genetic algorithm and a tabu search algorithm. Using test instances motivated by actual theme park data, we conduct a computational study to compare the effectiveness of our algorithms.

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.

scholarly journals Improved layout structure with complexity measures for the Manufacturer’s Pallet Loading Problem (MPLP] using a Block approach

2021 ◽  
Vol 14 (2) ◽  
pp. 231
Author(s):  
Deemah Aljuhani ◽  
Lazaros Papageorgiou
Keyword(s):  
Mixed Integer Linear Programming ◽  
Real Life ◽  
Mixed Integer ◽  
Data Sets ◽  
Complexity Measures ◽  
Pallet Loading ◽  
Layout Structure ◽  
Loading Problem ◽  
Graphical Layout ◽  
Block Approach

Purpose: The purpose of this paper is to study the Manufacturers pallet-loading problem (MPLP), by loading identical small boxes onto a rectangle pallet to maximise the pallet utilization percentage while reducing the Complexity of loading.Design/methodology/approach: In this research a Block approach is proposed using a Mixed integer linear programming (MILP) model that generates layouts of an improved structure, which is very effective due to its properties in grouping boxes in a certain orientation along the X and Y axis. Also, a novel complexity index is introduced to compare the complexity for different pallet loading, which have the same pallet size but different box arrangements.Findings: The proposed algorithm has been tested against available data-sets in literature and the complexity measure and graphical layout results clearly demonstrate the superiority of the proposed approach compared with literature Manufacturers pallet-loading problem layouts.Originality/value: This study aids real life manufactures operations when less complex operations are essential to reduce the complexity of pallet loading.

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