scholarly journals An Insight into the Characteristic Equation for an Integer Program

2021 ◽  
Vol 6 (2) ◽  
pp. 611-620
Author(s):  
Santosh Kumar ◽  
Elias Munapo ◽  
Philimon Nyamugure
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Characteristic Equation ◽  
Programming Model ◽  
Integer Program ◽  
Optimal Solutions ◽  
Integer Programs ◽  
Linear Integer Programming ◽  
Enhanced Properties ◽  
Insight Into

This article enhances properties and applications associated with the characteristic equation (CE) developed to find an optimal and other ranked-optimal solutions of linear integer programming model. These enhanced properties have applications in the analysis of the multi-objective linear integer programs. The paper also identifies why the CE approach is not possible for some special linear programming (LP) models and creates a challenge for further investigation.

scholarly journals Non-linear Integer Programming Model and Algorithms for Connected p-facility Location Problem

2014 ◽  
Vol 2 (5) ◽  
pp. 451-460 ◽  
Author(s):  
Jianming Zhu
Keyword(s):  
Integer Programming ◽  
Facility Location ◽  
Shortest Path ◽  
Location Problem ◽  
Programming Model ◽  
Maximum Clique ◽  
Facility Location Problem ◽  
Linear Integer Programming ◽  
Non Linear ◽  
The Cost

AbstractIn this paper, a new location analysis method is presented. Given a connected graphG= (V, E)with nonnegative edge costcefor each edgee∊E,dijis the cost of the shortest path between verticesiandjin the graph. TheConnected p-facility Location Problem(CpLP) is to choosepvertices fromVso as to minimize the total cost of shortest path of pair-wise of thesepvertices. This problem is proved to be NP-hard and non-linear integer programming is formulated. Then, two algorithms are designed for solving the CpLP. One is a heuristic algorithm based on classical maximum clique approach, while the second one is genetic algorithm. Finally, computational results show the comparison between these two algorithms.

scholarly journals Linear Integer Model for the Course Timetabling Problem of a Faculty in Rio de Janeiro

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Valdecy Pereira ◽  
Helder Gomes Costa
Keyword(s):  
Integer Programming ◽  
Response Time ◽  
Rio De Janeiro ◽  
Programming Model ◽  
Specific Weight ◽  
Timetabling Problem ◽  
Linear Integer Programming ◽  
Integer Linear Model ◽  
Course Timetabling Problem ◽  
Conflicting Goals

This work presents a linear integer programming model that solves a timetabling problem of a faculty in Rio de Janeiro, Brazil. The model was designed to generate solutions that meet the preferences of the faculty’s managers, namely, allocating the maximum number of lecturers with highest academic title and minimising costs by merging courses with equivalent syllabuses. The integer linear model also finds solutions that meet lecturers’ scheduling preferences, thereby generating more practical and comfortable schedules for these professionals. Preferences were represented in the objective function, each with a specific weight. The model outperformed manual solutions in terms of response time and quality. The model was also able to demonstrate that lecturers’ scheduling preferences are actually conflicting goals. The model was approved by the faculty’s managers and has been used since the second semester of 2011.

scholarly journals Phylogenetic Clustering by Linear Integer Programming (PhyCLIP)

2018 ◽  
Author(s):  
Alvin X. Han ◽  
Edyth Parker ◽  
Frits Scholer ◽  
Sebastian Maurer-Stroh ◽  
Colin A. Russell
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Sequence Data ◽  
Ground Truth ◽  
Human Papillomaviruses ◽  
Clustering Methods ◽  
Distance Threshold ◽  
Phylogenetic Clustering ◽  
Linear Integer Programming ◽  
Patristic Distance

AbstractSub-species nomenclature systems of pathogens are increasingly based on sequence data. The use of phylogenetics to identify and differentiate between clusters of genetically similar pathogens is particularly prevalent in virology from the nomenclature of human papillomaviruses to highly pathogenic avian influenza (HPAI) H5Nx viruses. These nomenclature systems rely on absolute genetic distance thresholds to define the maximum genetic divergence tolerated between viruses designated as closely related. However, the phylogenetic clustering methods used in these nomenclature systems are limited by the arbitrariness of setting intra- and inter-cluster diversity thresholds. The lack of a consensus ground truth to define well-delineated, meaningful phylogenetic subpopulations amplifies the difficulties in identifying an informative distance threshold. Consequently, phylogenetic clustering often becomes an exploratory, ad-hoc exercise.Phylogenetic Clustering by Linear Integer Programming (PhyCLIP) was developed to provide a statistically-principled phylogenetic clustering framework that negates the need for an arbitrarily-defined distance threshold. Using the pairwise patristic distance distributions of an input phylogeny, PhyCLIP parameterises the intra- and inter-cluster divergence limits as statistical bounds in an integer linear programming model which is subsequently optimised to cluster as many sequences as possible. When applied to the haemagglutinin phylogeny of HPAI H5Nx viruses, PhyCLIP was not only able to recapitulate the current WHO/OIE/FAO H5 nomenclature system but also further delineated informative higher resolution clusters that capture geographically-distinct subpopulations of viruses. PhyCLIP is pathogen-agnostic and can be generalised to a wide variety of research questions concerning the identification of biologically informative clusters in pathogen phylogenies. PhyCLIP is freely available at http://github.com/alvinxhan/PhyCLIP.

scholarly journals MODEL PENJADWALAN KEBERANGKATAN BUS DENGAN STRATEGI ALTERNATING DEADHEADING: STUDI KASUS DI PO RAYA

2013 ◽  
Vol 12 (2) ◽  
pp. 1
Author(s):  
R. A. CAHYADI ◽  
A. AMAN ◽  
F. HANUM
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Integer Programming Model ◽  
Linear Integer Programming

Penjadwalan keberangkatan bus merupakan salah satu hal yang penting dalam pengelolaan perusahaan otobus untuk menekan biaya operasional. Masalah penjadwalan ini diformulasikan sebagai suatu model linear integer programming. Model ini bertujuan untuk mengatur banyaknya bus yang akan diberangkatkan dari masing-masing kota untuk memenuhi permintaan transportasi. Strategi yang digunakan untuk mengatur penjadwalan bus yaitu strategi deadheading. Strategi deadheading merupakan strategi penjadwalan bus yang dilakukan apabila terjadi ketidakseimbangan akan banyaknya penumpang di suatu kota dan adanya keterbatasan bus yang beroperasi. Model penjadwalan dengan deadheading ini merupakan salah satu upaya untuk menurunkan frekuensi keberangkatan bus sehingga dapat meningkatkan efisiensi biaya operasional.

scholarly journals Modeling Heterogeneous Fleet Vehicle Allocation Problem with Emissions Considerations

2021 ◽  
Vol 15 (1) ◽  
pp. 93-107
Author(s):  
Hande C. Kazanç ◽  
Mehmet Soysal ◽  
Mustafa Çimen
Keyword(s):  
Integer Programming ◽  
Programming Model ◽  
Profit Maximization ◽  
Freight Transportation ◽  
Decision Makers ◽  
Heterogeneous Fleet ◽  
Linear Integer Programming ◽  
Scenario Analyses ◽  
Total Profit ◽  
Vehicle Allocation

Aims: This study proposes a bi-objective linear integer programming model for heterogeneous fleet VAP with emissions considerations. Profit maximization and emissions minimization objectives are employed to handle economic and environmental sustainability purposes. Background: Our literature survey shows that there is no model for the heterogeneous fleet VAP with emissions considerations that simultaneously consider vehicle heterogeneity, penalty costs for unmet demands, and emissions from transportation operations. Objective: The model is employed to also make several scenario analyses on sustainable freight logistics management to understand the trade-offs among economic and environmental objectives. In freight transportation problems, decision-makers need to be able to maintain profitability and to reduce emissions. Methods: In this study, a bi-objective linear integer programming model is proposed for a heterogeneous fleet Vehicle Allocation Problem (VAP) with emissions considerations encountered in the field of sustainable freight transportation. Results: In the numerical analyses, various practical assumptions that can be confronted by decision-makers in real life are discussed. In each analysis, total profit and emissions amounts are revealed along with several other KPIs. The results of the analyses provided in this study could also be useful in terms of understanding the relations among pillars of sustainability in VAPs. Conclusion: It is thought that the proposed model has the potential to aid decision-making processes in sustainable logistics management. In the base case analyses, the total profit obtained under profit maximization is about nine times higher than that obtained under emissions minimization. When the aim is to minimize emissions, the total emissions are found to be nearly one-tenth of that of profit maximization. Supported by also additional scenario analyses, it can be concluded that it might not economically viable to be environmentally-friendly for companies. Therefore, companies have to be encouraged or forced to take environmentally and socially responsible actions through legislation. The analyses demonstrated that various legislative policies on emissions may affect the transportation plans differently in such vehicle allocation systems.

scholarly journals Optimum Cropping Pattern for Farmers of Bidar District, Karnataka.

2019 ◽  
Vol 9 (1) ◽  
pp. 4320-4326
Keyword(s):  
Linear Programming ◽  
Programming Model ◽  
Linear Programming Model ◽  
Farm Size ◽  
Cropping Pattern ◽  
Small Farmers ◽  
Optimal Solutions ◽  
Small Farmer ◽  
Net Returns ◽  
The Impact

In the present study optimal solutions were found for net farm returns using Linear Programming model on the sample farmers of Bidar District.The LINGO 17.0 package was used to get the solutions. The sample was of 120 small and large farmers collected from 15 villages from five Tehsils. From each village eight farmers comprising small and large farmers were selected. A total of EIGHT models were developed. They were classified as small farmers S1, S2, S3, S4 and large farmers L1, L2, L3, and L4. The results were compared with existing cropping pattern of small and large farmers. The model S1, small farmers with existing technology and restricted capital registered an increase of in net returns per hectare by 27%, S2 small farmer with existing technology and relaxed capital, returns increased by 34%, S3 small farmer with recommended technology and restricted capital, returns increased by 55%, S4 small farmer with recommended technology and relaxed capital, the returns increased by 65% per hectare. Similarly the net returns per hectare in case of large farmers L1, L2, L3, L4 increased by 47%, 65%, 49%, 76% respectively. The impact of credit on net farm returns in small farmers was Rs: 8322 and the same in large farmers was Rs: 615276. The impact of credit on employment was seen in large farmers in terms of tractor power which rose to 256% followed by man days labour which was increased to 224 percent. It was noted that credit played an important role in augmenting income of farmers; the credit required was directly related to farm size while credit on income inversely related to farm size

scholarly journals Performance Comparing and Analysis for Slot Allocation Model

2019 ◽  
Author(s):  
ZhiJian Ye ◽  
YanWei Li ◽  
JingTing Bai ◽  
Xinxin Zheng
Keyword(s):  
Integer Programming ◽  
Decision Maker ◽  
Programming Model ◽  
Allocation Scheme ◽  
Slot Allocation ◽  
Allocation Model ◽  
Average Displacement ◽  
Linear Integer Programming ◽  
Key Factor ◽  
Difficulty Index

The purpose of this study was to ascertain the effect of weight setting of objectives on displacement and implementation difficulty in slot allocation model. A linear integer programming model including three kinds of evaluation objectives with different weight is designed to compare and analysis displacement and implementation difficulty in slot allocation model. The average difficulty is very sensitive to the average displacement. The difficulty of implementation can be significantly reduced by weight setting with a little increase of displacement. Movements list descent according to priority or not have great impact on displacement and implementation difficulty in slot allocation model. Capacity is a key factor affecting displacement and implementation difficulties. The difficulty index proposed in this work is very useful in identifying which slot allocation scheme is better for decision maker. Our research can promote regulator to upgrade slot allocation policies.

scholarly journals RetSynth: Solving all optimal retrosynthesis solutions using dynamically constrained integer linear programming

2017 ◽  
Author(s):  
Leanne S. Whitmore ◽  
Ali Pinar ◽  
Anthe George ◽  
Corey M. Hudson
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Metabolic Network ◽  
Integer Linear Programming ◽  
Software Package ◽  
Singular Solution ◽  
Linear Integer Programming ◽  
Pathway Search ◽  
Large Corpus

AbstractMotivationNaive determination of all the optimal pathways to production of a target chemical on an arbitrarily defined chassis organism is computationally intractable. Methods like linear integer programming can provide a singular solution to this problem, but fail to provide all optimal pathways.ResultsHere we present RetSynth, an algorithm for determining all optimal biological retrosynthesis solutions, given a starting biological chassis and target chemical. By dynamically scaling constraints, additional pathway search scales relative to the number of fully independent branches in the optimal pathways, and not relative to the number of reactions in the database or size of the metabolic network. This feature allows all optimal pathways to be determined for a very large number of chemicals and for a large corpus of potential chassis organisms.AvailabilityThis algorithm is distributed as part of the RetSynth software package, under a BSD 2-clause license at https://www.github.com/sandialabs/RetSynth/

Sign in / Sign up

Export Citation Format

Share Document