Integer Programming Methodology Research Articles

Development of a Model for Analyzing the Optimal Utilization of Classroom Space at the Federal Polytechnic, Nasarawa.

Managing the distribution of limited resources to meet the needs of people has always been a global issue that faces managers, administrators, business owners, leaders of institution and individuals alike. With the increase in number of students admitted in Federal Polytechnic Nasarawa, with a large population of about 10,000, there would be undue stress on the facilities on campus. The class rooms are not sufficient or adequate and not well-assigned compared to the measurable number of students available. This has given rise to the reduction in the length of time a lecturer spends in class, distractions from students because of classroom proximity, amongst others. These cause extreme distress on the students and lecturers alike as they are unable to study or teach, respectively, to their highest potential as a result of resources or amenities that are inadequate or wanting. Data were collected from Federal Polytechnic Nasarawa Central Examination Committee for 2022/2023 Academic Session. The linear and integer programming methodology was employed. From the result of the linear programming (LP), seven (7) out of the seventy-eight (78) available classrooms has been fully utilized. The study revealed that if the remaining seventy-one (71) classrooms are fully utilized and maximized, they will improve the current objective function with a seating capacity of 4, 640. The result of the integer programming (IP) using the branch and bound method revealed that fourteen (14) out of the seventy-eight (78) available classrooms has been fully utilized. It asserted that if the remaining sixty-four (64) classrooms are fully utilized and maximized they will improve the current objective function with a seating capacity of 7,131. The result of the sensitivity analysis indicates that the entire classroom has an allowable increase thus validating the proposed models. The study therefore concludes that classroom space utilization is being underutilized leading to congestion and overflow in the utilized classrooms.

Production Scheduling for Strategic Open Pit Mine Planning: A Mixed-Integer Programming Approach

Production scheduling is a large-scale optimization problem that must be solved on a yearly basis by every open pit mining project throughout the world. Surprisingly, however, this problem has only recently started to receive much attention from the operations research community. In this article, O. Rivera, D. Espinoza, M. Goycoolea, E. Moreno, and G. Muñoz propose an integer programming methodology for tackling this problem that combines new classes of preprocessing schemes, cutting planes, heuristics, and branching mechanisms. This methodology is shown to compute near-optimal solutions on a number of real-world planning problems whose complexity is beyond the capabilities of preexisting approaches.

Scale Reduction Techniques for Computing Maximum Induced Bicliques

Given a simple, undirected graph G, a biclique is a subset of vertices inducing a complete bipartite subgraph in G. In this paper, we consider two associated optimization problems, the maximum biclique problem, which asks for a biclique of the maximum cardinality in the graph, and the maximum edge biclique problem, aiming to find a biclique with the maximum number of edges in the graph. These NP-hard problems find applications in biclustering-type tasks arising in complex network analysis. Real-life instances of these problems often involve massive, but sparse networks. We develop exact approaches for detecting optimal bicliques in large-scale graphs that combine effective scale reduction techniques with integer programming methodology. Results of computational experiments with numerous real-life network instances demonstrate the performance of the proposed approach.

Imposing Connectivity Constraints in Forest Planning Models

Connectivity requirements are a common component of forest planning models, with important examples arising in wildlife habitat protection. In harvest scheduling models, one way of addressing preservation concerns consists of requiring that large contiguous patches of mature forest are maintained. In the context of nature reserve design, it is common practice to select a connected region of forest, as a reserve, in such a way as to maximize the number of species and habitats protected. Although a number of integer programming formulations have been proposed for these forest planning problems, most are impractical in that they fail to solve reasonably sized scheduling instances. We present a new integer programming methodology and test an implementation of it on five medium-sized forest instances publicly available in the Forest Management Optimization Site repository. Our approach allows us to obtain near-optimal solutions for multiple time-period instances in fewer than four hours.

In This Issue

In This Issue

Optimal codon randomization via mathematical programming

Codon randomization via degenerate oligonucleotides is a widely used approach for generating protein libraries. We use integer programming methodology to model and solve the problem of computing the minimal mixture of oligonucleotides required to induce an arbitrary target probability over the 20 standard amino acids. We consider both randomization via conventional degenerate oligonucleotides, which incorporate at each position of the randomized codon certain nucleotides in equal probabilities, and randomization via spiked oligonucleotides, which admit arbitrary nucleotide distribution at each of the codon's positions. Existing methods for computing such mixtures rely on various heuristics.

The Revealed Preference Approach to Collective Consumption Behaviour: Testing and Sharing Rule Recovery

We present a revealed preference methodology for empirically analysing collective consumption behaviour. First, we introduce an integer programming (IP) methodology for testing data consistency with collective consumption models that account for publicly as well as privately consumed goods. This IP methodology can include information on assignable for private goods. Next, we show that the IP methodology allows for recovering the personalized (Lindahl) prices for the public goods and the personalized quantities for the private goods. In turn, this implies recovery of the sharing rule (i.e. personalized income share levels). An empirical application demonstrates the practical usefulness of the methodology. © The Author 2011. Published by Oxford University Press.

Multi-impact optimization to reduce aviation noise and emissions

This paper describes a multi-indicator assessment and minimization problem focused on aviation “Community” noise. The model explores a combined noise and emission objective for airfreight movements at Luxembourg’s Findel Airport. Community noise is evaluated via four population impact indicators emissions are tabulated from in-flight segments in the proximity of the airport and from the contribution of taxiing. A set of scenarios based on trajectory, aircraft scheduling, fleet composition, operational procedures are implemented in software. An integer programming methodology is used to search for minimal environmental impact. An on/off switch allows for an evaluation of each indicator in the objective. Different impacts on the population are explored in a case study involving the Cargolux Airlines International S.A.

The Revealed Preference Approach to Collective Consumption Behavior: Nonparametric Testing and Sharing Rule Recovery

We present a nonparametric revealed preference methodology for empirically analyzing collective consumption behavior. First, we introduce an integer programming (IP) methodology for testing data consistency with collective consumption models that account for publicly as well as privately consumed goods.This IP methodology can include information on assignable quantities.for private goods. Next, we show that the IP methodology allows for recovering the personalized (Lindahl) prices for the public goods and the personalized quantities for the private goods. In turn, this implies recovery of the sharing rule (i.e. personalized income share levels). Numerical examples and an empirical application demonstrate the practical usefulness of the methodology.

Testable Implications of General Equilibrium Models: An Integer Programming Approach

Focusing on the testable implications on the equilibrium manifold, we show that the rationalizability problem is NP-complete. Subsequently, we present an integer programming (IP) approach to characterizing general equilibrium models. This approach avoids the use of the Tarski-Seidenberg algorithm for quantifier elimination that is commonly used in the literature. The IP approach naturally applies to settings with any number of observations, which is attractive for empirical applications. In addition, it can easily be adjusted to analyze the testable implications of alternative general equilibrium models (that include, e.g., public goods, externalities and/or production). Further, we show that the IP framework can easily address recoverability questions (pertaining to the structural model that underlies the observed equilibrium behavior), and account for empirical issues when bringing the IP methodology to the data (such as goodness-of-fit and power). Finally, we show how to develop easy-to-implement heuristics that give a quick (but possibly inconclusive) answer to whether or not the data satisfy the general equilibrium models.

The Revealed Preference Approach to Collective Consumption Behavior: Testing, Recovery, and Welfare Analysis

We present a nonparametric 'revealed preference' methodology for empirically analyzing collective consumption behavior. First, we introduce an integer programming (IP) methodology for testing data consistency with alternative collective consumption models: the 'general' case in which any good can be publicly consumed as well as privately consumed, possibly with externalities; and 'special' cases that impose specific prior structure (e.g. the case with all goods publicly consumed, and the case with all goods privately consumed without externalities). In addition, we show that this IP methodology can include information on 'assignable quantities' for particular goods. Next, we demonstrate that the IP methodology allows for recovering the structural collective decision model (including the sharing rule) from the observed collective consumption behavior. In turn, this makes it possible to address welfare-related questions that are specific to the collective consumption model.

Minimum Cost Irrigation Network Design Using Interactive Fuzzy Integer Programming

Minimum cost irrigation network design has been conventionally based on crisp pressure requirements at the hydrants of the network. In order to incorporate obscure knowledge on these pressure requirements at the design stage, an interactive fuzzy integer programming methodology is proposed. In the integer linear programming, formulation membership functions are adopted for expressing pressure constraints. Also, the interactive character of the proposed methodology enables the designer to select a less demanding range of pressures at some “critical” hydrants. By using the proposed methodology significant economic gains may be achieved reducing the cost of the network, since the energy line is adapted more satisfactorily to the ranging pressure requirements. Finally, an application of the methodology to an irrigation network is presented.

An approach to optimal wetland mitigation using mathematical programming and geographic information system based wetland function estimation

We developed and tested a quantitative geographic information system (GIS)-based approach for selecting wetland restoration sites. Our approach uses a combination of an existing wetland function evaluation program, a GIS and integer programming methodology with an objective to minimize cost of restoration subject to meet environmental requirements. Investigations were conducted on the formulation to examine the effects of problem size, site ordering for input, and restoration targets. The formulation could be solved for the largest problem size tested of 996 integer variables. The larger the problem, the more time it took to solve. Larger restoration targets usually took more sites and more time to solve. Sorting sites by size was found to lead to inefficient and often unfeasible solutions. Random sorting of sites was found to be the more efficient method of inputting restoration sites into analysis.

Mixed integer programming methods for computing nonmonotonic deductive databases

Though the declarative semantics of both explicit and nonmonotonic negation in logic programs has been studied extensively, relatively little work has been done on computation and implementation of these semantics. In this paper, we study three different approaches to computing stable models of logic programs based on mixed integer linear programming methods for automated deduction introduced by R. Jeroslow. We subsequently discuss the relative efficiency of these algorithms. The results of experiments with a prototype compiler implemented by us tend to confirm our theoretical discussion. In contrast to resolution, the mixed integer programming methodology is both fully declarative and handles reuse of old computations gracefully. We also introduce, compare, implement, and experiment with linear constraints corresponding to four semantics for “explicit” negation in logic programs: the four-valued annotated semantics [Blair and Subrahmanian 1989], the Gelfond-Lifschitz semantics [1990], the over-determined models [Grant and Subrahmanian 1989], the Gelfond-Lifschitz semantics [1990], the over-determined models [Grant and Subrahmanian 1990], and the classical logic semantics. Gelfond and Lifschitz[1990] argue for simultaneous use of two modes of negation in logic programs, “classical” and “nonmonotonic,” so we give algorithms for computing “answer sets” for such logic programs too.