A Criterion Space Branch-and-Cut Algorithm for Mixed Integer Bilinear Maximum Multiplicative Programs

This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash bargaining solution (Nash social welfare optimization), capacity allocation markets, reliability optimization, etc. The proposed algorithm applies multiobjective optimization principles to solve MIBL-MMPs exploiting a special characteristic in these problems. That is, taking each multiplicative term in the objective function as a dummy objective function, the projection of an optimal solution of MIBL-MMPs is a nondominated point in the space of dummy objectives. Moreover, several enhancements are applied and adjusted to tighten the bounds and improve the performance of the algorithm. The performance of the algorithm is investigated by 400 randomly generated sample instances of MIBL-MMPs. The obtained result is compared against the outputs of the mixed-integer second order cone programming (SOCP) solver in CPLEX and a state-of-the-art algorithm in the literature for this problem. Our analysis on this comparison shows that the proposed algorithm outperforms the fastest existing method, that is, the SOCP solver, by a factor of 6.54 on average. Summary of Contribution: The scope of this paper is defined over a class of mixed-integer programs, the so-called mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). The importance of MIBL-MMPs is highlighted by the fact that they are encountered in applications, such as Nash bargaining, capacity allocation markets, reliability optimization, etc. The mission of the paper is to introduce a novel and effective criterion space branch-and-cut algorithm to solve MIBL-MMPs by solving a finite number of single-objective mixed-integer linear programs. Starting with an initial set of primal and dual bounds, our proposed approach explores the efficient set of the multiobjective problem counterpart of the MIBL-MMP through a criterion space–based branch-and-cut paradigm and iteratively improves the bounds using a branch-and-bound scheme. The bounds are obtained using novel operations developed based on Chebyshev distance and piecewise McCormick envelopes. An extensive computational study demonstrates the efficacy of the proposed algorithm.

Decision analysis of warehouse productivity performance indicators to enhance logistics operational efficiency

PurposeThe warehouse industry is one of the backbones in the logistics operation which involves several activities i.e. storage, receiving, picking and shipping of goods/cargoes. This study analyzes the most important warehouse productivity indicators for improving warehouse operation efficiency.Design/methodology/approachThis study presents an empirical methodology of the fuzzy analytical hierarchy process (FAHP) method, an integration between the fuzzy logic method with an analytical hierarchy process (AHP) method incorporated with the adoption of quantitative and systems theories under the modern management theory approach.FindingsThe results indicate that the weight values of the main criteria which lead by the criterion “Space (0.4005)” at the top ranking, followed by Information System (0.2445), Labor (0.2065) and Equipment (0.1484). In addition, the weight values and ranking of the 16 sub-criteria are also highlighted which the sub-criterion “Warehouse Management System (0.2445)” scores the highest weight value and followed by Storage Space Utilization (0.1043) and Throughput (0.0722) accordingly.Research limitations/implicationsFinally, this research contributed to enrich the literature, while highlighting a series of recommendations on the top three most significant productivity performance indicators that can be useful in further research.Originality/valueA generic analysis model developed with the adoption of three study theories: quantitative, system and productivity theories.

Map-Based Exploratory Evaluation of Non-Medical Determinants of Population Health

Multi‐criteria evaluation (MCE) and decision‐making are increasingly combined with interactive tools to assist users with visual thinking and exploring decision strategies. The interactive control of criterion combination rules and the simultaneous observation of geographic space and criterion space provide a means of investigating the sensitivity of the decision outcome to the decision‐maker's preferences. The Analytic Hierarchy Process (AHP) is an MCE method that has been successfully implemented in management processes including those addressed by Geographic Information Systems. In this paper, we present a map‐based, interactive AHP implementation, which provides a link between a well‐understood decision support method and exploratory geographic visualization. Using a case study with public health data for the Province of Ontario, Canada, we demonstrate that exploratory map use increases the effectiveness of the AHP‐based evaluation of population health.

Map-Based Exploratory Evaluation of Non-Medical Determinants of Population Health

Multi‐criteria evaluation (MCE) and decision‐making are increasingly combined with interactive tools to assist users with visual thinking and exploring decision strategies. The interactive control of criterion combination rules and the simultaneous observation of geographic space and criterion space provide a means of investigating the sensitivity of the decision outcome to the decision‐maker's preferences. The Analytic Hierarchy Process (AHP) is an MCE method that has been successfully implemented in management processes including those addressed by Geographic Information Systems. In this paper, we present a map‐based, interactive AHP implementation, which provides a link between a well‐understood decision support method and exploratory geographic visualization. Using a case study with public health data for the Province of Ontario, Canada, we demonstrate that exploratory map use increases the effectiveness of the AHP‐based evaluation of population health.

Behavioral Information Security: Defining the Criterion Space

The success of information security appears to depend in part upon the effective behavior of the individuals involved in its use. Appropriate and constructive behavior by end users, system administrators, and others can enhance the effectiveness of information security while inappropriate and destructive behaviors can substantially inhibit its effectiveness. The present research focuses on “behavioral information security” which is defined as the complexes of human action that influence the availability, confidentiality, and integrity of information systems. Because research in this area is so new, in the present in study we focused on delineating and understanding the behavioral domain. Our goal for this study was to construct and test a taxonomy of information security behaviors. We expect that this knowledge can support later research efforts that focus on understanding the antecedents and consequences of information security behavior.

Ship optimization using the preferences of the designer

В статье рассматривается подход к решению задачи оптимизации характеристик корабля на ранних стадиях проектирования. Задача оптимизационного проектирования формулируется как многокритериальная. Дается краткий обзор подходов к решению задач математического программирования такого класса. Рассматривается такой метод многокритериальной оптимизации, широко используемый в экономических задачах, как оптимизация по Парето. Для решения задач, связанных с созданием технических систем, характерно большое количество частных критериев эффективности, выраженных, как правило, нелинейными функциями, а иногда описанными алгоритмическими процедурами. Следовательно, поверхность эффективных точек Парето, на которой ищется наилучший вариант проекта, представляет собой сложный геометрический объект в n- мерном пространстве частных критериев. Выбор наилучшего решения предлагается путем использования предпочтения проектанта, сформулированными в виде функции ценности. Функция ценности также является сложной поверхностью в n-мерном критериальном пространстве. Аналитическое решение, дающее координаты точек касания этих поверхностей, представляет сложную математическую проблему. В статье предлагается численный метод решения задачи оптимизации по Парето для сложной технической системы, каковой является корабль. The article considers an approach to solving the problem of optimizing the ship's characteristics at the early stages of design. The optimization design problem is formulated as a multi-criteria one. A brief overview of approaches to solving mathematical programming problems of this class is given. We consider such a method of multi-criteria optimization, widely used in economic problems, as Pareto optimization. To solve problems related to the creation of technical systems, a large number of specific performance criteria are characteristic, expressed, as a rule, by nonlinear functions, and sometimes described by algorithmic procedures. Consequently, the surface of effective Pareto points, on which the best variant of the project is sought, is a complex geometric object in the n-dimensional space of partial criteria. The choice of the best solution is proposed by using the preferences of the designer, formulated in the form of a value function. The value function is also a complex surface in the n-dimensional criterion space. The analytical solution that gives the coordinates of the points of contact of these surfaces is a complex mathematical problem. The paper proposes a numerical method for solving the Pareto optimization problem for a complex technical system, such as a ship.

Multi-Objective Optimization of Production Objectives Based on Surrogate Model

The article addresses an approximate solution to the multi-objective optimization problem for a black-box function of a manufacturing system. We employ the surrogate of the discrete-event simulation model of a batch production system in an analytical form. Integration of simulation, Design of Experiments methods, and Weighted Sum and Weighted Product multi-objective methods are used in an arrangement of a priori defined preferences to find a solution near the Pareto optimal solution in a criterion space. We compare the results obtained through the analytical approach to the outcomes of simulation-based optimization. The observed results indicate a possibility to apply the suitable analytical model for quickly finding the acceptable approximate solution close to the Pareto optimal front.

Assessing protopectin transformation potential of plant tissue using a zoned criterion space

Introduction. The existing diversity of plant raw materials and products predetermine the prospects of studying their potential as sources of pectin substances. However all current classifications are either fragmented or inconsistent. Study objects and methods. Our theoretical ivestigation aimed to develop an adequate classification for all taxa of plant origin, as well as their tissues and derivatives as pectin-containing materials. We developed criteria for assessing transformation potential of the protopectin complex based on the mass fractions of biologically active non-uronide components, native water-soluble pectin, the protopectin complex, and pectin substances. Individual boundary conditions were based on individual pectin potential, protopectin fragmentation potential, and pectin isolation potential. Results and discussion. Based on the boundary conditions, we defined an universal criterion space that included a set of points M in the coordinates expressed by three main criteria. According to individual boundary conditions, the criterion space was divided, or zoned, into four domains corresponding to protopectin fragmentation potential. They were characterized by: 1) lack of pectin potential, 2) ineffective protopectin fragmentation, 3) ineffective isolation of fragmentation products, and 4) effective isolation. Finally, we developed a generalized algorithm to determine the location of points M[μ1, μ2 , μ3 ] in the zoned criterion space, characterizing the plant tissue. Conclusion. Our approach can be used to assess any plant tissue for its protopectin transformation potential, which determines the technological influence on its pectin potential. This approach is universal, i.e., applicable to both plant tissue and its derivatives.