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Optimizing consistency improvement of positive reciprocal matrices with implications for Monte Carlo Analytic Hierarchy Process

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COMPUTERS & INDUSTRIAL ENGINEERING 2018年 124卷 113-124页

作者： Negahban, Ashkan Penn State Univ Sch Grad Profess Studies Malvern PA 19355 USA

Motivated by a situation encountered in a real-world application of the Analytic Hierarchy Process (AHP), this paper extends previous work on improving consistency of positive reciprocal judgment matrices by optimizing their transformation into near-consistent matrices. A sampling-optimization-adjustment approach is proposed and integrated into the Monte Carlo AHP framework, allowing it to deal with situations where no or insufficient distinct near-consistent matrices can be generated by directly sampling from the original pairwise comparison distributions a situation that prohibits meaningful statistical analysis and effective decision-making using the traditional Monte Carlo AHP. Three mixed-integer nonlinear programing models are formulated for minimizing the sum of adjustments, maximum adjustment, and number of adjusted elements. Four heuristic algorithms are proposed to solve the models. The most appropriate heuristic(s) under each objective function and matrix size is detennined through extensive statistical analysis of numerical experiments. The paper also presents an application of the proposed enhanced Monte Carlo AHP in a real-world industrial example of facility layout design selection, where the traditional Monte Carlo AHP fails to provide sufficient information to perform any statistical analysis on the final ranks and weights for the components in the hierarchy.

关键词： Monte Carlo simulation Analytic hierarchy process mixed-integer nonlinear programing Consistency ratio Facility layout

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Route Optimization for Multiple Searchers

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NAVAL RESEARCH LOGISTICS 2010年第8期57卷 701-717页

作者： Royset, Johannes O. Sato, Hiroyuki USN Postgrad Sch Dept Operat Res Monterey CA 93943 USA

We consider a discrete time-and-space route-optimization problem across a finite time horizon in which multiple searchers seek to detect one or more probabilistically moving targets. This article formulates a novel convex mixed-integer nonlinear program for this problem that generalizes earlier models to situations with multiple targets, searcher deconfliction, and target-and location-dependent search effectiveness. We present two solution approaches, one based on the cutting-plane method and the other on linearization. These approaches result in the first practical exact algorithms for solving this important problem, which arises broadly in military, rescue, law enforcement, and border patrol operations. The cutting-plane approach solves many realistically sized problem instances in a few minutes, while existing branch-and-bound algorithms fail. A specialized cut improves solution time by 50% in difficult problem instances. The approach based on linearization, which is applicable in important special cases, may further reduce solution time with one or two orders of magnitude. The solution time for the cutting-plane approach tends to remain constant as the number of searchers grows. In part, then, we overcome the difficulty that earlier solution methods have with many searchers. (C) 2010 Wiley Periodicals, *** Naval Research Logistics 57: 701-717, 2010

关键词： military operations research search and surveillance route planning mixed-integer nonlinear programing

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Production planning decision of a dairy under supply disruption and demand uncertainty

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JOURNAL OF MODELLING IN MANAGEMENT 2022年第1期17卷 256-271页

作者： Jena, Dayanidhi Ray, Pritee Govt Coll Engn Dept Mech Engn Keonjhar Odisha India Indian Inst Management Ranchi Dept Operat Management Jharkhand India

Purpose The purpose of this paper is to develop a model for the production planning decision of a dairy plant in a multi-product setting under supply disruption risk and demand uncertainty while determining the optimal product-mix and material planning requirement. Design/methodology/approach A mixed-integer nonlinear programming model is proposed to determine the optimal product-mix that maximizes the expected profit of a dairy. The data are collected through visits to the dairy site, conducting brainstorming sessions with the plant manager and marketing head at the corporate office. Disruption data are collected from the India Meteorological Department, Odisha. Findings From the analysis, it is recommended that the dairy should not produce curd during the planning period. Moreover, turnover from toned, double toned and baby food is maximum than that of the curd and these products are produced in the planning period. The expected profit increases from its present value when an optimal product-mix is followed. Sensitivity analysis is performed to analyze the effect of demand uncertainty, supply disruption and production quota. The expected profit decreases as the supply failure probability increases. Research limitations/implications The model is implemented in a dairy plant under Orissa State Cooperative Milk Producers Federation, Odisha, India. The proposed methodology has not been validated, theoretically. The concerned dairy is based on the Indian context, but the authors believe that the study is highly relevant to other dairies as well. Practical implications This study provides a methodology for dairy plant managers to plan production effectively under supply disruption risk with demand uncertainty. It also suggests material requirement planning at different factories of the dairy plant. Originality/value This paper develops a mathematical model for the production planning decision of a dairy plant that determines the optimal product-mix, which maximizes the

关键词： Decision-making Optimization Planning Production nonlinear programing Supply chain management Demand uncertainty mixed-integer nonlinear programing Production planning Supply disruption Dairy industry

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Global Product Design Platforming: A Comparison of Two Equilibrium Solution Methods

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JOURNAL OF MECHANICAL DESIGN 2023年第6期145卷 061702-061702页

作者： Case, Sarah Michalek, Jeremy J. Whitefoot, Kate S. Carnegie Mellon Univ Mech Engn Pittsburgh PA 15213 USA Carnegie Mellon Univ Mech Engn Engn & Publ Policy Civil & Environm Engn by Courtesy Pittsburgh PA 15213 USA Carnegie Mellon Univ Mech Engn Engn & Publ Policy Pittsburgh PA 15213 USA

Global product platforms can reduce production costs through economies of scale and learning but may decrease revenues by restricting the ability to customize for each market. We model the global platforming problem as a Nash equilibrium among oligopolistic competing firms, each maximizing its profit across markets with respect to its pricing, design, and platforming decisions. We develop and compare two methods to identify Nash equilibria: (1) a sequential iterative optimization (SIO) algorithm, in which each firm solves a mixed-integer nonlinear programming problem globally, with firms iterating until convergence;and (2) a mathematical program with equilibrium constraints (MPEC) that solves the Karush Kuhn Tucker conditions for all firms simultaneously. The algorithms' performance and results are compared in a case study of plug-in hybrid electric vehicles where firms choose optimal battery capacity and whether to platform or differentiate battery capacity across the US and Chinese markets. We examine a variety of scenarios for (1) learning rate and (2) consumer willingness to pay (WTP) for range in each market. For the case of two firms, both approaches find the Nash equilibrium in all scenarios. On average, the SIO approach solves 200 times faster than the MPEC approach, and the MPEC approach is more sensitive to the starting point. Results show that the optimum for each firm is to platform when learning rates are high or the difference between consumer willingness to pay for range in each market is relatively small. Otherwise, the PHEVs are differentiated with low-range for China and high-range for the US.

关键词： product platform learning by doing design for market systems designoptimization mixed-integer nonlinear programing global optimization mathematical programming with equilibrium constraints mathematical programming with complementarity constraints Nash equilibrium oligopoly product design product familydesign product platform design

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A Generalized Framework for Reactor Network Synthesis: A Graph Theoretic Approach

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COMPUTERS & CHEMICAL ENGINEERING 2022年 160卷 107722-107722页

作者： de Lima, Arthur E. Pastore Maravelias, Christos T. Univ Wisconsin Dept Chem & Biol Engn 1415 Engn Dr Madison WI 53706 USA Princeton Univ Dept Chem & Biol Engn Princeton NJ 08544 USA Princeton Univ Andlinger Ctr Energy & Environm Princeton NJ 08544 USA

We propose a generalized superstructure-based framework for reactor network synthesis that allows seamless coupling with approaches for separation network synthesis. The proposed framework addresses a generalized problem statement that considers additional degrees of freedom in terms of inlet streams and candidate reactions modeled through tasks assigned to reactors. We develop a graph theoretic approach to systematically build the reactor network superstructure. First, we represent the reactions and tasks through multiple graphs and identify competition among tasks. A group of competing tasks includes tasks that can play similar roles and are represented as subsets of vertices that are fully connected in a task competition graph. Second, we solve optimization problems, based on the task competition graph, to minimize the number of reactors required in the superstructure. Finally, we formulate and solve the optimization model for the integrated synthesis problem. The applicability and flexibility of the framework is illustrated through several examples. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： Reactor network synthesis Graph theory Clique covering problem Process synthesis Superstructure mixed-integer nonlinear programing

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