Comparative evaluation of prior versus progressive articulation of preference in bicriterion optimization

Procedures for solving multiple criteria problems are receiving increasing attention. Two major solution approaches are those involving prior articulation and progressive articulation of preference information. A progressive articulation (interactive) optimization approach, called the Paired Comparison Method (PCM) is compared to the prior articulation approach of a priori utility function measurement in a quality control decision environment from the perspective of the decision maker. The three major issues investigated included: (1) the ease of use of each method, (2) the preferences of solutions obtained, and (3) the insight provided by the methodology into the nature and structure of the problem. The problem setting involved management students who were rquired to determine an acceptance sampling plan using both methods. The PCM provided the most preferred solutions and was considered easier to use and understand. The prior articulation of preference method was found to give more insight into the problem structure. The results suggest that a hybrid approach, combining both prior preference assessment and an interactive procedure exploiting the advantages of each, should be employed to solve multiple criteria problems.     

基于遗传算法的协同多目标攻击空战决策方法

多机协同多目标攻击是未来空对空作战的一种重要形式。首先建立了多机协同空战的自主优势矩阵 ,并依据多人冲突决策理论构造了空战的总体优化指标向量 ,然后针对其他优化算法的不足 ,提出用遗传算法优化该指标向量 ,实现多机协同多目标攻击空战决策 ,最后对 2∶ 2空战进行了仿真。仿真结果证明了上述思想的正确性。     

A combined approach to solve binary multicriteria problems

An implicit enumeration algorithm is developed to determine the set of efficient points in zero-one multiple criteria problems. The algorithm is specialized for the solution of a particular class of facility location problems. The procedure is complemented with the use of the utility function of the decision maker to identify a subset of efficient point candidates for the final selection. Computational results are provided and discussed.     

Risk preference,multiple attributes,and multiple criteria in bayesian acceptance sampling plans

Although there has been considerable research directed toward developing Bayesian acceptance sampling plans, little consideration has been given to incorporating a decision-maker's risk attitude or treating such problems in terms of multiple-type defects and multiple criteria. We review our own work which is focused on the above issues. A model incorporating risk preference is shown to yield substantial differences in the characteristics of an optimal sampling plan relative to a typical Bayesian linear cost (risk neutral) model. Bayesian models and optimization schemes for a variety of multiple-type defect plans are reviewed. A bicriterion acceptance model, employing average outgoing quality and average inspection cost is also formulated. Traditional versus interactive optimization procedures are compared empirically in terms of ease of use, satisfaction with solutions, and insight gained into the problem.     

MABAC method for multiple attribute group decision making under q-rung orthopair fuzzy environment

As the generalization of intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS), the q-rung orthopair fuzzy set (q-ROFS) has emerged as a more meaningful and effective tool to solve multiple attribute group decision making (MAGDM) problems in management and scientific domains. The MABAC (multi-attributive border approximation area comparison) model, which handles the complex and uncertain decision making issues by computing the distance between each alternative and the bored approximation area (BAA), has been investigated by an increasing number of researchers more recent years. In our article, consider the conventional MABAC model and some fundamental theories of q-rung orthopair fuzzy set (q-ROFS), we shall introduce the q-rung orthopair fuzzy MABAC model to solve MADM problems. at first, we briefly review some basic theories related to q-ROFS and conventional MABAC model. Furthermore, the q-rung orthopair fuzzy MABAC model is built and the decision making steps are described. In the end, An actual MADM application has been given to testify this new model and some comparisons between this novel MABAC model and two q-ROFNs aggregation operators are provided to further demonstrate the merits of the q-rung orthopair fuzzy MABAC model.     

An interactive procedure for selecting acceptable alternatives in the presence of multiple criteria

In this paper, we consider the multiple criteria decision‐making problem of partitioning alternatives into acceptable and unacceptable sets. We develop interactive procedures for the cases when the underlying utility function of the decision maker is linear, quasiconcave, and general monotone. We present an application of the procedures to the problem of admitting students to the master's degree program at the Industrial Engineering Department, Middle East Technical University. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 592–606, 2001.     

面向多最优解组合优化问题的决策求解算法

针对具有固定物品总和、多最优解特征的组合优化问题,以固定总和实数子集问题和购买鸡翅问题为例,给出了这类多最优解组合优化问题的形式化表示。在分析枚举等经典算法基础上,提出了基于整数状态表示和实数状态表示的0-1决策递归搜索多最优解动态规划算法。针对该算法在最优解数量较大时,时间复杂度趋向O(mⁿ)的问题,提出了基于相同决策路径合并和基于0-x决策的两种改进算法。实验中两种改进算法的计算时间基本符合与O(nb+nm)的正比关系,表明对于这类多最优解组合优化问题具有良好的求解性能。     

Dynamic programming approaches to the multiple criteria knapsack problem

We study the integer multiple criteria knapsack problem and propose dynamic‐programming‐based approaches to finding all the nondominated solutions. Different and more complex models are discussed, including the binary multiple criteria knapsack problem, problems with more than one constraint, and multiperiod as well as time‐dependent models. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 57–76, 2000     

合成分队火力分配协同决策模型研究

针对合成分队火力分配效率和科学性不高的问题,采用协同决策思想对合成分队火力优化分配方法进行了研究。针对合成分队的作战特点提出了3种模型:建立了攻击力量类型相同的多种准则的火力分配模型,建立了攻击力量类型不同的基于双层规划的火力分配模型,建立了具有上级指定任务的分队内和分队间的火力协同分配模型,并对相关模型进行了实例仿真验证。提出的这3种模型能够解决合成分队在火力分配中的协同决策问题,可提高作战指挥决策的实时性和科学性。     

Maximizing deviation method for multiple attribute decision making under q-rung orthopair fuzzy environment

Because of the uncertainty and subjectivity of decision makers in the complex decision-making environment, the evaluation information of alternatives given by decision makers is often fuzzy and uncertain. As a generalization of intuitionistic fuzzy set (IFSs) and Pythagoras fuzzy set (PFSs), q-rung orthopair fuzzy set (q-ROFS) is more suitable for expressing fuzzy and uncertain information. But, in actual multiple attribute decision making (MADM) problems, the weights of DMs and attributes are always completely unknown or partly known, to date, the maximizing deviation method is a good tool to deal with such issues. Thus, combine the q-ROFS and conventional maximizing deviation method, we will study the maximizing deviation method under q-ROFSs and q-RIVOFSs in this paper. Firstly, we briefly introduce the basic concept of q-rung orthopair fuzzy sets (q-ROFSs) and q-rung interval-valued orthopair fuzzy sets (q-RIVOFSs). Then, combine the maximizing deviation method with q-rung orthopair fuzzy information, we establish two new decision making models. On this basis, the proposed models are applied to MADM problems with q-rung orthopair fuzzy information. Compared with existing methods, the effectiveness and superiority of the new model are analyzed. This method can effectively solve the MADM problem whose decision information is represented by q-rung orthopair fuzzy numbers (q-ROFNs) and whose attributes are incomplete.     

A sequential auction‐bargaining procurement model

One of the most important decisions that a firm faces in managing its supply chain is a procurement decision: selecting suitable suppliers among many potential competing sellers and reducing the purchase cost. While both auctions and bargaining have been extensively studied in the literature, the research that combines auctions and bargaining is limited. In this article, we consider a combined auction‐bargaining model in a setting where a single buyer procures an indivisible good from one of many competing sellers. The procurement model that we analyze is a sequential model consisting of the auction phase followed by the bargaining phase. In the auction phase, the sellers submit bids, and the seller with the lowest bid is selected as the winning bidder. In the bargaining phase, the buyer audits the cost of the winning seller and then negotiates with him to determine the final price. For this auction‐bargaining model, we find a symmetric equilibrium bidding strategy for the sellers in a closed form, which is simple to understand and closely related to the classical results in the auction and bargaining literature. We also show that the auction‐bargaining model generates at least as much profit to the buyer as the standard auction or sequential bargaining model. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Coordinated replenishments from multiple suppliers with price discounts

In this study we present an integer programming model for determining an optimal inbound consolidation strategy for a purchasing manager who receives items from several suppliers. The model considers multiple suppliers with limited capacity, transportation economies, and quantity discounts. We propose an integrated branch and bound procedure for solving the model. This procedure, applied to a Lagrangean dual at every node of the search tree, combines the subgradient method with a primal heuristic that interact to change the Lagrangean multipliers and tighten the upper and lower bounds. An enhancement to the branch and bound procedure is developed using surrogate constraints, which is found to be beneficial for solving large problems. We report computational results for a variety of problems, with as many as 70,200 variables and 3665 constraints. Computational testing indicates that our procedure is significantly faster than the general purpose integer programming code OSL. A regression analysis is performed to determine the most significant parameters of our model. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 579–598, 1998     

A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity

In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity, and contract capacity. We use a scenario tree to model the uncertainty, and build a multi‐stage stochastic integer program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 600–614, 2017     

模糊Petri网在装备保障指挥决策中的应用研究

针对装备保障指挥决策的非结构化特点,结合模糊Petri网的基本理论,建立了一类装备保障指挥决策的模糊Petri网模型(ZYFPN).给出了模型中模糊推理过程的形式化推理算法,算法考虑了推理过程中的众多约束条件,包括命题在规则中的权重、变迁触发的闲值、规则的可信度以及多结论规则等.以装备保障配置地域转移决策为例,描述了从决策问题分析到ZYFPN模型建立,以及基于矩阵运算的决策推理过程的相关问题.应用这一模型,可以提高基于规则的装备保障指挥辅助决策系统的设计、分析和维护效率.     

Incorporation dynamic aspects and uncertainty in 1‐median location problems

In this paper we present several 1‐median formulations on a tree network which incorporate dynamic evolution and/or uncertainty of node demands and transportation costs over a planning horizon. Dynamic evolution is modeled using linear demand functions for the nodes and linear length functions for the edges. Uncertainty is modeled with the use of multiple scenarios, where a scenario is a complete specification of the uncertain node demands and/or edge lengths. We formulate our objective using minimax regret like criteria. We use two different criteria, namely, robust deviation and relative robustness. We discuss what motivated the introduction of these objectives, as well as their relation to existing literature and decision making practices. For all of the models presented, we provide low‐order polynomial time algorithms. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 147–168, 1999     

Stochastic allocation of inspection capacity to competitive processes

Optimal allocation and control of limited inspection capacity for multiple production processes are considered. The production processes, which operate independently but share inspection capacity, are subject to random failures and are partially observed through inspection. This study proposes an approach of stochastic allocation, using a Markov decision process, to minimize expected total discounted cost over an infinite time horizon. Both an optimal model and a disaggregate approximation model are introduced. The study provides some structural results and establishes that the control policy is of a threshold type. Numerical experiments demonstrate a significantly decreased amount of computational time required for the disaggregate approach when compared to the optimal solution, while generating very good control policies. © 2002 John Wiley & Sons, Inc. Naval Research Logistics, 49: 78–94, 2002; DOI 10.1002/nav.1049     

Multiple-attribute decision making with partial information: The comparative hypervolume criterion

A new approach is presented for analyzing multiple-attribute decision problems in which the set of actions is finite and the utility function is additive. The problem can be resolved if the decision makers (or group of decision makers) specifies a set of nonnegative weights for the various attributes or criteria, but we here assume that the decision maker(s) cannot provide a numerical value for each such weight. Ordinal information about these weights is therefore obtained from the decision maker(s), and this information is translated into a set of linear constraints which restrict the values of the weights. These constraints are then used to construct a polytope W of feasible weight vectors, and the subsets H_i (polytopes) of W over which each action a_i has the greatest utility are determined. With the Comparative Hypervolume Criterion we calculate for each action the ratio of the hypervolume of H_i to the hypervolume of W and suggest the choice of an action with the largest such ratio. Justification of this choice criterion is given, and a computational method for accurately approximating the hypervolume ratios is described. A simple example is provided to evaluate the efficiency of a computer code developed to implement the method.     

Route optimization for multiple searchers

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[percnt] 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. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

An interactive branch-and-bound algorithm for bicriterion nonconvex/mixed integer programming

Although there has been extensive research on interactive multiple objective decision making in the last two decades, there is still a need for specialized interactive algorithms that exploit the relatively simple structure of bicriterion programming problems. This article develops an interactive branch-and-bound algorithm for bicriterion nonconvex programming problems. The algorithm searches among only the set of nondominated solutions since one of them is a most preferred solution that maximizes the overall value function of the decision maker over the set of achievable solutions. The interactive branch-and-bound algorithm requires only pairwise preference comparisons from the decision maker. Based on the decision maker's responses, the algorithm reduces the set of nondominated solutions and terminates with his most preferred nondominated solution. Branching corresponds to dividing the subset of nondominated solutions considered at a node into two subsets. The incumbent solution is updated based on the preference of the decision maker between two nondominated solutions. Fathoming decisions are based on the decision maker's preference between the incumbent solution and the ideal solution of the node in consideration.     

Optimal control of a capacitated inventory system with multiple demand classes

This article studies the optimal control of a periodic‐review make‐to‐stock system with limited production capacity and multiple demand classes. In this system, a single product is produced to fulfill several classes of demands. The manager has to make the production and inventory allocation decisions. His objective is to minimize the expected total discounted cost. The production decision is made at the beginning of each period and determines the amount of products to be produced. The inventory allocation decision is made after receiving the random demands and determines the amount of demands to be satisfied. A modified base stock policy is shown to be optimal for production, and a multi‐level rationing policy is shown to be optimal for inventory allocation. Then a heuristic algorithm is proposed to approximate the optimal policy. The numerical studies show that the heuristic algorithm is very effective. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 43–58, 2011