An integrated approach for deriving priorities in analytic network process

A multiple objective programming approach for the analytic network process (ANP) is proposed to obtain all local priorities for crisp or interval judgments at one time, even in an inconsistent situation. The weakness of the ANP and fuzzy ANP (FANP) is that the complexity of generating priorities is equal to the number of comparison matrices. In the proposed approach, all sets of crisp priorities for each pairwise comparison matrix can be obtained directly. Moreover, from the outcomes of three examples, the power to reach a limiting supermatrix is less than or equal to the power of the FANP. Thus, the proposed approach can be regarded as an efficient alternative of the fuzzy ANP.     

An analytic network process approach to operationalization of five forces model

The five forces model has been one of the most influential frameworks for strategic management. In contrast to its importance as a centerpiece of textbooks, however, it has attracted less attention from both academic researchers and practicing managers. This is due to its innate weakness, difficulty in operationalization. The vital requisites for operationalizing the five forces model are to deal with it as a complex system composed of interrelated forces and their sub-forces, and to prioritize them with consideration of their interdependency. The tenet of this study is the requisites can be achieved through the analytic network process (ANP). The ANP, which is a generalization of the analytic hierarchy process (AHP), produces priorities of elements in a complex network model with consideration of interdependency among elements. The five forces model is transformed into a network model of the ANP. The ANP procedure is then carried out to obtain the priority weights of the forces. Combining the derived weights and ratings on the forces produces the state-of-industry-competition index (SICI) values that represent the overall competitive condition of a given industry. The working of the proposed approach is provided with the help of a case study example of the Web portal Industry of Korea. The proposed ANP approach is expected to expand the five forces model into a workable system of analysis by improving its analytical power.     

Valuation of urban industrial land: An analytic network process approach

In this paper an application of the Analytic Network Process (ANP) to asset valuation is presented. It has two purposes: solving some of the drawbacks found in classical asset valuation methods and broadening the scope of current approaches. The ANP is a method based on Multiple Criteria Decision Analysis (MCDA) that accurately models complex environments. This approach is particularly useful in problems which work with partially available data, qualitative variables and influences among the variables, which are very common situations in the valuation context. As an illustration, the new approach has been applied to a real case study of an industrial park located in Valencia (Spain) using three different models. The results confirm the validity of the methodology and show that the more information is incorporated into the model, the more accurate the solution will be, so the presented methodology stands out as a good alternative to current valuation approaches.     

An effective Markov based approach for calculating the Limit Matrix in the analytic network process

Analytic network process is a multiple criteria decision analysis (MCDA) method that aids decision makers to choose among a number of possible alternatives or prioritize the criteria for making a decision in terms of importance. It handles both qualitative and quantitative criteria, that are compared in pairs, in order to forge a best compromise answer according to the different criteria and influences involved. The method has been widely applied and the literature review reveals a rising trend of ANP-related articles. The ‘power’ matrix method, a procedure necessary for the stability of the decision system, is one of the critical calculations in the mathematical part of the method. The present study proposes an alternative mathematical approach that is based on Markov chain processes and the well-known Gauss-Jordan elimination. The new approach obtains practically the same results as the power matrix method, requires slightly less time and number of calculations and handles effectively cyclic supermatrices, optimizing thus the whole procedure.     

An efficient heuristic approach for a multi-period logistics network redesign problem

In this paper, a multi-period logistics network redesign problem arising in the context of strategic supply chain planning is studied. Several aspects of practical relevance are captured, namely, multiple echelons with different types of facilities, product flows between facilities in the same echelon, direct shipments to customers, and facility relocation. A two-phase heuristic approach is proposed to obtain high-quality feasible solutions to the problem, which is initially modeled as a large-scale mixed-integer linear program. In the first phase of the heuristic, a linear programming rounding strategy is applied to find initial values for the binary location variables. The second phase of the heuristic uses local search to correct the initial variable choices when a feasible solution is not identified, or to improve the initial feasible solution when its quality does not meet given criteria. The results of a computational study are reported for randomly generated instances comprising a variety of logistics networks.     

An analytic approach to stability

The stability method is very useful for obtaining exact solutions of many extremal graph problems. Its key step is to establish the stability property which, roughly speaking, states that any two almost optimal graphs of the same order n can be made isomorphic by changing o(n²) edges.Here we show how the recently developed theory of graph limits can be used to give an analytic approach to stability. As an application, we present a new proof of the Erd?s-Simonovits stability theorem.Also, we investigate various properties of the edit distance. In particular, we show that the combinatorial and fractional versions are within a constant factor from each other, thus answering a question of Goldreich, Krivelevich, Newman, and Rozenberg.     

A utility approach to the analytic hierarchy process

This paper attempts to examine the utility foundation of the Analytic Hierarchy Process (AHP). It identifies the conditions under which the selection of an alternative is consistent with the maximization of an underlying utility function, or more precisely, the conditions under which the AHP-recommended choice corresponds with the solution attained from maximizing the respondent's utility function.     

Decision method for the optimal number of logistics service providers with service quality guarantee and revenue fairness

This study investigates the problem that logistics service integrator (LSI) selects the optimal number of its functional logistics service providers (FLSPs) based on the service quality defect guarantee promised by FLSP and the revenue fairness concerns of LSI. This paper introduces a fairness entropy function to establish a new game model for determining the optimal number of FLSPs. Some conclusions about the impact of parameters on the optimal number of FLSPs are proposed with numerical analysis. For example, as the fairness constraints are satisfied, LSI prefers FLSPs who have higher level of business capacity which results a smaller number of FLSPs.     

Advanced routing for city logistics service providers based on time-dependent travel times

Increasing traffic demand, recurring congestion and sophisticated e-commerce business models lead to enormous challenges for routing in city logistics. We introduce a planning system for city logistics service providers, which faces those challenges by more realistic vehicle routing considering time-dependent travel times. Time-dependent travel times arise from telematics-based traffic data collection city-wide. Well-known heuristics for the Traveling Salesman Problem and for the Vehicle Routing Problem are adapted to time-dependent planning data. Computational experiments allow for insights into the efficiency of individual heuristics, their adaptability to time-dependent planning data sets, and the quality and structure of resulting delivery tours.     

The approach to consistency in the analytic hierarchy process

In his first book on the Analytic Hierarchy Process, T. L. Saaty left open several mathematical questions about the structure of the set of positive reciprocal matrices. In this paper we consider three of these questions: Given an eigenvector and all matrices which give rise to it, can one go from one of them to any order by making small perturbations in the entries? Given two positive column vectors v and w is there a perturbation which carries the set of all positive reciprocal matrices with principal right eigenvector v to the set of positive reciprocal matrices with principal right eigenvector w? Does the set of positive reciprocal n×n matrices whose left and right principal eigenvectors are reciprocals coincide with the set of consistent matrices for n⩾4?     

An analytic approach to stochastic calculus

An Itô type stochastic differential calculus is constructed in an analytic way, without use of the notion of filtration, for processes that satisfy certain homogeneity and smoothness conditions. This calculus is developed in the framework of Lie groups.     

An inventory sharing and allocation method for a multi-location service parts logistics network with time-based service levels

We consider a model to allocate stock levels at warehouses in a service parts logistics network. The network is a two-echelon distribution system with one central warehouse with infinite capacity and a number of local warehouses, each facing Poisson demands from geographically dispersed customers. Each local warehouse uses a potentially different base stock policy. The warehouses are collectively required to satisfy time-based service targets: Certain percentages of overall demand need to be satisfied from facilities within specified time windows. These service levels not only depend on the distance between customers and the warehouses, but also depend on the part availabilities at the warehouses. Moreover, the warehouses share their inventory as a way to increase achieved service levels, i.e., when a local warehouse is out of stock, demand is satisfied with an emergency shipment from another close-by warehouse. Observing that the problem of finding minimum-cost stock levels is an integer non-linear program, we develop an implicit enumeration-based method which adapts an existing inventory sharing model from the literature, prioritizes the warehouses for emergency shipments, and makes use of a lower bound. The results show that the proposed inventory sharing strategy results in considerable cost reduction when compared to the no-sharing case and the method is quite efficient for the considered test problems.     

An integrated model for logistics network design

In this paper we introduce a new formulation of the logistics network design problem encountered in deterministic, single-country, single-period contexts. Our formulation is flexible and integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, product range assignment and product flows. We next describe two approaches for solving the problem---a simplex-based branch-and-bound and a Benders decomposition approach. We then propose valid inequalities to strengthen the LP relaxation of the model and improve both algorithms. The computational experiments we conducted on realistic randomly generated data sets show that Benders decomposition is somewhat more advantageous on the more difficult problems. They also highlight the considerable performance improvement that the valid inequalities produce in both solution methods. Furthermore, when these constraints are incorporated in the Benders decomposition algorithm, this offers outstanding reoptimization capabilities.     

An advanced quality function deployment model using fuzzy analytic network process

Quality function deployment (QFD) is a customer-oriented design tool used to ensure that the voice of customers is employed throughout the product planning and design stages. QFD uses the house of quality (HOQ), which is a matrix that provides a conceptual map for inter-functional planning and communication. In this paper, an advanced QFD model, based on fuzzy analytic network process (ANP) approach, is proposed to systematically take into account the interrelationship between and within the QFD components. The proposed method is aimed at expanding the current research scope from the product planning phase to the part deployment phase to provide product developers with more valuable information (ex. the importance and bottleneck level of part characteristics). Both customer requirements and the company’s production demands will be used as the inputs for the QFD process to enhance the completeness and accuracy of the QFD analysis results. A case study is presented to illustrate the application of the proposed method.     

Decision-making on prioritization of projects in higher education institutions using the analytic network process approach

The prioritization of projects in higher education institutions is a complex decision-making problem. In this paper we deal with two scenarios within Higher Education Institutions. The first scenario is a need to prepare an action plan for activities that will result in the implementation of a portfolio of projects at the institutional level. The second scenario is making a decision on whether to start a new project application, and if so, which project to choose in a situation where project teams have several project ideas and limited resources. The purpose of the paper is to show how to include corporate strategy in the decision-making process and use the Analytic Network Process as a multiple criteria decision-making methodology which can be used in solving project selection problems.     

An analytic approach to the normalized Ricci flow-like equation

This paper is concerned with a parabolic equation with a non-local term defined on a compact two-dimensional Riemannian surface Ω. If the total mass of the solution, λ, is equal to 8π and Ω is the standard sphere S², it is a Hamilton’s normalized Ricci flow. We obtain the global in time existence of the solution to this problem for 0<λ≤8π. If 0<λ<8π, the orbit is compact while for λ=8π, there is a time sequence along which the solution converges to a stationary solution.     

Farmland appraisal based on the analytic network process

This paper presents an application of the Analytic Network Process (ANP) to farmland appraisal. The purpose of this new methodology is to solve some of the drawbacks found in comparative and capitalisation methods, called classical appraisal methods, which cannot deal with contexts where only partial information is available and/or qualitative variables are used. The ANP is a method based on the Multiple Criteria Decision Analysis (MCDA). Previous works have already applied other MCDA techniques to the appraisal context, such as the Analytic Hierarchy Process (AHP), however they have not been able to handle all the complexities of many real world appraisal problems. The ANP provides a more accurate approach for modelling complex environment because it allows the general study of the quantitative and qualitative explanatory variables of the price and the incorporation of feedback and interdependence relationships among variables. The new proposed methodology has been applied to a case study of a farm located in Valencia (Spain) in order to demonstrate its goodness. Both quantitative and qualitative variables, such as the age of the trees, productivity or water quality, have been considered to assess the market value of the farm. Six farms from the same region have been selected as reference assets. The appraisal problem has been solved in three different ways in order to study the influence of each model on the value of the problem farm. In this study it has been proved that the more information is incorporated into the model, the higher accuracy of the solution. From the results of this work we can conclude that the approach proposed stands out as a good alternative to current farmland appraisal approaches, as it has proven to be useful when data are only partially available, qualitative variables are used and influences among the explanatory variables are present.     

An approach to the selection of hyperplane for recognition algorithms

An approach to improving the classification quality of correct algorithms based on a linear combination of algorithms based on the separation of objects by hyperplanes is proposed.     

Implementing the balanced scorecard using the analytic hierarchy process &amp; the analytic network process

The balanced scorecard (BSC) is a multi-attribute evaluation concept that highlights the importance of non-financial attributes. By incorporating a wider set of non-financial attributes into the measurement system of a firm, the BSC captures not only a firm's current performance, but also the drivers of its future performance. Although there is an abundance of literature on the BSC framework, there is a scarcity of literature on how the framework should be properly implemented. In this paper, we use the analytic hierarchy process (AHP) and its variant the analytic network process (ANP) to facilitate the implementation of the BSC. We show that the AHP and the ANP can be tailor-made for specific situations and can be used to overcome some of the traditional problems of BSC implementation, such as the dependency relationship between measures and the use of subjective versus objective measures. Numerical examples are included throughout.