Lawrence C. Leung

On consistency and ranking of alternatives in fuzzy AHP

Abstract In fuzzy AHP where pairwise comparisons are described by membership values, the treatment of consistency has largely been sketchy. This paper proposes a fuzzy consistency definition with consideration of a tolerance deviation. Essentially, the fuzzy ratios of relative importance, allowing certain tolerance deviation, are formulated as constraints on the membership values of the local priorities. The fuzzy local and global weights are determined via the extension principle. The alternatives are ranked on the basis of the global weights by application of a maximum–minimum set ranking method. Our analysis uses only the data which are considered as consistent. The proposed approach is computationally efficient as it consists of solving only linear programs. An example is included for illustrative purpose.

Implementing the balanced scorecard using the analytic hierarchy process & 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 firms 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.

Modifying inconsistent comparison matrix in analytic hierarchy process: A heuristic approach

Test of consistency is a critical step in the AHP methodology. When a pairwise comparison matrix fails to satisfy the consistency requirement, a decision maker needs to make revisions. To aid the decision makers revising process, several approaches identify changes to the consistency requirement with respect to changes to a single entry in the original inconsistent matrix [P.T. Harker, Derivatives of the Perron root of a positive reciprocal matrix: with application to the analytic hierarchy process, Applied Mathematics and Computation, 22, 217-232 (1987); T.L. Saaty, Decision-making with the AHP: Why is the principal eigenvector necessary, European Journal of Operational Research, 145, 85-91 (2003)]. Instead of revising single entries, Xu and Wei [Z. Xu and C. Wei, A consistency improving method in the analytic hierarchy process, European Journal of Operational Research, V.116, 443-449 (1999)] derived a consistent matrix by an auto-adaptive process based on the original inconsistent matrix. In this paper, we develop a heuristic approach that auto-generates a consistent matrix based on the original inconsistent matrix. Expressing the inconsistent matrix in terms of a deviation matrix, an iterative process adjusts the deviation matrix to improve the consistency ratio, while preserving most of the original comparison information. We show that the proposed method is able to preserve more original comparison information than Xu and Wei [Z. Xu and C. Wei, A consistency improving method in the analytic hierarchy process, European Journal of Operational Research, V.116, 443-449 (1999)]. It is also shown that the heuristic approach can be used to examine the effects of revising a sub-bloc as well as revising a single entry of the original matrix.

Minimizing weighted tardiness of job-shop scheduling using a hybrid genetic algorithm

Relative to job-shop scheduling problems that optimize makespan or flow time, due-date-related problems are usually much more computationally complex and are classified as strongly NP-hard. In this paper, a hybrid framework integrating a heuristic and a genetic algorithm (GA) is utilized for job-shop scheduling to minimize weighted tardiness. For each new generation of schedules, the GA determines the first operation of each machine, and the heuristic determines the assignment of the remaining operations. Schedules with inferior tardiness are discarded before the next round of evolution. Extensive numerical experiments were conducted for different levels of due-date tightness. The results show that the hybrid framework performs significantly better than does either a heuristic or GA alone. It is also found to be superior to a well-recognized heuristic improvement procedure (lead-time iterations). Specifically, the combination of the RM this combination is, however, outperformed by the heuristic of Kreipl [Kreipl, S., 2000. A large step random walk for minimizing total weighted tardiness in a job shop. Journal of Scheduling 3, 125-138]. We also develop a generalized hybrid framework that can adapt to different job-shop problems--with or without sequence-dependent setups and with different objectives (e.g., makespan, tardiness, flow time). The new framework allows the interaction of parallel evolutions, extending the GA-heuristic environment to the solving of multi-objective scheduling problems.

Evolution of e-commerce Web sites: A conceptual framework and a longitudinal study

Before the 1990s, the digital exchange of information between companies was achieved using electronic data interchange (EDI) and needed agreement between the organizations. The early 1990s saw the commercialization of the Internet and the advent of open computer technology and connectivity became affordable for individuals as well as businesses. The consequence was the World Wide Web. As e-commerce activities extended across businesses, enterprises, and industries, a genre of Web sites emerged allowing the integrative management of business operations. Here, we provide an evolutionary perspective of e-commerce Web sites. We posited that there have been four eras. To chart the evolution of e-commerce Web sites, a conceptual framework was developed to characterize such sites. Based on the framework, we conducted a longitudinal study between 1993 and 2001. The result showed that the proposed four eras were clearly discernible.

An intelligent decision support system for service network planning

The joint use of an optimization model and a simulation model as a two-stage methodology has been successfully applied in various operation planning situations, such as service network planning. While using the two-stage methodology, the decisionmaker, who is normally a domain expert, also needs to be familiar with the models. He/she manipulates the two models iteratively to reach a planning solution. This paper presents an intelligent decision support system (IDSS), which integrates a decision support system (DSS) with an expert system (ES), to provide guidance to the decision-maker during the planning process. As proof of this concept, a PC-based IDSS prototype was built and implemented in the design of a service network for a major air-express courier.

On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy

Abstract AHP is a multi-attribute decision-making methodology widely used by both practitioners and researchers. In the 1980s, critics had raised questions regarding its proper use. There were quite a few suggested modifications to overcome the supposed limitations of AHP. These modifications are themselves limited as they typically impede the applicability of AHP. In this paper, we revisit some of the earlier criticisms. We have two objectives (1) to articulate the proper use of AHP by highlighting the assumptions and implications underlying AHP, and (2) to show that Sinarchy can be used to address the earlier criticisms while maintaining the applicability of the AHP framework. We identify that in AHP, tradeoffs between criteria vary amongst individual alternatives and are dependent on the alternative’s proportion of contribution towards each criterion. For problems where tradeoffs between criteria are in terms of their relative measurements, Sinarchy should be used. It is also shown that Sinarchy can prevent rank reversal. Illustrative examples are included throughout.

Fuzzy production planning model for fresh tomato packing

Abstract A fuzzy mathematical program is formed when the strict requirements within a mathematical program (objective coefficients, right-hand-side values, inequality conditions, etc.) are fuzzified. In general, such fuzzifying is appropriate for situations where the values or conditions are subjects of perception. In tomato packing, uncertain elements attributed to human perception are quite common. Such elements include harvest time, tomato packing rate, and shortage cost. In this paper, we first provide an LP formulation to determine the production schedule for a fresh tomato packinghouse. Then the corresponding fuzzy elements are fuzzified into a fuzzy model which is solved using an auxiliary model (mixed 0–1 LP). Using real-life data, we compare the cost obtained from the LP to that from the fuzzy model. It is found that the cost from the former is substantially higher. We observe that the rigid requirements in the LP results in an unrealistic optimal solution, while the fuzzy programming seeks to realize a desirable solution (as perceived by the user) by relaxing some resource restrictions. It is further observed that such opportunistic relaxation of constraints to achieve a better solution is typical of decision-making behavior in tomato packing.

Analysis of compatibility between interdependent matrices in ANP

Analytic network process (ANP) addresses multi-attribute decision-making where attributes exhibit dependencies. A principal characteristic of such problems is that pairwise comparisons are needed for attributes that have interdependencies. We propose that before such comparison matrices are used—in addition to a test that assesses the consistency of a pairwise comparison matrix—a test must also be conducted to assess ‘consistency’ across interdependent matrices. We call such a cross-matrix consistency test as a compatibility test. In this paper, we design a compatibility test for interdependent matrices between two clusters of attributes. We motivate our exposition by addressing compatibility in Sinarchy, a special form of ANP where interdependency exists between the last and next-to-last level. The developed compatibility test is applicable to any pair of interdependent matrices that are a part of an ANP.

Airfreight forwarder shipment planning: A mixed 0–1 model and managerial issues in the integration and consolidation of shipments

The planning and management of air cargo logistics is a complex endeavor, involving collaboration of multiple logistics agents to deliver shipments timely, safely and economically. Airfreight forwarders are third-party brokers/operators who coordinate and manage cargo shipments for their clients. It is important for a forwarder to develop a shipment plan to evaluate the possible integrations and consolidations, to assess whether shipments can meet their respective target delivery dates, and to estimate the amount of costs involved. In this paper, we formulate a forwarders shipment planning problem as a mixed 0-1 LP. Effects of integration and consolidation - on the timely delivery of shipments during any phase of the shipping process - are explicitly addressed. A forwarders in-house capacity, as well as the available capacity of its partners and sub-contracting agents, are incorporated. We also consider the target cost for a shipment. Based on the special characteristics of the model, we design a customized tabu-search algorithm. We also provide an illustrative case to examine several managerial issues.