The decision tree polytope and its application to sequential decision problems

This paper describes a new mathematical programming approach to sequential decision problems that have an underlying decision tree structure. The approach, based upon a characterization of strategies as extreme points of a 0–1 polytope called the ‘decision tree polytope’, is particularly suited to the direct examination of risk-return and other tradeoffs amongst strategies. However, it can also be used for conventional utility maximization if a utility function is available. Further, the approach requires no algorithmic development—it can be implemented using commercially available algebraic modeling software and can solve large problems. A related, and already known, approach can be used for some more general Markov decision problems. © 1998 John Wiley & Sons, Ltd.     

Optimal trade-offs of multiple factors in transfer pricing problems

Transfer pricing problems have been extensively researched by a number of scholars. It is well recognized that transfer pricing problems have a multiple-criteria (objectives) feature and can be formulated as a model of multiple-criteria linear programming. However, few methods have the capability of dealing with all possible optimal trade-offs of multiple criteria in optimal solutions of the models. In this paper a linear multiple-factor model is developed to provide managers with a more systematic and comprehensive scenario of all possible optimal transfer prices depending on both multiple criteria and multiple constraint levels. The trade-offs of all possible optimal transfer prices can be used as a basis for managers of a corporation to make a high-quality decision in selecting their transfer pricing systems for business competition. © 1998 John Wiley & Sons, Ltd.     

A note on the use of goal programming for the multiplicative AHP

The main aim of this paper is to identify the opportunities of utilizing goal programming (GP) in the multiplicative analytic hierarchy process (MAHP). It starts with the issue of weight derivation from judgemental matrices. The use of GP for the weight derivation problem is not new, but GP is viewed in this paper from the perspective of augmenting the capabilities of the widely used row geometric mean method (RGMM) of the logarithmic least squares technique (LLST). Different possible approaches using GP are discussed. It is shown that the formulation of the GP problem can be easily modified to provide the same weights as those of the LLST. While this proposed GP technique is not superior to the RGMM in terms of computational ease or speed, it is quite useful in solving certain other problems of the MAHP, such as interval judgements and missing judgements, which cannot be readily solved by the RGMM. The proposed technique provides extensive scope for utilizing the vast literature on non-linear programming, say, for conducting sensitivity analysis. It also has the potential to be useful to more complicated issues of the MAHP, such as group decision making and interlevel dependence, hitherto little explored areas of the MAHP. © 1997 John Wiley & Sons, Ltd.     

A Multiobjective Diet Planning Support System Using the Satisficing Trade-off Method

This paper shows that the satisficing trade-off method (STOM), one of the interactive multiobjective programming techniques, can be applied effectively to the formulation of livestock rations. Nutrient requirements are considered as soft constraints whose right-hand sides are flexible to some extent. This is easily done by regarding the values of the right-hand sides of the constraints as aspiration levels of the decision maker for objective functions. In this way a well-balanced solution can be obtained by STOM with automatic trade-off analysis. In STOM, moreover, because the objective functions and the constraint functions are interchangeable, decision makers are not required to consider the role of objective and constraint as fixed from the beginning. The authors’ experience is that the method makes ration formulation very easy, rapid and flexible. In addition, this paper shows how effectively STOM can be applied not only to diet planning but also to nutritional diagnosis. © 1997 by John Wiley & Sons, Ltd. J. Multi-Crit. Decis. Anal. 6 : 131–139 (1997) No. of Figures: 1. No. of Tables: 3. No. of References: 28.     

Origins,uses of,and relations between goal programming and data envelopment analysis

Origins and uses of ‘goal programming’ and ‘data envelopment analysis’ (DEA) are identified and discussed. The purpose of this paper is not only to review some of the history of these developments, but also to show some of their uses (e.g. in statistical regression formulations) in order to suggest paths for possible further developments. Turning to how the two types of models relate to each other, the ‘additive model’ of DEA is shown to have the same structure as a goal programming model in which only ‘one‐sided deviations’ are permitted. A way for formally relating the two to each other is then provided. However, the objectives are differently oriented because goal programming is directed to future performances as part of the planning function whereas DEA is directed to evaluating past performances as part of the control function of management. Other possible ways of comparing and combining the two approaches are also noted including statistical regressions that utilize goal programming to ensure that the resulting estimates satisfy the multi‐criteria conditions that are often encountered in managerial applications. Both goal programming and DEA originated in actual applications that were successfully addressed. The research was then generalized and published. This leads to what is referred to as an ‘applications‐driven theory’ strategy for research that is also described in this paper. Copyright © 2006 John Wiley & Sons, Ltd.     

A Bibliographic Survey of the Activities and International Nature of Multiple Criteria Decision Making

One of the fascinating things about multiple criteria decision making (MCDM) is the degree to which the contributions that have built the field have come from all over the world. In this paper the international nature of the authorships of the 1216 refereed journal articles published on MCDM between 1987 and 1992, and the journals in which they have appeared, is examined. Also, an analysis of the 217 books and 31 journal special issues that have been published on MCDM, and 143 conferences that have been held on MCDM since the inception of the field, is similarly conducted. The paper concludes with a conference organizer, author and special issue guest editor index.     

Seeing vs. believing: Is believing sufficient to activate the processes of response co-representation?

It has been suggested that the observation of another person's action affects the behavior of the observer because the observation of action leads to the excitation of similar response codes in the observer. It is unknown, however, if one must witness the action or if it is sufficient for one to believe that the other agent is responding for response co-representation to occur. To this end, participants in the present study performed a joint spatial-compatibility task with a confederate when: (1) the confederate sat beside the participant; and, (2) the confederate left the room and told the participant that they would continue to perform their component of the task on a networked computer in another room. Even though participants believed that the confederate performed the task in another room, joint spatial-compatibility was only observed when the confederate was present. These results reveal that the actions of another person may only be represented by the observer when the observer is able to witness a portion of the action.     

The effects of programming common stimuli for enhancing stimulus generalization of academic behavior

Programming common stimuli is a strategy for generalizing behavior across settings (Stokes & Baer, 1977). The present study programmed common stimuli (i.e., goal statement and use of a pictorial icon) to generalize the effects of a reinforcement-based intervention for students identified as either developmentally delayed or emotionally disturbed. Results supported the effectiveness of the strategy in producing generalized responding from training to the generalization setting. The importance of methodological rigor in future research exploring generalization and the need to compare generalization strategies are discussed.     

Integer programs for one- and two-mode blockmodeling based on prespecified image matrices for structural and regular equivalence

Establishing blockmodels for one- and two-mode binary network matrices has typically been accomplished using multiple restarts of heuristic algorithms that minimize functions of inconsistency with an ideal block structure. Although these algorithms likely yield exceptional performance, they are not assured to provide blockmodels that optimize the functional indices. In this paper, we present integer programming models that, for a prespecified image matrix, can produce guaranteed optimal solutions for matrices of nontrivial size. Accordingly, analysts performing a confirmatory analysis of a prespecified blockmodel structure can apply our models directly to obtain an optimal solution. In exploratory cases where a blockmodel structure is not prespecified, we recommend a two-stage procedure, where a heuristic method is first used to identify an image matrix and the integer program is subsequently formulated and solved to identify the optimal solution for that image matrix. Although best suited for ideal block structures associated with structural equivalence, the integer programming models have the flexibility to accommodate functional indices pertaining to regular equivalence. Computational results are reported for a variety of one- and two-mode matrices from the blockmodeling literature.