An improvement to multiple criteria ABC inventory classification

In this paper we presented an extended version of the Ng-modelg [W.L. Ng, A simple classifier for multiple criteria ABC analysis, European Journal of Operational Research 177 (2007) 344–353] for multi-criteria inventory classification. The proposed model is a nonlinear programming model which determines a common set of weights for all the items. Our model not only incorporates multiple criteria for ABC classification, but also maintains the effects of weights in the final solution, an improvement over the model proposed by Ng. An illustrative example is presented to compare our model and the Ng-model.     

A simple classifier for multiple criteria ABC analysis

To have an efficient control of a huge amount of inventory items, traditional approach is to classify the inventory into different groups. Different inventory control policies can then applied to different groups. The well-known ABC classification is simple-to-understand and easy-to-use. However, ABC analysis is based on only single measurement such as annual dollar usage. It has been recognized that other criteria are also important in inventory classification.     

A group of knowledge-incorporated multiple criteria linear programming classifiers

Classification is a main data mining task, which aims at predicting the class label of new input data on the basis of a set of pre-classified samples. Multiple criteria linear programming (MCLP) is used as a classification method in the data mining area, which can separate two or more classes by finding a discriminate hyperplane. Although MCLP shows good performance in dealing with linear separable data, it is no longer applicable when facing with nonlinear separable problems. A kernel-based multiple criteria linear programming (KMCLP) model is developed to solve nonlinear separable problems. In this method, a kernel function is introduced to project the data into a higher-dimensional space in which the data will have more chance to be linear separable. KMCLP performs well in some real applications. However, just as other prevalent data mining classifiers, MCLP and KMCLP learn only from training examples. In the traditional machine learning area, there are also classification tasks in which data sets are classified only by prior knowledge, i.e. expert systems. Some works combine the above two classification principles to overcome the faults of each approach. In this paper, we provide our recent works which combine the prior knowledge and the MCLP or KMCLP model to solve the problem when the input consists of not only training examples, but also prior knowledge. Specifically, how to deal with linear and nonlinear knowledge in MCLP and KMCLP models is the main concern of this paper. Numerical tests on the above models indicate that these models are effective in classifying data with prior knowledge.     

A new approach to multi-criteria sorting based on fuzzy outranking relations: The THESEUS method

In this paper, we propose the THESEUS method, a new approach based on fuzzy outranking relations to multi-criteria sorting problems. Compared with other outranking-based methods, THESEUS is inspired by another view of multi-criteria classification problems. It utilizes a new way of evaluating the assignment of an object to an element of the set of ordered categories that were previously defined. This way is based on comparing every possible assignment with the information from various preference relations that are derived from a fuzzy outranking relation defined on the universe of objects. The appropriate assignment is determined by solving a simple selection problem.The capacity of a reference set for making appropriate assignments is related to a good characterization of the categories. A single reference action characterizing a category may be insufficient to achieve well-determined assignments. In this paper, the reference set capacity to perform appropriate assignments is characterized by some new concepts. This capacity may be increased when more objects are added to the reference set. THESEUS is a method for handling the preference information contained in such larger reference sets.     

Modeling uncertainty in multi-criteria decision analysis

his paper provides a review of multiple criteria decision analysis (MCDA) for cases where attribute evaluations are uncertain. The main aim is to identify different tools which can be used to represent uncertain evaluations, and to broadly survey the available decision models that can be used to support uncertain decision making. The review includes models using probabilities or probability-like quantities; explicit risk measures such as quantiles and variances; fuzzy numbers, and scenarios. The practical assessment of uncertain outcomes and preferences associated with these outcomes is also discussed.     

A multiplicative version of Promethee II applied to multiobjective optimization problems

The method Promethee II has produced attractive results in the choice of the most satisfactory optimal solution of convex multiobjective problems. However, according to the current literature, it may not work properly with nonconvex problems. A modified version of this method, called multiplicative Promethee, is proposed in this paper. Both versions are applied to some analytical problems, previously optimized by an evolutionary algorithm. The multiplicative Promethee got much better results than the original Promethee II, being capable of solving convex and nonconvex problems, with continuous and discontinuous Pareto fronts.     

Preference elicitation from inconsistent judgments using multi-objective optimization

Several decision-making techniques involve pairwise comparisons to elicit the preferences of a decision maker (DM). This paper proposes a new approach for prioritization from pairwise comparisons using the concept of indirect judgments. No method exists that simultaneously minimizes deviations from both direct and indirect judgments. In order to estimate preferences, it is sensible to consider both the acquired judgments and the other judgments latent in the DM’s mind. Hence, a technique is developed here to minimize the deviations from both types of judgments.     

A multi-criteria model for auditing a Predictive Maintenance Programme

Auditing tools can play a key role in the continuous improvement of maintenance policies, in particular to enhance predictive maintenance (PM). This paper proposes a multi-criteria model for auditing a Predictive Maintenance Programme (PMP) developed and implemented in the General Hospital of Ciudad Real (GHCR) in Spain. The model has a two-level structure, with top level auditing areas specified by second level auditing criteria on which the performance of the PMP should be appraised. This structure resulted from the analysis and discussion of an internal questionnaire to the management, technical and consulting staff of GHCR. This also guided the association of a performance scale with each criterion, describing several reference levels of accomplishment. Using the MACBETH (Measuring Attractiveness by a Categorical Based Evaluation Technique) approach, a hierarchical additive value model was constructed, with criteria weights and value scales derived from staff judgments of comparison of different reference levels and profiles of performance. This model enables managers to measure the performance of the PMP and its added value for the hospital, not only against each audit criterion individually, but also on each area and in overall terms. Integrated in a management “tableau de bord”, the model outputs permit the identification of PMP deficiencies requiring urgent intervention and corrective measures for its continuous improvement.     

A note on coalitional manipulation and centralized inventory management

In this note we deal with inventory games as defined in Meca et al. (Math. Methods Oper. Res. 57:483–491, 2003). In that context we introduce the property of immunity to coalitional manipulation, and demonstrate that the SOC-rule (Share the Ordering Cost) is the unique allocation rule for inventory games which satisfies this property. The authors acknowledge the financial support of Ministerio de Educación y Ciencia, FEDER and Xunta de Galicia through projects SEJ2005-07637-C02-02 and PGIDIT06PXIC207038PN.     

A note on scale transformations in the PROMETHEE V method

As already noted by Mavrotas et al. (2006), the PROMETHEE V method for multi-attribute analysis of portfolio problems will fail to include an item in a portfolio if it has a negative net flow with respect to other items, although adding such an item might actually improve the entire portfolio. However, the model formulated by Mavrotas et al. introduces a bias in favor of large portfolios because the PROMETHEE V method is sensitive to scale transformations. The present paper analyzes this effect and proposes a method to correct it.     

Lost-sales inventory theory: A review

In classic inventory models it is common to assume that excess demand is backordered. However, studies analyzing customer behavior in practice show that most unfulfilled demand is lost or an alternative item/location is looked for in many retail environments. Inventory systems that include this lost-sales characteristic appear to be more difficult to analyze and to solve. Furthermore, lost-sales inventory systems require different replenishment policies to minimize costs compared to backorder systems. In this paper, we classify the models in the literature based on the characteristics of the inventory system and review the proposed replenishment policies. For each classification and type of replenishment policy we discuss the available models and their performance. Furthermore, directions for future research are proposed.     

Learning multicriteria classification models from examples: Decision rules in continuous space

The classification problem statement of multicriteria decision analysis is to model the classification of the alternatives/actions according to the decision maker's preferences. These models are based on outranking relations, utility functions or (linear) discriminant functions. Model parameters can be given explicitly or learnt from a preclassified set of alternatives/actions.In this paper we propose a novel approach, the Continuous Decision (CD) method, to learn parameters of a discriminant function, and we also introduce its extension, the Continuous Decision Tree (CDT) method, which describes the classification more accurately.The proposed methods are results of integration of Machine Learning methods in Decision Analysis. From a Machine Learning point of view, the CDT method can be considered as an extension of the C4.5 decision tree building algorithm that handles only numeric criteria but applies more complex tests in the inner nodes of the tree. For the sake of easier interpretation, the decision trees are transformed to rules.     

Verbal ordinal classification with multicriteria decision aiding

Professionals in neuropsychology usually perform diagnoses of patients’ behaviour in a verbal rather than in a numerical form. This fact generates interest in decision support systems that process verbal data. It also motivates us to develop methods for the classification of such data. In this paper, we describe ways of aiding classification of a discrete set of objects, evaluated on set of criteria that may have verbal estimations, into ordered decision classes. In some situations, there is no explicit additional information available, while in others it is possible to order the criteria lexicographically. We consider both of these cases. The proposed Dichotomic Classification (DC) method is based on the principles of Verbal Decision Analysis (VDA). Verbal Decision Analysis methods are especially helpful when verbal data, in criteria values, are to be handled. When compared to the previously developed Verbal Decision Analysis classification methods, Dichotomic Classification method performs better on the same data sets and is able to cope with larger sizes of the object sets to be classified. We present an interactive classification procedure, estimate the effectiveness and computational complexity of the new method and compare it to one of the previously developed Verbal Decision Analysis methods. The developed and studied methods are implemented in the framework of a decision support system, and the results of testing on artificial sets of data are reported.     

A note on the inventory models for deteriorating items with ramp type demand rate

In this research we study the inventory models for deteriorating items with ramp type demand rate. We first clearly point out some questionable results that appeared in (Mandal, B., Pal, A.K., 1998. Order level inventory system with ramp type demand rate for deteriorating items. Journal of Interdisciplinary Mathematics 1, 49–66 and Wu, K.S., Ouyang, L.Y., 2000. A replenishment policy for deteriorating items with ramp type demand rate (Short Communication). Proceedings of National Science Council ROC (A) 24, 279–286). And then resolve the similar problem by offering a rigorous and efficient method to derive the optimal solution. In addition, we also propose an extended inventory model with ramp type demand rate and its optimal feasible solution to amend the incompleteness in the previous work. Moreover, we also proposed a very good inventory replenishment policy for this kind of inventory model. We believe that our work will provide a solid foundation for the further study of this sort of important inventory models with ramp type demand rate.     

A note on fuzzy inventory model with storage space and budget constraints

In 1997, Roy and Maiti developed a fuzzy EOQ model with fuzzy budget and storage capacity constraints where demand is influenced by the unit price and the setup cost varies with the quantity purchased [T.K. Roy, M. Maiti, A fuzzy EOQ model with demand-dependent unit cost under limited storage capacity, Eur. J. Oper. Res. 99 (1997) 425–432]. However, their procedure has some questionable points and their numerical examples contain rather peculiar results. The purpose of this paper is threefold. First, for the same inventory model with fuzzy constraints, based on the max–min operator, we proposed an improved solution procedure. Second, we review the solution procedure by Roy and Maiti that is based on Kuhn–Tucker approach to point out their questionable results. Third, we compare Roy and Maiti’s approach with ours to explain why our approach can solve the problem and theirs cannot. Numerical examples provided by them also support our findings.     

A simulation-based test of stochastic multicriteria acceptability analysis using achievement functions

Stochastic multicriteria acceptability analysis using achievement functions (SMAA-A) is a preference model for discrete-choice decision making that inverts the traditional goal programming process by asking what combinations of aspirations are necessary to make each alternative the preferred one, rather than what alternative is preferred given a set of aspirations. In this paper, we test the ability of the model to discern good-performing alternatives from poorly-performing ones using a simulation study. Simulation results show that a suitably detailed construction of the acceptability index is particularly important, and that the resulting model can be fruitfully applied in the selection of a shortlist of alternatives from a larger set with only very limited decision maker involvement.     

Technical note on inventory model with trapezoidal type demand

This note is a response to optimal policy for deteriorating items with trapezoidal type demand and partial backlogging by Cheng et al. [4]. In the above mentioned paper, a new inventory model was created, but both their model and their solution procedure contained some questionable results. In this note a detailed examination of their paper will be provided, offering an enhancement to their important inventory model and solution procedure. Numerical examples and detailed analysis of the four scenarios are used to illustrate our findings.     

A note on “Two-warehouse inventory model with deterioration under FIFO dispatch policy”

A recently published paper by Lee [C.C. Lee, Two-warehouse inventory model with deterioration under FIFO dispatching policy, European Journal of Operational Research 174 (2006) 861–873] considers different dispatching models for the two-warehouse inventory system with deteriorating items, in which Pakkala and Achary’s LIFO (last-in–first-out) model [T.P.M. Pakkala, K.K. Achary, A deterministic inventory model for deteriorating items with two warehouses and finite replenishment rate, European Journal of Operational Research 57 (1992) 71–76] is first modified, and then the author concludes that the modified LIFO model always has a lower cost than Pakkala and Achary’s LIFO model under a particular condition specified by him. The present note points out that this conclusion is incorrect and misleading. Alternatively, we provide a new sufficient condition such that the modified LIFO model always has a lower cost than Pakkala and Achary’s model. Besides, we also compare Pakkala and Achary’s original LIFO model with Lee’s FIFO (first-in–first-out) model for the special case where the two warehouses have the same deteriorating rates. Finally, numerical examples are provided to investigate and examine the impact of corresponding parameters on policy choice. The results in this note give a much clearer picture than those at Lee’s paper about the relationships between the different dispatching policies for the two-warehouse inventory system with deterioration items.