Aggregating classifiers with mathematical programming

This paper aims to develop a suitable restoration method by a joint usage of an Expert system (ES) and a Mathematical Programming (MP) approach. Under this devise, the optimal target system for storation is formulated as an MP problem and solved efficiently by the decomposition-coordination strategy; that is a whole problem is decomposed into subproblems according to the generic knowledge of experts. The introduction of a new concept ?>restorative operation cost ?> that reflects the various restoration strategies has decreased the number of rules in the knowledge-base to one third that of typical existing ES's. The validity and effectiveness of the combined method have been demonstrated by applying it to a practical size restoration problem.

This paper proposes a new mathematical programming approach to represent the dimensions of the discriminant space for the multiple-group classification problem. Few papers have investigated generalizations of two-group mathematical programming approaches for the classification of multiple groups. While several papers have proposed mathematical programming models for separating groups of observations, the issue of considering the classification problem by finding discriminant linear functions to describe the groups in fewer dimensions has not been addressed. The new mathematical programming approach proposed in this paper first solves the multiple-group problem using a single discriminant function, which essentially represents the separation of the groups in one dimension. Then the multiple-group problem is successively solved using single discriminant functions with the requirement that successive linear discriminant functions have a sample covariance equal to zero. An algorithm is proposed to classify observations from multiple groups using the linear discriminant functions from the mathematical programming approach in a reduced number of dimensions.

In revenue management, booking limits are commonly used to restrict access to classes of products, to subsequently make way for more profitable ones. Frequently, this inventory control policy assumes that products are nested in decreasing order of revenue, and that less profitable products are denied access first. In this article, we propose for the computation of nested booking limits a flexible mathematical programming framework that can accommodate business rules and technical constraints common in the industry. Under the assumption that customers are characterized by ordered lists of their preferences, optimal policies are set through the solution of a mixed integer program that is amenable to an efficient and scalable column generation algorithm. Numerical tests illustrate the improved performance of the resulting policies, which are numerically tested against alternative proposals from the current literature.

In this paper we present a mathematical programming based approach for revenue management in cargo airlines. The approach is based on a modified version of a multicommodity network flow model which has been developed in a decision support approach for schedule planning in cargo airlines. We think that using the same concept for planning and revenue management is essential for consistency of planning and operation. To meet the real-time requirements of revenue management special computational strategies for solving the large models are necessary.

Robust fuzzy structural safety assessment using mathematical programming approach

In this chapter, a formulation for applying Ant Colony Optimization (ACO) to power plant maintenance scheduling optimization (PPMSO) has been developed and successfully tested using four case studies (original and modified versions of two benchmark case studies from the literature). In particular, the performance of the heuristic formulation developed, the two local search algorithms introduced and the overall utility of the ACO-PPMSO formulation were investigated. The results obtained have shown that the heuristic formulation improves the performance of the ACO-PPMSO algorithm significantly when applied to the four case studies investigated. It was found that while the PPMSO-2-opt local search operator seems to work well for unconstrained problems, it is not suitable for highlyconstrained PPMSO problems. Lastly, the results obtained by ACO-PPMSO for the two original case studies were better than those obtained by other optimisation methods, such as various genetic algorithm (GAs) formulations and simulated annealing (SA). For the 21-unit and 22-unit case studies, a new optimal solution has been found by the ACO-PPMSO

Returns to beef research in Canada: A comparison of time series and mathematical programming approaches

Mathematical programming methods for consistency and consensus in group decision making with intuitionistic fuzzy preference relations

This study compares the benefits of using digestate and compost in Burkina Faso. A mathematical programming model was used to simulate the advantages under three scenarios. The baseline scenario reflected the typical situation of farmers, followed by the introduction of digestate and compost as soil amendments. The model applied these to improve poor soils and recover fallow land. As a result, the production of maize, cotton, rice, millet and sorghum increased, while groundnut cultivation and fallow land decreased. Gains were most notable with digestate. During poor cropping seasons, income rose by 238% with digestate and by 132% with compost. During good seasons, income increased by 164% and 98%, respectively. The use of digestate and compost helped reduce poverty and promote food security, although credit and labour constraints remain important considerations.

Forecasting future productivity is a critical task to every organization. However, the existing methods for productivity forecasting have two problems. First, the logarithmic or log-sigmoid value, rather than the original value, of productivity is dealt with. Second, the objective functions are not consistent with those adopted in practice. To address these problems, a fuzzy polynomial fitting and mathematical programming (FPF-MP) approach are proposed in this study. The FPF-MP approach solves two polynomial programming problems, based on the original value of productivity, in two steps to optimize accuracy and precision of forecasting future productivity, respectively. A real case was adopted to validate the effectiveness of the proposed methodology. According to the experimental results, the proposed FPF-MP approach outperformed six existing methods in improving the forecasting accuracy and precision.

The dynamic nature of today's competitive markets compels organizations to an incessant reassessment in an effort to respond to continuous challenges. Therefore, warehouses as an important link in most supply chains, must be continually re-evaluated to ensure that they are consistent with both market's demands and management's strategies. A number of warehouse decision support models have been proposed in the literature but considerable difficulties in applying these models still remain, due to the large amount of information to be processed and to the large number of possible alternatives. In this paper we discuss a mathematical programming model aiming to support some warehouse management and inventory decisions. In particular a large mixed-integer nonlinear programming model (MINLP) is presented to capture the trade-offs among the different inventory and warehouse costs in order to achieve global optimal design satisfying throughput requirements.

Abandonment value in capital budgeting: A mathematical programming approach

Previous research in the optimal allocation of airline seats has followed one of two themes: marginal seat revenue or mathematical programming. Both approaches capture important elements of the revenue management problem. The marginal seat revenue approach accounts for the “nesting” of fare classes in computer reservation systems, but can only control seat inventory by bookings on legs. The mathematical programming approach will handle realistically large problems and will account for multiple origin–destination itineraries and side constraints, but it does not account for fare class nesting in the reservation systems. This paper combines both approaches by developing equations to find the optimal allocation of seats when fare classes are nested on an origin–destination itinerary and the inventory is not shared among origin–destinations. These results are applicable to seat allocation in certain reservations systems, point-of-sale control, and acceptance of groups over their entire itinerary. A special case of the analysis produces the optimal booking limits for leg-based seat allocation with nested fare classes.

Subset selection in multiple linear regression: a new mathematical programming approach

For the operation and control of flow manufacturing in a high-mix and low-volume production environment, a method of flow path management is introduced. It involves the dynamic formation and control of adaptable flow paths corresponding to different product families. A mathematical programming approach is presented for the design of flow paths, which takes into consideration the sharing of machines among various product families. The objective is to maximize the throughput in a predefined planning period and to minimize the number of shared machines. An illustrative example is given for demonstrating the use of the proposed method.