A fuzzy multidimensional multiple-choice knapsack model for project portfolio selection using an evolutionary algorithm

Project portfolio selection problems are inherently complex problems with multiple and often conflicting objectives. Numerous analytical techniques ranging from simple weighted scoring to complex mathematical programming approaches have been proposed to solve these problems with precise data. However, the project data in real-world problems are often imprecise or ambiguous. We propose a fuzzy Multidimensional Multiple-choice Knapsack Problem (MMKP) formulation for project portfolio selection. The proposed model is composed of an Efficient Epsilon-Constraint (EEC) method and a customized multi-objective evolutionary algorithm. A Data Envelopment Analysis (DEA) model is used to prune the generated solutions into a limited and manageable set of implementable alternatives. Statistical analysis is performed to investigate the effectiveness of the proposed approach in comparison with the competing methods in the literature. A case study is presented to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms.     

The simplest proof of Lieb concavity theorem

In this paper, by applying jointly concavity and jointly convexity of generalized perspective of some elementary functions, we give the simplest proof of the well-known Lieb concavity theorem and Ando convexity theorem.     

Normal spectral emissivity of platinum in the red and in the green in vacuum and helium

The spectral emissivity of platinum for λ=0.645 μm and λ=0.546 μm has been measured by using a De Vos blackbody in ultrahigh vacuum and in helium. Changes in enissivity brought about by heat treatment and changing ambiences, are illustrated and discussed and the results are compared with previously published data. The emissivities determined turned out to be appreciably lower than the measurements of previous investigators. The determined values for 1100<T(K)<1800 are for 0.645 μ between 0.237 and 0.249 in vacuum, and between 0.185 and 0.290 in helium; and for 0.546 μm between 0.250 and 0.312 for vacuum and between 0.219 and 0.321 in helium.     

Note On a Comparative Evaluation of Nine Well-Known Algorithms for Solving the Cell Formation Problem in Group Technology

Over the last three decades, numerous algorithms have been proposed to solve the work-cell formation problem. For practicing manufacturing managers it would be nice to know as to which algorithm would be most effective and efficient for their specific situation. While several studies have attempted to fulfill this need, most have not resulted in any definitive recommendations and a better methodology of evaluation of cell formation algorithms is urgently needed. Prima facie, the methodology underlying Miltenburg and Zhang's (M&Z) (1991) evaluation of nine well-known cell formation algorithms seems very promising. The primary performance measure proposed by M&Z effectively captures the objectives of a good solution to a cell formation problem and is worthy of use in future studies. Unfortunately, a critical review of M&Z's methodology also reveals certain important flaws in M&Z's methodology. For example, M&Z may not have duplicated each algorithm precisely as the developer(s) of that algorithm intended. Second, M&Z's misrepresent Chandrasekharan and Rajagopalan's [C&R's] (1986) grouping efficiency measure. Third, M&Z's secondary performance measures lead them to unnecessarily ambivalent results. Fourth, several of M&Z's empirical conclusions can be theoretically deduced. It is hoped that future evaluations of cell formation algorithms will benefit from both the strengths and weaknesses of M&Z's work.