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We review a number of methods that have recently been proposed to decompose changes in industrial energy consumption. We then propose two parametric methods based on the Divisia index, where the integral path problem in the Divisia index is transformed into a parameter estimation problem. It is shown that there can be an infinite number of sets of decomposition results, each corresponding to a particular combination of parameter values, and that several recently proposed methods are in fact special cases of these two methods. We then introduce an approach to estimate the parameter values uniquely. Referred to as the Adaptive Weighting Divisia Method, this method is supported by vigorous mathematical analysis and does not involve arbitrary guesses of parameter values as is the case for the existing methods. We also discuss the application and the associated statistical problems of the various decomposition methods, and present the results of a study using the data for Singapore industry.

The time-constrained traveling salesman problem (TCTSP) is a variant of the classical traveling salesman problem, where only a subset of the customers can be visited due to the time limit constraint. In this paper, we consider the TCTSP with stochastic travel and service times. Given the normal working hours T and a tolerance time ΔT, the total travel and service times of a route can exceed T as long as it is within T+ΔT, though a penalty proportional to the amount in excess of T will be imposed. The problem consists of optimally selecting and sequencing a subset of customers to visit in the presence of random travel and service times to maximize the expected profit while satisfying the time limit constraint. We formulate the problem as a two-stage stochastic program with recourse, and propose an integer L-shaped solution method for solving it. Computational results show that the algorithm can solve problems with moderate size to optimality within reasonable time.

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