This paper studies a single-machine scheduling problem with a non-renewable resource (NR-SSP) and total weighted completion time criterion. The non-renewable resource is consumed when the machine starts processing a job. We consider the case where each job's weight in the objective function is proportional to its resource consumption amount. The problem is known to be NP-hard in this case. We propose a 3-approximation list scheduling algorithm for this problem. Besides, we show that the approximation ratio 3 is tight for the algorithm.
In this paper, two different variants (constrained and unconstrained) of a data envelopment analysis (DEA) model are used to compare inferences about production correspondence of the life insurance industry in India. While the unconstrained model implicitly assumes input substitutions and output transformations without their empirical verification, the constrained model explicitly incorporates weight restrictions on those inputs and outputs that are not substitutable and transformable, respectively. Our key findings are as follows. First, although the constrained model seems closely related to the notion of industry (structural) efficiency model, this link remains unexplored: we suggest a link between both models. Second, though the constrained model generates efficiency scores that are no more than those of its unconstrained counterpart, both models are in broad agreement in revealing that the life insurance industry experiences a sustained surge in its efficiency due to competition arising from insurance reforms adopted by the government over years, thus supporting the competition and X-efficiency hypothesis. Third, when the economic requirement of input substitutions is absent, both the models are found to give statistically significant results on efficiency ratings, returns to scale possibilities, and total factor productivity growth. In such a case, the unconstrained model generates benchmarking results based on an incorrect production frontier, which are potentially misleading and can hardly be used in managerial contexts. This finding, therefore, cautions the researchers not to blindly use any unconstrained model to evaluate the efficiency, productivity growth and returns to scale characterizations of firms without empirically verifying the presence/absence of input substitutions and output transformations.
This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is often used in implementing Ramaswami's recursion for computing the stationary distribution. We show that if the equilibrium level-increment distribution (in steady state) is long-tailed then its tail decay speed is asymptotically equal to the convergence speed of the level-wise difference between the original stationary distribution and its LI truncation approximation. We also show that the total variation norm of the relative level-wise (not whole) difference of the original stationary distribution and its LI truncation approximation is asymptotically independent of the level.
This study elucidates the degree of the influence of marketing measures and product loyalty (i.e.,convenience, shopping, and specialty goods) on department store customers' purchase amounts using a model formed by a Bayesian hierarchical regression model framework. In addition, we use a Tobit model to infer the latent characteristics of zero purchase amounts and estimate customers' inertial purchasing behaviors by modeling loyalty variables. Direct mail (DM) sent to each customer is used as the marketing measure. To build a different purchase amount mechanism for each customer, we incorporate a variable selection model. The results of the empirical analysis provide information about strategies department stores can adopt to increase customers' purchase amounts.