Generating effective project scheduling heuristics by abstraction and reconstitution

A project scheduling problem consists of a finite set of jobs, each with fixed integer duration, requiring one or more resources such as personnel or equipment, and each subject to a set of precedence relations, which specify allowable job orderings, and a set of mutual exclusion relations, which specify jobs that cannot overlap. No job can be interrupted once started. The objective is to minimize project duration. This objective arises in nearly every large construction project--from software to hardware to buildings. Because such project scheduling problems are NP-hard, they are typically solved by branch-and-bound algorithms. In these algorithms, lower-bound duration estimates (admissible heuristics) are used to improve efficiency. One way to obtain an admissible heuristic is to remove (abstract) all resources and mutual exclusion constraints and then obtain the minimal project duration for the abstracted problem; this minimal duration is the admissible heuristic. Although such abstracted problems can be solved efficiently, they yield inaccurate admissible heuristics precisely because those constraints that are central to solving the original problem are abstracted. This paper describes a method to reconstitute the abstracted constraints back into the solution to the abstracted problem while maintaining efficiency, thereby generating better admissible heuristics. Our results suggest that reconstitution can make good admissible heuristics even better

The Relationship between Working Capital Management Efficiency and EBIT

This paper is aimed at analyzing the relationship between Working Capital Management Efficiency (WCME) and Earnings before Interest&Taxes (EBIT) of the Paper Industry in India during 1997–1998 to 2005–2006. Tomeasure the WCME three index values viz., Performance Index (PI), Utilization Index (UI), and Efficiency Index (EI) are computed, and are associated with explanatory variables, viz., Cash Conversion Cycle (CCC), Accounts Payable Days (APDAYS), Accounts Receivables Days (ARDAYS), Inventory Days (INVDAYS). Further, Fixed Financial Assets Ratio (FIXDFARA), Financial Debt Ratio (FINDBTRA) and Size (Natural log of Sales) are considered as control variables in the analysis, and are associated with the EBIT. The study reveals that the Paper Industry has managed the WC satisfactorily. The APDAYS has a significant (–)ve relationship with EBIT, which indicates that by deploying payment to suppliers they improve the EBIT. The Paper Industry in India performs remarkably well during the period, however, less profitable firms wait longer to pay their bills, and pursue a decrease in CCC.Working Capital Management Efficiency, Earnings before Interest and Taxes, Current Assets, Current Liabilities, Performance Index, Utilization Index, Efficiency Index

Perturbation of Burkholder's martingale transform and Monge--Amp\`ere equation

Let $\{d_k\}_{k \geq 0}$ be a complex martingale difference in $L^p[0,1],$ where $1<p<\infty,$ and \{\e_k\}_{k \geq 0} a sequence in $\{\pm 1\}.$ We obtain the following generalization of Burkholder's famous result. If $\tau \in [-\frac 12, \frac 12]$ and $n \in \Z_+$ then |\sum_{k=0}^n{(\{c} \e_k \tau) d_k}|_{L^p([0,1], \C^2)} \leq ((p^*-1)^2 + \tau^2)^{\frac 12}|\sum_{k=0}^n{d_k}|_{L^p([0,1], \C)}, where $((p^*-1)^2 + \tau^2)^{\frac 12}$ is sharp and $p^*-1 = \max\{p-1, \frac 1{p-1}\}.$ For $2\leq p<\infty$ the result is also true with sharp constant for $\tau \in \R.$Comment: 45 pages, 13 figure

Design and Analysis of SD_DWCA - A Mobility based clustering of Homogeneous MANETs

This paper deals with the design and analysis of the distributed weighted clustering algorithm SD_DWCA proposed for homogeneous mobile ad hoc networks. It is a connectivity, mobility and energy based clustering algorithm which is suitable for scalable ad hoc networks. The algorithm uses a new graph parameter called strong degree defined based on the quality of neighbours of a node. The parameters are so chosen to ensure high connectivity, cluster stability and energy efficient communication among nodes of high dynamic nature. This paper also includes the experimental results of the algorithm implemented using the network simulator NS2. The experimental results show that the algorithm is suitable for high speed networks and generate stable clusters with less maintenance overhead