4. Weighted sum of completion times 1 Eugene L. Lawler, Maurice Queyranne, Andreas S. Schulz, David B. Shmoys 4.1. Smith’s ratio rule 2 4.2. Preference orders on jobs 5 4.3. Preference orders on sequences and series-parallel precedence constraints 8 4.4. NP-hardness of further constrained min-sum problems 14 4.5. The ratio rule via linear programming 18 4.6. Approximation algorithms for 1|prec|...

The purpose of this paper is to find an explicit formula and asymptotic estimate for the total number sum weighted records over set partitions [ n ] in terms Bell numbers. For that we study generating function according statistic records.

We study the classic problem of estimating the sum of n variables. The traditional uniform sampling approach requires a linear number of samples to provide any non-trivial guarantees on the estimated sum. In this paper we consider various sampling methods besides uniform sampling, in particular sampling a variable with probability proportional to its value, referred to as linear weighted sampli...

The role of the information technology is growing rapidly in the world of business, to communicate with the customers effectively. Computer network is the back bone of any organization. It helps in effective utilization of resources such as time, money etc. Server plays an important role in the network, to store the data. A wide variety of servers exist in the market. This paper focuses on the ...

Optimization is the discipline of adjusting a process so as to optimize some specific set of parameters, without violating some constraints. In this paper an optimization is made by means of weighted sum method, after a multi-objective programming model formed based upon the power supply radius from a substation. The main aim of the model is to enlarge the radius of power supply as much as poss...

This paper presents a new mathematical model for a hybrid flow shop scheduling problem with multiprocessor tasks in which sequence dependent set up times and preemption are considered. The objective is to minimize the weighted sum of makespan and maximum tardiness. Three meta-heuristic methods based on genetic algorithm (GA), imperialist competitive algorithm (ICA) and a hybrid approach of GA a...

Vendor managed inventory is a continuous replenishment program that is designed to provide major cost saving benefits for both vendors and retailers. Previous research on this area mainly included single objective optimization models where the objective is to minimize the total supply chain costs or to maximize the total supply chain benefits. This paper presents a bi-objective mathematical mod...

Sensitivity is an important complexity measure of Boolean functions. In this paper we present properties of the minimal and maximal sensitivity of the simplified weighted sum function. A simple close formula of the minimal sensitivity of the simplified weighted sum function is obtained. A phenomenon is exhibited that the minimal sensitivity of the weighted sum function is indeed an indicator of...