‎a common approach to determine efficient solutions of a multiple objective optimization problem‎ ‎is reformulating it to a parameter dependent scalar optimization problem‎. ‎this reformulation is called scalarization approach‎. here, a well-known scalarization approach named pascoletti-serafini scalarization is considered‎. first, some difficulties of this scalarization are discussed and then ...

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.

In this paper we introduce a new facility location model, called backup multifacility location problem by considering the ideal radius for each customer. In this problem the location of clients are given in the plane. A radius is assigned to each client. We should find the location of new facilities, which some of them may fail with a given probability, such that the sum of weighted distances f...

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...