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Toward an Efficient Resolution for a Single-machine Bi-objective Scheduling Problem with Rejection

Moghaddam Atefeh, Teghem Jacques, Tuyttens Daniel, Yalaoui Farouk, Amodeo Lionel

Foundations of Computing and Decision Sciences

2019

Vol. 44, No. 2

179--211

We consider a single-machine bi-objective scheduling problem with rejection. In this problem, it is possible to reject some jobs. Four algorithms are provided to solve this scheduling problem. The two objectives are the total weighted completion time and the total rejection cost. The aim is to determine the set of efficient solutions. Four heuristics are described; they are implicit enumeration algorithms forming a branching tree, each one having two versions according to the root of the tree corresponding either to acceptance or rejection of all the jobs. The algorithms are first illustrated by a didactic example. Then they are compared on a large set of instances of various dimension and their respective performances are analysed.

A reference point approach to bi-objective dynamic portfolio optimization

Sawik B.

Decision Making in Manufacturing and Services

2009

Vol. 3, no. 1-2

73-85

The portfolio selection problem presented in this paper is formulated as a bi-objective mixed integer program. The portfolio selection problem considered is based on a dynamic model of investment, in which the investor buys and sells securities in successive investment periods. The problem objective is to dynamically allocate the wealth on different securities to optimize by reference point method the portfolio expected return and the probability that the return is not less than a required level. In computational experiments the dataset of daily quotations from the Warsaw Stock Exchange were used.