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Optimality conditions in multiobjective programming problems with interval valued objective functions

Ahmad I., Singh D., Dar B. A.

Control and Cybernetics

2015

Vol. 44, no. 1

19--45

We devote this paper to study of multiobjective programming problems with interval valued objective functions. For this, we consider two order relations LU and LS on the set of all closed intervals and propose several concepts of Pareto optimal solutions and generalized convexity. Based on generalized convexity (viz. LU and LS-pseudoconvexity) and generalized diﬀerentiability (viz. gHdiﬀerentiablity) of interval valued functions, the KKT optimality conditions for aforesaid problems are obtained. The theoretical development is illustrated by suitable examples.

Bicriteria scheduling of minimizing maximum lateness and makespan on a serial-batching machine

He C., Lin Y., Yuan J.

Foundations of Computing and Decision Sciences

2008

Vol. 33, No. 4

369-376

This paper studies the bicriteria problem of scheduling n jobs on a serial-batching machine to minimize maximum lateness and makespan simultaneously. A serial-batching machine is a machine that can handle up to b jobs in a batch and jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the sum of the processing times of jobs in the batch. When a new batch starts, a constant setup time s occurs. We concentrate on the unbounded model, where 6 > n. We present an O(n2) algorithm for finding all Pareto optimal solutions of this bicriteria scheduling problem.