Abstract
The paper considers the solution of one combinatorial optimization problemunder uncertainty. Its functional in deterministic formulation is a linear convolution of weights and arbitrary characteristics of a feasible solution. A constructive algorithm for its solving is a general linear programming problem solution algorithm. Under the uncertainty we mean the ambiguity of the weight values in the functional we optimize.We propose a new approach for finding a compromise solution by the criterion ofminimizing the total weighted excess of “desirable” upper bounds on the optimalvalues of particular functionals. The basis of this approach is the construction andsolution of some linear programming problem. We illustrate this approach on atransportation problem example in conditions of uncertainty.Ref. 15, tabl. 2
Highlights
Various decisions have to be regularly made in business practice
Papers [1, 2] introduced a new class of combinatorial optimization problems under uncertainty with the following properties: 1) the optimization criterion is a linear convolution of weights and arbitrary numerical characteristics of a feasible solution; 2) there exists an efficient algorithm for the problem solving in a deterministic formulation and any structural change in its range of feasible solutions makes the algorithm’s application impossible; 3) the uncertainty in the combinatorial optimization problem solution refers to the ambiguity of the weight coefficients’ values included in the optimization criterion
Authors of many publications use a linear convolution for problems solving under uncertainty
Summary
Various decisions have to be regularly made in business practice. An important condition for rational decision making is to have as accurate information as possible about the decision subject and its consequences. Authors of many publications use a linear convolution for problems solving under uncertainty. The method of finding a compromise solution to the two-criteria linear programming problem in [8] uses the Lp-metric. A comprehensive literature survey of aggregate production planning under uncertainty given in [13] concluded that a large portion of the existing research studies the deterministic state of the planning and ignores its inherent uncertain nature This may lead to considerable errors and imprecise decisions. The authors propose there five compromise criteria for the uncertainty resolving They identify new properties of linear convolution that form the basis of efficient formal procedures for compromise solutions finding. The paper substantiates the extension of the class of combinatorial optimization problems under uncertainty introduced in [1, 2]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
