Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on...

‎we consider a linear programming problem in a general form and suppose that all coefficients may vary in some prescribed intervals‎. ‎contrary to classical models‎, ‎where parameters can attain any value from the interval domains independently‎, ‎we study problems with linear dependencies between the parameters‎. ‎we present a class of problems that are easily solved by reduction to the classi...

Most research on bilevel linear programming problem  is focused on its deterministic form, in which the coefficients and decision variables in the objective functions and constraints are assumed to be crisp. In fact, due to inaccurate information, it is difficult to know exactly values of coefficients that used to construct a bilevel model. The interval set theory is suitable for describing and...

in this paper we investigate multi-objective integer linear programming (moilp) problems with unbounded feasible region and introduce recession direction for moilp problems. then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of moilp problems. finally we present some examples with unbounded feasible region and fi...

In the classical secretary problem an employer would like to choose the best candidate among n competing candidates that arrive in a random order. This basic concept of n elements arriving in a random order and irrevocable decisions made by an algorithm have been explored extensively over the years, and used for modeling the behavior of many processes. Our main contribution is a new linear prog...

Fuzzy Linear Programming models and methods has been one ofthe most and well studied topics inside the broad area of Soft Computing. Itsapplications as well as practical realizations can be found in all the real worldareas. In this paper a basic introduction to the main models and methods infuzzy mathematical programming, with special emphasis on those developedby the authors, is presented. As ...

the fuzzy linear regression model with fuzzy input-output data andcrisp coefficients is studied in this paper. a linear programmingmodel based on goal programming is proposed to calculate theregression coefficients. in contrast with most of the previous works, theproposed model takes into account the centers of fuzzy data as animportant feature as well as their spreads in the procedure ofconstr...

Hierarchical multimodal hub location problem is a cost-minimizing hub covering problem where two types of hubs and hub links, accounting for ground and air transportation, are to be established, while ensuring time-definite deliveries. We propose a mixed-integer programming formulation and perform a comprehensive sensitivity analysis on the Turkish network. We show that the locations of airport...

We de ne a natural product on integer programming problems with nonnegative coe cients. Hypergraph covering problems are a special case of such integer programs, and the product we de ne is a generalization of the usual hypergraph product. The main theorem of this paper gives a su cient condition under which the solution to the nth power of an integer program is asymptotically as good as the so...