Computing the exact ideal and nadir criterion values is a very ‎important subject in ‎multi-‎objective linear programming (MOLP) ‎problems‎‎. In fact‎, ‎these values define the ideal and nadir points as lower and ‎upper bounds on the nondominated points‎. ‎Whereas determining the ‎ideal point is an easy work‎, ‎because it is equivalent to optimize a ‎convex function (linear function) over a con...

Mixed-integer conic programming is a generalization of mixed-integer linear programming. In this paper, we present an extension of the duality theory for mixed-integer linear programming (see [4], [11]) to the case of mixed-integer conic programming. In particular, we construct a subadditive dual for mixed-integer conic programming problems. Under a simple condition on the primal problem, we ar...

over the two last decades, distribution companies have been aware of the importance of paying attention to the all aspects of a distribution system simultaneously to be successful in the global market. these aspects are the economic, the environmental, the social and the safety aspects. in the vehicle routing problem (vrp) literature, the economic issue has often been used, while the environmen...

in some industries as foundries, it is not technically feasible to interrupt a processor between jobs. this restriction gives rise to a scheduling problem called no-idle scheduling. this paper deals with scheduling of no-idle open shops to minimize maximum completion time of jobs, called makespan. the problem is first mathematically formulated by three different mixed integer linear programming...

The beauty of linear programming theory arises from linear programming duality that provides a short certificate that a given pair of primal and dual feasible solutions are optimal. One of the central fundaments of this duality result is the so-called Farkas Lemma that establishes that a given system of linear inequalities has a solution if and only if another system of linear inequalities is i...

Protein threading is a method of computational protein structure prediction used for protein sequences which have the same fold as proteins of known structures but do not have homologous proteins with known structure. The most popular algorithm is based on linear integer programming. In this paper, we consider methods based on nonlinear integer programming. Actually, the existing linear integer...