Dynamic lot sizing problem is one of the significant problem in industrial units and it has been considered by  many researchers. Considering the quantity discount in  purchasing cost is one of the important and practical assumptions in the field of inventory control models and it has been less focused in terms of stochastic version of dynamic lot sizing problem. In  this paper, stochastic dyn...

The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs). To solve such games, a new methodology has been derived based on the notion of weighted average operator and score function of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying the score function of THFEs, we transform these two problems in...

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...

Some of the real life decisions are made in decentralized manner under uncertainty. Stochastic bi-level linear programming problems are used to handle such decision making problems. In this paper, we have proposed stochastic bi-level linear programming problems where some of the right hand side parameters of the constraints in both first (leader) and second level (follower) as normal and log-no...

Finding the location for plans like factories or warehousesfor any organization is an important and strategic decision. Costs oftransportation which are the main part of the price of the goods, is thefunction of the location of these projects. to find the optimum locationof these projects, there have been various methods proposed which areusually defined (not random). In reality and in dealing ...

Uncertainties are widespread in the optimization of process systems, such as uncertainties technologies, prices, and customer demands. In this paper, we review basic concepts recent advances a risk-neutral mathematical framework called “stochastic programming” its applications solving systems engineering problems under uncertainty. This intends to provide both tutorial for beginners without pri...