yard crane is an important resource in container terminals. efficient utilization of the yard crane significantly improves the productivity and the profitability of the container terminal. this paper presents a mixed integer programming model for the yard crane scheduling problem with non- interference constraint that is nphard in nature. in other words, one of the most important constraints in...

‎In this paper, using the idea of convexificators, we study boundedness and nonemptiness of Lagrange multipliers satisfying the first order necessary conditions. We consider a class of nons- mooth fractional programming problems with equality, inequality constraints and an arbitrary set constraint. Within this context, define generalized Mangasarian-Fromovitz constraint qualification and sh...

The basic principles of constraint programming (constraint satisfaction problems, search, constraint propagation) are introduced by discussing how constraint programming can be used to solve a specific optimization problem. A set of orchestral pieces is to be rehearsed and the problem requires finding a sequence that will minimize the time that players are at the rehearsal but not playing, if t...

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and sto...