Browsing by Subject "valid inequalities"

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    Valid inequalities for the problem of optimizing a nonseparable piecewise linear function on 0-1 variables
    (2011) Aksüt, Ziyaattin Hüsrev
    In many procurement and transportation applications, the unit prices depend on the amount purchased or transported. This results in piecewise linear cost functions. Our aim is to study the structure that arises due to a piecewise linear objective function and to propose valid inequalities that can be used to solve large procurement and transportation problems. We consider the problem of optimizing a nonseparable piecewise linear function on 0-1 variables. We linearize this problem using a multiple-choice model and investigate properties of facet defining inequalities. We propose valid inequalities and lifting results.
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    Vendor location problem
    (2009) Çınar, Yüce
    In this study, we aim to design a distribution system with the following components: the location of vendors, the number of vendors, the service region of the vendors, the number of vehicles and workers, and the assignment of demand points to these vendors and vehicles. We define our problem as a two-level capacitated discrete facility location problem with minimum profit constraints and call it Vendor Location Problem. In order to formulate the problem, two different objective functions are used: vendors’s profit maximization and maximization of the demand covered. Integer linear programs for these two versions of the problem are formulated. Valid inequalities are used to strengthen the upper bounds. Finally, the performance of these models with different parameters are compared in terms of linear programming relaxation gap, optimality gap, CPU time, and the number of opened nodes for four different types of instances: instances with demand and profit which are independent of distance; profit function of distance; demand function of distance; demand and profit function of distance.