Browsing by Subject "Lagrangian relaxation"

Now showing 1 - 5 of 5

Open Access
Advances in business analytics at HP laboratories
(Springer, Boston, 2010) Beyer, D.; Clearwater, S.; Chen, K. Y.; Feng, Q.; Huberman, B. A.; Jain, S.; Jamal, Z.; Şen, Alper; Tang, H. K.; Tarjan, B.; Ward, J.; Zhang, A.; Zhang, B.; Sodhi, M. S.; Tang, C. S.
HP Labs’ Business Optimization Lab is a group of researchers focused on developing innovations in business analytics that deliver value to HP. This chapter describes several activities of the Business Optimization Lab, including work in product portfolio management, prediction markets, modeling of rare events in marketing, and supply chain network design.
Open Access
Lagrangian relaxation for airport gate assignment problem
(2023-07) Okur, Göksu Ece
In this study we focus on the Airport Gate Assignment Problem that minimizes the total walking distance of passengers while ensuring that the number of aircraft assigned to apron is at its minimum. We utilize an alternative formulation for the problem compared to the ones in the literature and propose approaches based on Lagrangian Relaxation so as to obtain tight lower bounds. The method also harnesses the power of a good initial upper bound and provides good quality solutions. To the best of our knowledge, the current studies in the literature rely only on upper bounds or the linear relaxation lower bounds to assess the quality of heuristic solutions. We propose using the tighter Lagrangian Relaxation based bounds as a better reference to assess solution quality. Our computational experiments demonstrate that our Lagrangian relaxation based method returns strong lower bounds and good quality upper bounds that are comparable to the state-of-the art results from the literature.
Open Access
A multi product loading problem: a model and a solution method
(Elsevier, 1997) Yuceer, U.
An important operational problem arises during the transportation and delivery of several products, which cannot be mixed, in the same vehicle at regular intervals. The vehicle has compartments to keep the products separately. Therefore, a scheme of allocation of compartments which we call vehicle loading problem to maximize the efficiency of the system while the demands for the products at the destination(s) are satisfied. A mixed binary model is developed for this multi-product loading problem. The solution method is based on simultaneously exploring the primal and dual structures derived from the Lagrangian relaxation. Subset sum problems are obtained as subproblems to the partial Lagrangian. An algorithm is developed and its convergence is proved. The efficiency of the method is demonstrated by running randomly chosen test problems. An initial solution finding method is also developed.
Open Access
Solving the hub location problem in a star-star network
(John Wiley & Sons, 2008) Labbé, M.; Yaman, H.
We consider the problem of locating hubs and assigning terminals to hubs for a telecommunication network. The hubs are directly connected to a central node and each terminal node is directly connected to a hub node. The aim is to minimize the cost of locating hubs, assigning terminals and routing the traffic between hubs and the central node. We present two formulations and show that the constraints are facet-defining inequalities in both cases. We test the formulations on a set of instances. Finally, we present a heuristic based on Lagrangian relaxation.
Open Access
Star p-hub median problem with modular arc capacities
(Elsevier, 2008) Yaman, H.
We consider the hub location problem, where p hubs are chosen from a given set of nodes, each nonhub node is connected to exactly one hub and each hub is connected to a central hub. Links are installed on the arcs of the resulting network to route the traffic. The aim is to find the hub locations and the connections to minimize the link installation cost. We propose two formulations and a heuristic algorithm to solve this problem. The heuristic is based on Lagrangian relaxation and local search. We present computational results where formulations are compared and the quality of the heuristic solutions are tested.