Journal of Global Optimization
Greedy approaches for a class of nonlinear Generalized Assignment Problems
Discrete Applied Mathematics
An Efficient Greedy Heuristic for Warehouse-Retailer Network Design Optimization
Transportation Science
A Knapsack-Based Approach to Bidding in Ad Auctions
Proceedings of the 2010 conference on ECAI 2010: 19th European Conference on Artificial Intelligence
An optimization algorithm for a penalized knapsack problem
Operations Research Letters
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In this paper, we propose a multiperiod single-sourcing problem (MPSSP), which takes both transportation and inventory into consideration, suitable for evaluating the performance of a logistics distribution network in a dynamic environment. We reformulate the MPSSP as a Generalized Assignment Problem (GAP) with a convex objective function. We then extend a branch-and-price algorithm that was developed for the GAP to this problem. The pricing problem is a so-called Penalized Knapsack Problem (PKP), which is a knapsack problem where the objective function includes an additional convex term penalizing the total use of capacity of the knapsack. The optimal solution of the relaxation of the integrality constraints in the PKP shows a similar structure to the optimal solution of the knapsack problem, that allows for an efficient solution procedure for the pricing problem. We perform an extensive numerical study of the branch-and-price algorithm.