  


Stochastic binary problems with simple penalties for capacity constraints violations
B Fortz (bfortzulb.ac.be) Abstract: This paper studies stochastic programs with firststage binary variables and capacity constraints, using simple penalties for capacities violations. In particular, we take a closer look at the knapsack problem with weights and capacity following independent random variables and prove that the problem is weakly \NPhard in general. We provide pseudopolynomial algorithms for three special cases of the problem: constant weights and capacity uniformly distributed, subset sum with Gaussian weights and arbitrary random capacity, and subset sum with constant weights and arbitrary random capacity. We then turn to a branchandcut algorithm based on the outer approximation of the objective function. We provide computational results for the stochastic knapsack problem (i) with Gaussian weights and constant capacity and (ii) with constant weights and capacity uniformly distributed, on randomly generated instances inspired by computational results for the knapsack problem. Keywords: tochastic programming, Knapsack problem, Pseudopolynomial algorithm, Mixedinteger nonlinear programming, Branchandcut algorithm Category 1: Stochastic Programming Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming ) Citation: ULB, March 2009. Download: [PDF] Entry Submitted: 03/24/2009 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  