The computational complexity of simultaneous diophantine approximation problems
SIAM Journal on Computing
Tight bounds and 2-approximation algorithms for integer programs with two variables per inequality
Mathematical Programming: Series A and B
Simple and Fast Algorithms for Linear and Integer Programs with Two Variables Per Inequality
SIAM Journal on Computing
Improved Algorithms for Linear Inequalities with Two Variables per Inequality
SIAM Journal on Computing
Deciding Linear Inequalities by Computing Loop Residues
Journal of the ACM (JACM)
The vehicle routing problem
Set-covering-based algorithms for the capacitated VRP
The vehicle routing problem
The vehicle routing problem
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Selected Topics in Column Generation
Operations Research
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We present an integer programming model for the integrated optimization of bus schedules and school starting times, which is a single-depot vehicle scheduling problem with additional coupling constraints among the time windows. For instances with wide time windows the linear relaxation is weak and feasible solutions found by an ILP solver are of poor quality. We apply a set partitioning relaxation to compute better lower bounds and, in combination with a primal construction heuristic, also better primal feasible solutions. Integer programs with at most two non-zero coefficient per constraint play a prominent role in our approach. Computational results for several random and a real-world instance are given and compared with results from a standard branch-and-cut approach.