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An analysis of approximations for maximizing submodular set functions—I
TLDR
It is shown that a “greedy” heuristic always produces a solution whose value is at least 1 −[(K − 1/K]K times the optimal value, which can be achieved for eachK and has a limiting value of (e − 1)/e, where e is the base of the natural logarithm.
Integer and Combinatorial Optimization
  • G. Nemhauser, L. Wolsey
  • Computer Science, Mathematics
    Wiley interscience series in discrete mathematics…
  • 16 June 1988
TLDR
This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Integer Programming
The principles of integer programming are directed toward finding solutions to problems from the fields of economic planning, engineering design, and combinatorial optimization. This highly respected
An analysis of the greedy algorithm for the submodular set covering problem
TLDR
This work generalises earlier results of Dobson and others on the applications of the greedy algorithm to the integer covering problem: min, which includes the problem of finding a minimum weight basis in a matroid.
Production Planning by Mixed Integer Programming
This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction
Best Algorithms for Approximating the Maximum of a Submodular Set Function
TLDR
This work presents a family of algorithms that involve the partial enumeration of all sets of cardinality q and then a greedy selection of the remaining elements, q = 0,..., K-1.
A recursive procedure to generate all cuts for 0–1 mixed integer programs
TLDR
It is shown how all valid inequalities for mixed 0–1 programs can be generated recursively from a simple subclass of the disjunctive inequalities.
bc -- prod: A Specialized Branch-and-Cut System for Lot-Sizing Problems
bc-prod is a prototype modelling and optimization system designed and able to tackle a wide variety of the discrete-time lot-sizing problems arising both in practice and in the literature. To use
Modelling Practical Lot-Sizing Problems as Mixed-Integer Programs
TLDR
A variety of aspects arising particularly in small and large bucket time period models such as start-ups, changeovers, minimum batch sizes, choice of one or two set-ups per period, etc are discussed.
Uncapacitated lot-sizing: The convex hull of solutions
TLDR
The convex hull of the solutions of the economic lot-sizing model is given, and an alternative formulation as a simple plant location problem is examined, and here too the convex Hull of solutions is obtained.
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