TY - UNPB

T1 - Computing good allocations for combinatorial optimization games

AU - Caprara, Alberto

AU - Letchford, Adam N.

N1 - This was eventually published as: A. Caprara & A.N. Letchford (2010) New techniques for cost sharing in combinatorial optimization games. Math. Program., 124(1-2), 93-118.

PY - 2005

Y1 - 2005

N2 - Much of the literature on cooperative games associated with combinatorial optimization problems is concerned with finding necessary or sufficient conditions under which the core is non-empty. In this paper however we are concerned with a rather different question, which may be of more use in practice: how to find partial cost allocations with high value. This question is addressed from both theoretical and algorithmic viewpoints. We begin by defining a very general class of games, called Integer Minimization (IM) games, and show that it includes many well-known combinatorial optimization games as special cases. We then show that finding the optimal allocation is strongly NP-hard for many IM games of interest. This gives the motivation for seeking general techniques for computing 'good' (though not necessarily optimal) allocations. We give three such techniques, based on column generation, row generation, or both. To illustrate the power of these techniques, we apply them to various travelling salesman and vehicle routing games.

AB - Much of the literature on cooperative games associated with combinatorial optimization problems is concerned with finding necessary or sufficient conditions under which the core is non-empty. In this paper however we are concerned with a rather different question, which may be of more use in practice: how to find partial cost allocations with high value. This question is addressed from both theoretical and algorithmic viewpoints. We begin by defining a very general class of games, called Integer Minimization (IM) games, and show that it includes many well-known combinatorial optimization games as special cases. We then show that finding the optimal allocation is strongly NP-hard for many IM games of interest. This gives the motivation for seeking general techniques for computing 'good' (though not necessarily optimal) allocations. We give three such techniques, based on column generation, row generation, or both. To illustrate the power of these techniques, we apply them to various travelling salesman and vehicle routing games.

KW - combinatorial optimization games

KW - travelling salesman problem

KW - vehicle routing

M3 - Working paper

T3 - Management Science Working Paper Series

BT - Computing good allocations for combinatorial optimization games

PB - The Department of Management Science

CY - Lancaster University

ER -