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In machine scheduling the first problem is to find a timetable that is optimal with respect to some efficiency criterion. If the jobs come from different clients the solution of the optimization problem is not the end of the story. In addition, we have to decide how the minimal total cost must be distributed among the parties involved. In this note, cost allocation problems will be considered to arise from one-machine scheduling problems with an additive and weakly increasing cost function. We will show that the cooperative games related to these cost allocation problems have a nonempty core. Furthermore, we give a rule that assigns a core element of the associated cost saving game to each scheduling problem of this kind and an initial order of the jobs.

A combinatorial optimization problem can often be understood as the problem to minimize cost in a complex situation. If more than one party is involved, the solution of the optimization problem is not the end of the story. In addition it has to be decided how the minimal total cost has to be distributed among the parties involved. In this paper cost allocation problems will be considered arising from one-machine scheduling under additive and weakly increasing cost functions. The approach of the problem will be game theoretical and we shall in fact show that in many cases the games related to the cost allocation problems are balanced.Key Words: cost allocation, cooperative game, one-machine scheduling.In combinatorial optimization the problem is often to compound -as cheaply as possible -a composite whole out of available components. The minimum cost spanning tree problem, for example, looks for a spanning tree of minimal cost composed from the arcs available in a graph. The traveling salesman problem asks for a hamiltonian cycle of minimal length consisting of arcs of a given graph. When the optimization problem has been solved we are often faced with a second problem, especially if the composition of the whole is in the interest of more than one agent. If, for example, the minimal cost spanning tree problem models the connection of villages with a water resource, then it is important for 0340-9422/93/38: 2/113-129 $2.50

In labor market models as well as in exchange economies with indivisible goods gross substitutability is used as a property to guarantee the existence of competitive equilibria. This paper develops an easy way to check gross substitutability for utility functions concerning a finite set of indivisible goods (or employees) and money. Concavity is one of the conditions that has to be satisfied. Only one other, but similar, type of relation must be checked to guarantee gross substitutability.

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This paper describes a fast algorithm to find the nucleolus of any game with a nonempty imputation set. It is based on the algorithm scheme of Maschler et al. (1992) for the general nucleolus.