Abstract
Suppose each member i from one class of objects (persons, firms) i = 1, …, n is matched with one object j from another class of equal size (jobs, locations) j = 1, …, n and the economic outcome is measurable in money terms aij. Let xij = 1 when object i is assigned to object j and xij = 0 otherwise. The payoff of this matching is then \( {\sum}_{ij}{a}_{ij}{x}_{ij} \).It represents gross profits (profits before wages or rents) in the assignment of persons to jobs and of firms to locations.
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Bibliography
Dubins, L.E., and D.A. Freedman. 1981. Machiavelli and the Gale–Shapley algorithm. American Mathematical Monthly 88: 485–494.
Gale, D., and L. Shapley. 1962. College admissions and the stability of marriage. American Mathematical Monthly 69: 9–15.
Geoffrion, A.M., and G.W. Graves. 1976. Scheduling parallel production lines with changeover costs: Practical application of a quadratic assignment–LP approach. Operations Research 24(4): 595–610.
Graves, G.W., and A.B. Whinston. 1970. An algorithm for the quadratic assignment problem. Management Science 17: 453–471.
Koopmans, T.C., and M. Beckmann. 1957. Assignment problems and the location of economic activities. Econometrica 25(1): 53–76.
Reiter, S., and G.R. Sherman. 1962. Allocating indivisible resources affording external economies or diseconomies. International Economic Review 3: 108–135.
Roth, A.E. 1982. The economics of matching: Stability and incentives. Mathematical Operations Research 7: 617–628.
Roth, A.E. 1984. The evolution of the labor market for medical interns and residents: A case study in game theory. Journal of Political Economy 92: 991–1016.
Roth, A.E. 1985. The college admissions problem is not equivalent to the marriage problem. Journal of Economic Theory 36: 277–288.
Thorndike, R.L. 1950. The problem of classification of personnel. Psychometrika 15: 215–235.
Von Neumann, J. 1953. A certain zero-sum two-person game equivalent to the optimal assignment problem. In Contributions to the theory of games, vol. 2, ed. H.W. Kuhn and A.W. Tucker. Princeton: Princeton University Press.
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Beckmann, M. (2018). Assignment Problems. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_429
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DOI: https://doi.org/10.1057/978-1-349-95189-5_429
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