Production systems and hierarchies of centres: The relationship between spatial and economic structures: Studies in Applied Regional Science, cartea 7

1. Definition of the problem and results.- 1.1. Some comments on the structure of systems of centres.- 1.2. A brief survey of problems.- 1.3. Summary and main conclusions.- 2. Earlier works on systems of centres.- 2.1. Necessary conditions for hierarchy.- 2.2. Models for vertically integrated industries.- 2.3. Models with input-output coefficients.- 3. Hierarchy of centres in Sweden at the beginning of the 1970s — an empirical test on Swedish data.- 3.1. Background and presentation of the problem.- 3.2. An empirical investigation for Sweden.- Supplement. Component analysis — presentation and use.- 4. An attempt to extend the problem of Tinbergen and Bos — capacities of plants given.- 4.1. Presentation of the problem.- 4.2. Models for testing whether a centre should be split up.- 4.3. A programming model.- 4.4. Some numerical examples.- 4.5. Problems when decision-making is individual and based on price information.- Supplement. Balas’ method for combinatorial solution of integer problems.- 5. The system of centres when capacities of plants are not given — a further extension of the problem.- 5.1. Presentation of the problem.- 5.2. Control and co-ordination costs.- 5.3. A model for quadratic programming.- Appendix 1.- Appendix 2.- Appendix 3.- Appendix 4.- References.