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**Extra info for A sixth bibliography of fractional programming**

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I=l U( ) is a proper concave function from R 1 to R , r G( ) is a proper convex function from R to R , and n. r. ,m n 1 1 Assume for the purpose of ruling out some pathological cases that ( 1 A . 1 ) has a finite optimal solution, x^ represents the decision variables of the i'th subunit. The U( ) function represents the objective of the organization. ( ) functions represent the local subunit constraints. CHAPTER 2 THE RELATIONSHIP BETWEEN THE "CONTINGENCY APPROACH" A N D THE MATHEMATICAL PROGRAMMING APPROACH The Contingency Approach to Organizational Design In Chapter 1 the basic ideas behind the contingency approach to organizational design were briefly presented.

All elements of A , B, C, and D are positive. The inequalities (a) and (b) represent the balancing. The inequality (c) represents the relation between the semifinished products and the finished products as specified by Ε and F. They may, for example, share some common resources. Notice, however, that there may exist many more constraints on x, y, and ζ than given in the three inequalities. Such constraints may be associated with goals, fixed resources, relations with products in other departments.

However, such a view is too simplistic. Is it more difficult to solve a big linear programming problem than a small stochastic problem? Does the basic structure of the problems have any impact on the conclusion? The answers to such questions are not obvious. One way to attempt an answer is to simulate the behavior of various models. Examples of such simulations are presented in Chapter 6. The environment plays an important role which can be analyzed by means of mathematical programming, but mathematical programming also provides a means for taking other important factors into consideration.