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Financial Analysis, Planning and Forecasting Theory and Application. Chapter 21. Elementary Applications of Programming Techniques in Working-Capital Management . By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University. Outline.
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Elementary Applications of Programming Techniques in Working-Capital Management
Alice C. Lee
San Francisco State University
John C. Lee
J.P. Morgan Chase
Cheng F. Lee
(Objective function), (21.1)
(i = 1, 2, 3) (21.7)
(i = 1, 2, …, m),
(j = 1, 2, …, n).
(j = 1, 2, …, n),
(i = 1, 2, …, m).
(i = 1, 2, 3, 4)
*Profit has a much higher priority than the working capital goal.
** The working capital goals have a much higher priority than the profit goal.
*** The priorities for all goals are similar.
Managing about the target balance
In this chapter, we have looked at a variety of financial-management problems and their solution through mathematical-programming techniques. As we have seen, linear-programming and goal-programming are very useful. We have also considered certain working-capital problems, including cash concentration and scheduling. In the next chapter we will again be using our linear-programming skills in long-range financial planning. We will use our knowledge gained from this chapter, in combination with other information, as inputs to our financial-planning models.
Following is a list of definitions of all variables used in the GP formulation
of the working-capital problem:
2 This appendix is reprinted from Sartoris, W. L., and M. L. Spruill, “Goal programming and working capital
management,” Financial Management (1974): 67-74, by permission of the authors and Financial
These weights are defined in Table 21.6 for ach of the three sets of priorities.
Using these definitions, the GP problem is formulated as follows:
The following list defines the constraint given by each row in the constraint matrix:
Row 1: Profit plus downside deviation = $2698.94;
Row 2: Time used in production at most 1000 hours;
Row3: At most 60 units of Y drawn from inventory;
Row 4: At most 30 units of Z drawn from inventory;
Row 5: At most 150 units of Y sold for cash;
Row 6: At most 100 units of Y sold on credit;
Row 7: At most 175 units of Z sold for cash;
Row 8: at most 250 units of Z sold on credit;
Row 9: Total cash goals 9;*
Row 10: Inventory loan constraint;*3
Row 11: Current ratio goal;*†
Row 12: Quick ratio goal; †
Row 13: Constraint requiring cash to be nonnegative;
Row 14: Sales of Y for cash plus sales of Y for credit must be greater than or equal to Y drawn from inventory;
Row 15: Sales of Z for cash plus sales of Z for credit must be greater than or equal to Z dawn from inventory.
*The numbers on the right-hand side include not only the goal but also constants carried to right-hand side of the equality from left-hand side.
† Both ratio goals have been linearized by multiplying right-hand side by denominator of ratio.
Cash: X8 = 5X1 -36X2 +7.5X3 -47X4 -3.5(60- X5)
-4.5(30- X6)+0.95X7 = 75;