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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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financial analysis planning and forecasting theory and application

Financial Analysis, Planning and ForecastingTheory 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
Outline
  • 21.1 Introduction
  • 21.2 Linear programming
  • 21.3 Working-capital model and short-term financial planning
  • 21.4 Goal programming
  • 21.5 Programming approach to cash transfer and concentration
  • 21.6 Summary and conclusion remarks
  • Appendix 21A. The simplex algorithm for solving eq. (21.8)
  • Appendix 21B. Mathematical formulation of goal programming
21 2 linear programming
21.2 Linear programming

(Objective function), (21.1)

21 3 working capital model and short term financial planning
21.3 Working-capital model and short-term financial planning
  • Questions to be answered
  • Model specification and its solution
  • Which constraints are causing bottlenecks?
  • How much more profit is being lost because of constraints?
  • How do the constraints affect the solution?
  • Duality and shadow prices
  • Short-term financial planning
21 3 working capital model and short term financial planning9
21.3 Working-capital model and short-term financial planning

(21.6)

(21.6a)

(i = 1, 2, 3) (21.7)

21 3 working capital model and short term financial planning12
21.3 Working-capital model and short-term financial planning

(21.9)

(i = 1, 2, …, m),

(j = 1, 2, …, n).

21 3 working capital model and short term financial planning13
21.3 Working-capital model and short-term financial planning

(21.10)

(j = 1, 2, …, n),

(i = 1, 2, …, m).

21 4 goal programming
21.4 Goal programming
  • Introduction
  • Application of GP to working-capital management
  • Summary and remarks on goal programming
21 4 goal programming16
21.4 Goal programming

(21.11a)

(21.11b)

(21.11c)

21 4 goal programming17
21.4 Goal programming

(21.11d)

(21.11e)

(21.11f)

21 4 goal programming20
21.4 Goal programming

*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.

21 5 programming approach to cash transfer and concentration
21.5 Programming approach to cash transfer and concentration
  • Transfer mechanisms
  • Cash-transfer Scheduling: contemporary practice
  • Weekend timing and dual balances
  • Limitations of the popular techniques
  • Mathematical-programming formulation
  • Relation of model formulation to current practice
21 5 programming approach to cash transfer and concentration25
21.5 Programming approach to cash transfer and concentration

TABLE 21.10

Managing about the target balance

21 5 programming approach to cash transfer and concentration27
21.5 Programming approach to cash transfer and concentration

(21.12)

(21.13)

(21.14)

21 5 programming approach to cash transfer and concentration28
21.5 Programming approach to cash transfer and concentration

(21.15)

(21.16)

(21.17)

21 5 programming approach to cash transfer and concentration29
21.5 Programming approach to cash transfer and concentration

(21.18)

(21.19)

(21.20)

21 6 summary and conclusion remarks
21.6 Summary and conclusion remarks

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.

appendix 21a the simplex algorithm for solving eq 21 834
Appendix 21A. The simplex algorithm for solving eq. (21.8)

(21.A.2a)

(21.A.2b)

(21.A.2c)

(21.A.2d)

appendix 21b mathematical formulation of goal programming
Appendix 21B. Mathematical formulation of goal programming

Following is a list of definitions of all variables used in the GP formulation

of the working-capital problem:

appendix 21b mathematical formulation of goal programming37
Appendix 21B. Mathematical formulation of goal programming

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

Management.

appendix 21b mathematical formulation of goal programming38
Appendix 21B. Mathematical formulation of goal programming

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:

Subject to:

appendix 21b mathematical formulation of goal programming40
Appendix 21B. Mathematical formulation of goal programming

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;*

appendix 21b mathematical formulation of goal programming41
Appendix 21B. Mathematical formulation of goal programming

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.

appendix 21b mathematical formulation of goal programming42
Appendix 21B. Mathematical formulation of goal programming

Cash: X8 = 5X1 -36X2 +7.5X3 -47X4 -3.5(60- X5)

-4.5(30- X6)+0.95X7 = 75;

(21.B.1)

Current ratio:

(21.B. 2)

Quick ratio:

(21.B. 3)