Handbook of Civil Engineering Calculations

TABLE 29. Values of P

Number of units demanded Y

Number of units

ordered^ 150 160 170 180 190 200

150 3750 3710 3670 3630 3590 3550

160 3310 4000 3960 3920 3880 3840

170 2870 3560 4250 4210 4170 4130

180 2430 3120 3810 4500 4460 4420

190 1990 2680 3370 4060 4750 4710

200 1550 2240 2930 3620 4310 5000

Probability of Y 0.08 0.13 0.20 0.32 0.18 0.09

diagonal from the upper left-hand corner to the lower right-hand corner by applying Eq.
a. In each column, proceed upward from this diagonal by successively deducting $290, in
accordance with Eq. c. Then proceed downward from the diagonal by successively de-
ducting $440, in accordance with Eq. b.

3. Compute the expected prof it corresponding to each value of X
   As stated earlier, if all possible values of a random variable are multiplied by their respec-
   tive probabilities and the products are added, the result equals the arithmetic mean of the
   variable in the long run, and it is also called the expected value of the variable. For con-
   venience, repeat the probability corresponding to every possible value of Y at the bottom
   of Table 29. Let E(P) = expected value of P. When X = 150, E(P) = $3750(0.08) +
   $3710(0.13) + $3670(0.20) + $3630(0.32) + $3590(0.18) + $3550(0.09) = $3643.60.
   When X= 160, E(P) = $3310(0.08) + $4000(0.13) + $3960(0.20) + $3920(0.32) +
   $3880(0.18) + $3840(0.09) = $3875.20. Continue these calculations to obtain: when X=
   170, E(P) = $4011.90; when X= 180, E(P) = $4002.60; when X= 190, E(P) = $3759.70;
   when X= 200, E(P) = $3385.40.


4. Determine how many units the firm should order
   The results in step 3 show that the expected profit is maximum when X= 170. Therefore,
   the firm should order 170 units. If the fluctuation in dema'nd follows the same pattern as
   in the past, the firm will maximize its profits in the long run by maintaining a stock of this
   size.

FINDING OPTIMAL INVENTORYBY

INCREMENTAL-PROFIT METHOD

With reference to the preceding calculation procedure, determine how many units the
firm should order by applying incremental analysis.

Calculation Procedure:

1. Set up the equation for expected incremental profit
   Consider that the firm increases the number of units ordered by 10. In doing this, the firm