The inventory manager at a warehouse distributor wants to predict inventory cost

Question

The inventory manager at a warehouse distributor wants to predict inventory cost based on order quantity. She thinks it may be a nonlinear relationship since its two primary components move in opposite directions: (1) order processing cost (costs of procurement personnel, shipping, transportation), which decreases as order quantity increases (due to fewer orders needed). and (2) holding cost (costs of capital, facility, warehouse quantity increases (due to more inventory held). She has collected monthly inventory costs and order quantites for the past 36 months. The data are shown in the accompanying table. Order Inventory Quantity Cost (units) (S1,000s) 844 54.4 503 52.1 300 60.2 869 53.8 525 51.7 1030 57.1 288 61.1 577 49.8 490 53.9 588 48.2 606 47.5 325 57.4 1160 59.6 1072 58.2 308 58.7 1140 58.1 627 48.4 214 63.4 207 62.5 1174 62.5 1190 62.7 1166 61.2 1067 55.9 655 51.3 384 57.1 367 58.2 927 55.8 890 54.9 495 54.7 780 50.2 1168 60.8 403 54.B 741 12 51.9 612 49.8 870 55.5

Explanation / Answer

Using Excel:

b)Linear model:

Cost= a+b*Qunatity

Cost= 54.42816253 + 0.007191808*Quantity

Quadratic model:

Cost= a+b*Quantity * c*Quantity^2

Cost' =75.64062315- 0.070236082*Quantity + 0.000050* Quantity^2

c-1) For significant explanatory value, t test must be rejected or p-value should be less than significant value.

Adjusted R-squared= -0.013599114 and Explantory variable is not significant. Because p-value of t-test is greater than 0.05.

c-2) Adjusted R-sqaured= 0.855406213 and Explantory variable is significant. because p-value of t-test is less than 0.05

d) Best fitted model. Because explanatory variable is significant and R-squared value 0.863668.

Cost' =75.64062315- 0.070236082*Quantity + 0.000050* Quantity^2

Quantity= 800

Cost' =75.64062315- 0.070236082*800 + 0.000050* 800^2= 51.33185556($1000's)

SUMMARY OUTPUT Regression Statistics Multiple R 0.12393894 R Square 0.015360861 Adjusted R Square -0.013599114 Standard Error 4.583916199 Observations 36 ANOVA df SS MS F Significance F Regression 1 11.1452731 11.1452731 0.530416928 0.471418225 Residual 34 714.4177825 21.01228772 Total 35 725.5630556 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 54.42816253 1.888664469 28.8183335 1.784E-25 50.58993456 58.26639051 Order 0.001791808 0.00246027 0.72829728 0.471418225 -0.003208062 0.006791677

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