Modern warehouses employ computerized and automated guided vehicles for material

Question

Modern warehouses employ computerized and automated guided vehicles for materials handling. Consequently, the physical layout of the warehouse must be carefully designed to prevent vehicle congestion and optimize response time. Optimal design of an automated warehouse was studied in The Journal of Engineering for Industry (Aug. 1993). The layout employed assumes that vehicles do not block each other when they travel within the warehouse, i.e., that there is no congestion. The validity of this assumption was checked by stimulating (on a computer) warehouse operations. In each simulation, the number of vehicles was varied and the congestion time (total time on vehicle blocked another) was recorded. The data are shown in the accompanying table. Of interest to the researchers the relationship between congestion time (y) and the number of vehicles (x) Conduct a simple linear regression analysis of the data, including a residual analysis. What conclusions can you draw from the data?

Number of vehicles Congestion time, minutes 1 0 2 0 3 0.02 4 0.01 5 0.01 6 0.01 7 0.03 8 0.03 9 0.02 10 0.04 11 0.04 12 0.04 13 0.03 14 0.04 15 0.05

Explanation / Answer

R-code

data=read.csv("regression.csv",header=T)

attach(data)

reg=lm(Number.of.vehicles~.,data=data)

reg=lm(Number.of.vehicles~Congestion.time..minutes,data=data)

Output:

Residuals:
Min 1Q Median 3Q Max
-3.8246 -1.1026 0.1381 1.1940 3.6567

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.7873 0.9858 1.813 0.093 .
Congestion.time..minutes 251.8657 33.8798 7.434 4.95e-06 ***
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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.025 on 13 degrees of freedom
Multiple R-squared: 0.8096,   Adjusted R-squared: 0.7949
F-statistic: 55.27 on 1 and 13 DF, p-value: 4.946e-06

Interpretition:

P-value is less than level of significance

so the regression model with parameter a = 251.8657 and b = 1.7873. where a = slop and b = intercept.

(i.e. y= ax+b) is well fitted to the given data.

Conclusion:

Number of vehicles is related to Congestion time in minutes with following equation:

Number of vehicles = 251.8657 * Congestion time in minutes + 1.7873

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