The trucking company you work for delivers product to a cust

The trucking company you work for delivers product to a customer’s warehouse. The target transportation time is 36 hours, but if the delivery is more than 6 hours late a $350 penalty is paid to the customer. Your company can choose the carrier. The most reliable carrier will deliver the product in 36 hours for $900, but if a cheaper carrier is used the rate declines at a rate of $20 for each hour of deviation allowed from the target.

A- What is the Taguchi Loss function constant, k? (2 points)

B- What is the Taguchi Loss Cost plus Process Cost at the target value of y=36 hours? (2 points)

C- What is the Taguchi Loss Cost plus Process Cost at a value of y=42 hours? (2 points)

D- What is the optimal value for y (in hours)? (2 points)

E- What is the Taguchi Loss Cost plus Process Cost at the optimal value of y? (2 points)

Solution

let x be the delay

900 - 20 *x is the delivery cost

loss = 350 if x>= 6

loss = 0 if x<0

so y = 36 , x= 0

cost = 900 + 0 (loss cost)

if y= 42 hrs

x = 6

cost = 900 - 20*6 + 350

optimal value for x . would be very large

when the penalty will only be 350 but we can save more than 350 on carrier.

say x = 45

process cost = 900-20*x = 0

total cost = 350 (for penalty)