ISEN 370 Sample Test 2 Questions with Solutions
1. The famous Ernie from Sesame Street continually faces replenishment decisions
concerning his cookie supply. The Cookie Monster devours the cookies at an average
rate of 200 per day. The cookies cost $0.03 each. Ernie is getting fed up with having to
go to the store once a week. His friend Bert has offered to do a study to help Ernie with
his problem.
a. If Ernie is implicitly following an EOQ policy already with his weekly replenishment, what
can Bert say about the implicit values of the two missing parameters?
Solution: Weekly demand equals 1,400 units, which implies an annual demand () of
72,800. Weekly replenishment implies a lot size of Q = 1,400 units. If this is equal to the
EOQ, then we must have
2𝐾𝜆 2𝐾(72800) 𝐾
𝑄=√ =√ = 2203.028√ .
𝑖𝑐 𝑖(0.03) 𝑖
Because Q = 1,400, this implies
𝐾 1400
√ = = 0.63549,
𝑖 2203.08
which implies
𝐾
= 0.40385.
𝑖
Note that if we use a daily demand of = 200, then we get K/i = 147.
Note that if we use a weekly demand of = 1400, then we get K/i = 21.
b. Suppose that Ernie is implicitly following the EOQ policy already with his weekly
replenishment, and the store offers a quantity discount such that if Ernie buys 10,000
cookies at a time or more, then it costs $0.02 per cookie. If K = $0.10, what quantity
should Ernie regularly purchase if this is the case?
Solution: If K = $0.20, then from part (a), i = 0.24762. At $0.02 per cookie, the EOQ would be
2(0.1)(72800)
√(0.24762)(0.02) = 1,714.64. This implies that the cost minimizing value of Q such that Q ≥
10,000 occurs at the breakpoint, i.e., Q = 10,000. Therefore, we compare the current
policy to the cost at Q = 10,000.
Ernie’s current policy cost:
G0(1400) = 0.03(72,800) + √2(0.1)(72,800)(0.24762)(0.03) = $2194.40
Ernie’s cost at Q = 10,000:
(0.1)(72,800) (0.24762)(0.02)(10,000)
G1(10000) = 0.02(72,800) + 10,000
+ 2
= $1481.49
Ernie should buy in batches of 10,000
, 2. An operating telephone company purchases large quantities of semiconductors to be
used in manufacturing electronic switching systems. Shortages are not allowed. The
demand rate is 250,000 units per year, and the order cost is $100 per order. The annual
inventory-carrying rate is 24% and is based on the value of average inventory. The
supplier’s price schedule is as follows:
Order Size Variable Cost Per Unit (for each unit)
0 < Q < 5000 $12
5000 Q 20,000 $11
20,000 Q 40,000 $10
40,000 Q $ 9
Determine the optimal order quantity and roughly sketch the step function for the total
cost.
Solution:
Q0 = sqrt(2*100*250000/(0.24*12)) = 4166.67 (feasible)
Q1 = sqrt(2*100*250000/(0.24*11)) = 4351.94 (infeasible)
Q2 = sqrt(2*100*250000/(0.24*10)) = 4564.35 (infeasible)
Q3 = sqrt(2*100*250000/(0.24*9)) = 4811.25 (infeasible)
Cost at Q0 = 250000*12 + 100*250000/4166.67 + (0.24*12)*4166.67/2 = $3,012,000
Cost at Q = 5000 = 250000*11 + 100*250000/5000 + (0.24*11)*5000/2 = $2,761,600
Cost at Q = 20000 = 250000*10 + 100*250000/20000 + (0.24*10)*20000/2 = $2,525,250
Cost at Q = 40000 = 250000*9 + 100*250000/40000 + (0.24*9)*40000/2 = $2,293,825
Optimal to order Q = 40000
1. The famous Ernie from Sesame Street continually faces replenishment decisions
concerning his cookie supply. The Cookie Monster devours the cookies at an average
rate of 200 per day. The cookies cost $0.03 each. Ernie is getting fed up with having to
go to the store once a week. His friend Bert has offered to do a study to help Ernie with
his problem.
a. If Ernie is implicitly following an EOQ policy already with his weekly replenishment, what
can Bert say about the implicit values of the two missing parameters?
Solution: Weekly demand equals 1,400 units, which implies an annual demand () of
72,800. Weekly replenishment implies a lot size of Q = 1,400 units. If this is equal to the
EOQ, then we must have
2𝐾𝜆 2𝐾(72800) 𝐾
𝑄=√ =√ = 2203.028√ .
𝑖𝑐 𝑖(0.03) 𝑖
Because Q = 1,400, this implies
𝐾 1400
√ = = 0.63549,
𝑖 2203.08
which implies
𝐾
= 0.40385.
𝑖
Note that if we use a daily demand of = 200, then we get K/i = 147.
Note that if we use a weekly demand of = 1400, then we get K/i = 21.
b. Suppose that Ernie is implicitly following the EOQ policy already with his weekly
replenishment, and the store offers a quantity discount such that if Ernie buys 10,000
cookies at a time or more, then it costs $0.02 per cookie. If K = $0.10, what quantity
should Ernie regularly purchase if this is the case?
Solution: If K = $0.20, then from part (a), i = 0.24762. At $0.02 per cookie, the EOQ would be
2(0.1)(72800)
√(0.24762)(0.02) = 1,714.64. This implies that the cost minimizing value of Q such that Q ≥
10,000 occurs at the breakpoint, i.e., Q = 10,000. Therefore, we compare the current
policy to the cost at Q = 10,000.
Ernie’s current policy cost:
G0(1400) = 0.03(72,800) + √2(0.1)(72,800)(0.24762)(0.03) = $2194.40
Ernie’s cost at Q = 10,000:
(0.1)(72,800) (0.24762)(0.02)(10,000)
G1(10000) = 0.02(72,800) + 10,000
+ 2
= $1481.49
Ernie should buy in batches of 10,000
, 2. An operating telephone company purchases large quantities of semiconductors to be
used in manufacturing electronic switching systems. Shortages are not allowed. The
demand rate is 250,000 units per year, and the order cost is $100 per order. The annual
inventory-carrying rate is 24% and is based on the value of average inventory. The
supplier’s price schedule is as follows:
Order Size Variable Cost Per Unit (for each unit)
0 < Q < 5000 $12
5000 Q 20,000 $11
20,000 Q 40,000 $10
40,000 Q $ 9
Determine the optimal order quantity and roughly sketch the step function for the total
cost.
Solution:
Q0 = sqrt(2*100*250000/(0.24*12)) = 4166.67 (feasible)
Q1 = sqrt(2*100*250000/(0.24*11)) = 4351.94 (infeasible)
Q2 = sqrt(2*100*250000/(0.24*10)) = 4564.35 (infeasible)
Q3 = sqrt(2*100*250000/(0.24*9)) = 4811.25 (infeasible)
Cost at Q0 = 250000*12 + 100*250000/4166.67 + (0.24*12)*4166.67/2 = $3,012,000
Cost at Q = 5000 = 250000*11 + 100*250000/5000 + (0.24*11)*5000/2 = $2,761,600
Cost at Q = 20000 = 250000*10 + 100*250000/20000 + (0.24*10)*20000/2 = $2,525,250
Cost at Q = 40000 = 250000*9 + 100*250000/40000 + (0.24*9)*40000/2 = $2,293,825
Optimal to order Q = 40000
