Operations HW & Sol

OPERATIONS QUESTIONS
WEEK 2: PROCESS ANALYSIS
Q2.3 (Inventory Cost)

A manufacturing company producing medical devices reported $60,000,000 in sales over the
last year. At the end of the same year, the company had $20,000,000 worth of inventory of
ready-to-ship devices.
a. Assuming that units in inventory are valued (based on COGS) at $1,000 per unit and are
sold for $2,000 per unit, how fast does the company turn its inventory? The company uses a
25% per year cost of inventory. That is , for a hypothetical case that one unit of $1,000 would
sit exactly one year in inventory, the company charges its operations division a $250
inventory cost.
Q2.7 (Industrial Baking Process)

Strohrmann, a large-scale bakery in Pennsylvania, is layout out a new production process for
their packaged bread, which they sell to several grocery chains. It takes
12 minutes to bake the bread. How large an oven is required so that the company is able to
produce 4,000 units of bread per hour?
WEEK 2: PROCESS ANALYSIS [SOLUTION]
Q2.3 Inventory Cost

Cost = $1000 per unit. Sold at $2000 per unit. Therefore, 50% is cost.
COGS = $60 mil * 50% = $30 mil.
Turns=R/I = 30/20 = 1.5
Per unit inventory costs (%) = 25%/Inventory Turns = 16.66%
Q2.7 Industrial Baking Process

R = 4000 units of bread per hour
T = 12 mins / packaged bread
I = R * T = 800 breads
WEEK 3: SetUp & Batches EOQ

Q7.12 (Millennium Liquors)
Millennium Liquors is a wholesaler of sparkling wines. Their most popular product is the
French Bete Noire. Weekly demands is for 45 cases. Assume demand occurs over 50 weeks
per year. The wine is shipped directly from France. Millennium’s annual cost
of capital is 15%, which also includes all other inventory-related costs. Below are the
relevant data on the costs of shipping, placing orders and refrigeration.
o Cost per case: $120
o Shipping cost (for any shipment size): $290
o Cost of labor to place and process an order: $10
o Fixed cost for refrigeration: $75/week
a. Calculate the weekly holding cost for one case of wine.
b. Use the EOQ model to find the number of cases per order and the average number
of orders per year.
c. Currently orders are placed by calling France and then following up with a letter.
Millennium and its supplier may switch to a simple ordering system using the internet.
The new system will require much less labor. What would be the impact of this system
on the ordering pattern?
Exercise 2:
Braneast Manufacturers makes 500 taillights per year. Each time an order is
placed, a setup cost of $5 is incurred. Each light costs 40cents and the holding
cost is 8 cents/light/year. Assume that demand occurs at a constant rate,
shortages are not allowed and the production rate p is 600 taillights per year.
o What is the EOQ?
o What is the average inventory level?
WEEK 3: SetUp & Batches EOQ [SOLUTION]
Q 4.1 (Empty System, Labour Utilisation)
Time to complete 100 units.
The process takes 10 + 6 + 16 minutes = 32 minutes to produce the first unit
Resource 2 is the bottleneck and the process capacity is 1/6 = 0.1666 unit/minute
Time to finish 100 units = 32 minutes + (99 units / 0.166 unit/minute) = 626 minutes.
Parts b, c, d
Capacities are 2/10 unit/min = 0.2 unit/min, 1/6 = 0.1666 and 3/16 = 0.1875 (resource 2 is the
bottleneck)
Since there is unlimited demand, the flow rate is determined by the capacity and therefore is
0.1666 unit/min  a cycle time of 6 minutes/unit
Cost of direct labour = (6 x $10/hour) / (60 mins/hour x 0.1666 unit/min) = $6/unit
Idle time of each worker for each unit:
6 min/unit x 2 - 10 mins = 2 mins/unit,
6 min/unit x 1 - 6 mins = 0 mins/unit,
6 min/unit x 3 - 16 mins = 2 mins/unit
Labour content = 10 + 6 + 16 = 32 mins.
Average labour utilisation = 32/(32 + 4) = 0.8888
Q 7.5 (Simple Setup)
a. Capacity = B / (S + Tb)
B = batch size, S = set-up time, Tb = time to process the entire batch
C for Step 1 = 50 / (20mins + 50mins) = 0.714 units/min = 42.86 units/hour
C for Step 2 = 50 / (0 + 2*50) = 30 units/hour
C for Step 3 = 50 / (0 + 1.5*50) = 40 units/hour
Process capacity = bottleneck = 30 units/hour
b. C for Step 1 = 10 / (20 + 10) = 20 units/hour
C for Step 2 = 10 / (0 + 2*10) = 0.5 units/minute = 30 units/hour
C for Step 3 = 10 / (0 + 1.5*10) = 0.67 units/minute = 40 units/hour
c. Step 1: 20mins (setup) + 50 mins for processing = 70mins
Step 2: 50*2mins = 100 mins
Step 3: 20*1.5 = 30mins
Therefore, 200 mins to process 20 parts.
Q7.12 (Millennium Liquors)

15%/50 per week * $120/case = $0.36 per week
Ordering cost = $290 + $10 = $300. EOQ = 273.9 cases per order. Average number of orders
per year = 45*50 / 273.9 = 8.2
We would get slightly lower ordering costs  more frequent orders and lower inventory
Orange juice production
Capacity = B / (S + (B * p))
4 hours * 100 barrels/hr = 400 barrels
= 400 barrels / (30 mins + (400 barrels * 60/100 minutes per barrel))
= 1.48 barrels/min
= 88.88 barrels/hr

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OPERATIONS QUESTIONS

WEEK 2: PROCESS ANALYSIS

Q2.3 (Inventory Cost)

Q2.7 (Industrial Baking Process)

WEEK 2: PROCESS ANALYSIS [SOLUTION]

Q2.3 Inventory Cost

Q2.7 Industrial Baking Process

WEEK 3: SetUp & Batches EOQ

a. Calculate the weekly holding cost for one case of wine.

WEEK 3: SetUp & Batches EOQ [SOLUTION]

Q 4.1 (Empty System, Labour Utilisation)

Time to complete 100 units.

The process takes 10 + 6 + 16 minutes = 32 minutes to produce the first unit

Idle time of each worker for each unit:

6 min/unit x 2 - 10 mins = 2 mins/unit,

6 min/unit x 1 - 6 mins = 0 mins/unit,

6 min/unit x 3 - 16 mins = 2 mins/unit

Labour content = 10 + 6 + 16 = 32 mins.

Average labour utilisation = 32/(32 + 4) = 0.8888

Q 7.5 (Simple Setup)

B = batch size, S = set-up time, Tb = time to process the entire batch

C for Step 1 = 50 / (20mins + 50mins) = 0.714 units/min = 42.86 units/hour

C for Step 2 = 50 / (0 + 2*50) = 30 units/hour

C for Step 3 = 50 / (0 + 1.5*50) = 40 units/hour

Process capacity = bottleneck = 30 units/hour

b. C for Step 1 = 10 / (20 + 10) = 20 units/hour

C for Step 2 = 10 / (0 + 2*10) = 0.5 units/minute = 30 units/hour

C for Step 3 = 10 / (0 + 1.5*10) = 0.67 units/minute = 40 units/hour

c. Step 1: 20mins (setup) + 50 mins for processing = 70mins

Step 2: 50*2mins = 100 mins

Step 3: 20*1.5 = 30mins

Therefore, 200 mins to process 20 parts.

Q7.12 (Millennium Liquors)

Orange juice production

4 hours * 100 barrels/hr = 400 barrels

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