1.
Aggregate Planning
1 Demand forecast for a PC manufacturer is shown for next six months. Every worker
assembles 2 PCs per day. Overtime cost is Rs. 3.00 per day per unit in excess of the
maximum capacity of the plant which is 200 units per day.
Months Jan Feb Mar Apr May Jun
Demand (No.) 1000 3000 1000 5000 7000 2000
Working days 24 25 20 22 20 24
Extra cost of changing output rate (positive or negative) as compared to previous month:
Range Cost (Rs.)
1 – 100 2000
101 – 200 5000
201 – 300
or more
8000
Inventory carrying cost is Rs. 2.00 per unit per year. Assume beginning inventory to be zero.
The inventory build up follows cyclical pattern.
The company wants to find out total cost involved in following plans:
(a) Level output rate plan
(b) Chase plan
(c) Intermediate (or Mix) plan: A combination of level output rate and chase plan
2 Prakash Industries produces a product that has six months demand cycle as shown in the table
below:
January February March April May June
Demand
Forecast
300 500 400 100 200 300
Workdays 22 19 21 21 22 20
Work
Hours @ 8
per day
176 152 168 168 176 160
Each unit requires 10 worker hours to produce, at a labour cost of Rs. 6 per hour regular rate (or
Rs. 9 per hour over time rate). The total cost per unit is estimated to be Rs. 200 but the units can
be subcontracted at a cost of Rs. 208 per unit. There are currently 20 workers employed in the
subject department. The hiring and training cost per worker is Rs. 300 per person. The layoff cost
is Rs. 400 per person. The company policy is to have 20% of the demand forecast as the safety
stock that becomes the beginning inventory for the next month. There are currently 50 units in the
stock. The inventory carrying cost per unit per month is Rs. 2 only. Unit shortage or stock outs
have been assigned a cost of Rs. 20 per unit per month.
2.
The firm must begin January with the 50 units on hand.
Compare the costs of the following three aggregate plans and suggest the minimum cost plan for
the company:
a) Vary workforce size to accommodate demand.
b) Maintain constant work force of 20, and use overtime and idle time to meet demand.
c) Maintain constant work force of 20, and build inventory or incur stock out cost.
3 A firm produces a product that has six months demand cycle as shown in the table below:
January February March April May June
Demand
Forecast
500 500 600 300 200 100
Workdays 22 19 21 21 22 20
Work
Hours @ 8
per day
176 152 168 168 176 160
Each unit requires 10 worker hours to produce, at a labour cost of Rs. 6 per hour regular rate (or
Rs. 9 per hour over time rate). The idle of a worker costs the company a sum of Rs.2 per hour.
There are currently 22 workers employed in the subject department. The hiring and training cost
per worker is Rs. 400 per person. The layoff cost is Rs. 600 per person. The company policy is to
have 10% of the demand forecast as the safety stock that becomes the beginning inventory for the
next month. There are currently 100 units in the stock. The inventory carrying cost per unit per
month is Rs. 2 only. Unit shortage or stock outs have been assigned a cost of Rs. 6 per unit per
month.
The firm must begin January with the 100 units on hand.
Compare the costs of the following three aggregate plans and suggest the minimum cost plan for
the company:
a) Vary workforce size to accommodate demand.
b) Maintain constant work force of 20, and use overtime and idle time to meet demand.
c) Maintain constant work force of 20, and build inventory or incur stock out cost.
Inventory & Supply Chain Management
4 An item has annual demand of 10000 units. Annual carrying cost is at the rate of 20%.
Ordering cost is Rs 150 per order & purchase cost is Rs. 5.00 per unit. Calculate EOQ,
Annual cost of ordering, Annual cost of carrying & Time between orders.
5 If in the above question the item is manufactured at the production rate of 500 units per week,
what will be the EMQ, Annual cost of ordering, Annual cost of carrying & Time between
orders.
3.
6 A computer reseller stocks three brands of PCs; HCL, Zenith & LG. Annual demands for
three brands are 12000 for HCL PCs, 1200 for Zenith PCs & 120 for LG PCs. Assume that
each model costs the reseller Rs. 25000. A fixed transportation cost of Rs. 15000 is incurred
each time an order is delivered. For each brand ordered and delivered on the same truck, an
additional fixed cost of Rs. 2500 is incurred for receiving & storage. The reseller incurs a
holding cost of 20 percent.
()a Evaluate the lot sizes that the manager at the reseller should order if lot for each brand are
ordered & delivered independently.
()b What would be the optimal lot size for each brand if the manager decides to aggregate
and order all three brands each time he places order.
7. A TV reseller stocks three brands of 21” TVs; LG, ONIDA & Bestavision. Annual demands
for three brands are 15000 for LG TVs, 1500 for ONIDA TVs & 150 for Bestavision TVs.
Assume that each model costs the reseller Rs. 6000. A fixed transportation cost of Rs. 4000 is
incurred each time an order is delivered. For each brand ordered and delivered on the same
truck, an additional fixed cost of Rs. 500 is incurred for receiving & storage. The reseller
incurs a holding cost of 20 percent.
(a) Evaluate the lot sizes that the manager at the reseller should order if lot for each brand are
ordered & delivered independently.
(b) What would be the optimal lot size for each brand if the manager decides to aggregate
and order all three brands each time he places order.
8. Twinkle Industries, a small scale unit, is a supplier of speedometers to Jumbo Corporation, a
large 150 cc two wheeler manufacturer. It supplies 20,000 speedometers to Jumbo annually.
At Jumbo the ordering cost per order is Rs. 5.00 and the carrying cost is 2.5% of the product
price. The price of a single unit is Rs. 200. The company presently has a policy of placing 10
orders every year. Advise the management of Jumbo as to whether it should continue with its
present policy or switch over to EOQ model.
9. Mr. Jain is a retailer of computer peripherals in Nehru Place. The fastest moving item from
his shop is Samsung 15 inch colour monitor. Demand for monitors from his shop is 1500 per
month. Mr. Jain incurs a fixed order placement, transportation and receiving cost of Rs. 3200
each time an order is placed. Each monitor costs Rs 3600 and the holding cost is 20%.
()a Evaluate the number of monitors Mr. Jain should order in each replenishment lot.
()b If Mr. Jain wishes to reduce the lot size to 200, by how much the order cost per lot should
be reduced?
10. Assume the weekly demand of 1 Kg pack of mango pickles at a Panch Ranga (a famous
brand of pickles) outlet is normally distributed with mean of 1500 and standard deviation of
300. The manufacturer takes one week to fill an order placed by the outlet. The store manager
currently orders 2,000 1Kg packs when the inventory on hand drops to 2000. Evaluate the
safety inventory and the average inventory carried by the outlet. Also evaluate the average
time spent by a pack of 1 Kg pickle at the outlet.
11. Annual demand is of 20000 boxes. Cost of placing an order is Rs. 100. Inventory carrying
cost is 20% and the purchase price of each box is Rs. 10. What should be the order quantity?
If the supplier offers a discount of 1% on an order of 4000 units in one lot, would you accept
this discount?
12. Daily demand of a product is 20 units with standard deviation of 4 units. The review
period is 30 days and lead time is 19 days. There are 250 working days in a year. The
cost of the product is Rs. 200 and the carrying cost is 2.5% per month. Management
has set a policy of satisfying 98% of customer demand from items in the stock. At the
4.
beginning of the review period there are 150 units in the stock. How many units
should be ordered? Also calculate inventory turns. (Value of Z at 98% if the rejection
area is only on right tail is 2.05 and if the rejection area is split equally on both the
tails the value of Z is 2.33)
13. Consider the inventory management of the following item that is being managed
using a fixed time period model with safety stock:
Weekly demand = 50 units, Review Cycle = 3 weeks, Safety Stock = 30 units
What are the average inventory level and the inventory turn for the item?
14. Suppose the inventory of the following item is being managed using a fixed order
quantity model with safety stock:
Annual Demand = 1000 units, Order quantity = 300 units and safety stock = 40 units
What are the average inventory level and the inventory turn for the item?
15. Actual demands for past six months and projected demand for next three months are
given below. The standard deviation of the demand as seen between Jul 07 and Dec
07 is 0.457. The lead time for procurement is 3 months. If the service level desired is
0.90 (Z value for P = 0.90 is 1.28 for one tail test and 1.65 for two tail test), calculate
the safety stock and the reorder point.
Past Sales in ’000 Forecasted Sales in ’000
Jul-07 Aug-07 Sep-07 Oct-07 Nov-07 Dec-07 Jan-08 Feb-08 Mar-08
5.91 5.01 5.03 5.29 5.97 5.89 5.5 5.5 5.5
16. Consider the following set of data pertaining to an inventory system and work out the
inventory policy i. e.,
Annual average demand = 20000 units
Unit price = Rs. 700
Ordering cost = Rs. 4000
Inventory carrying cost = 5%
Average lead time = 4 weeks
Service level = 75%
(a) EOQ and ROP when demand rate is constant and supply lead time is fixed
(b) EOQ and ROP with uncertain demand but fixed lead time: Standard deviation of the
demand per week = 54 units
(c) EOQ and ROP with uncertain demand and uncertain lead time: Standard deviation of the
demand per week = 54 units and Standard deviation of the lead time = 2 weeks
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