PRODUCTIONS/OPERATIONS MANAGEMENT

1
How can it be that mathematics, being after all a
product of human thought independent of
experience, is so admirably adapted to the
objects of reality Albert Einstein
2
Importance of Inventory

• A typical hospital spends about 20 of its budget
  on medical, surgical, and pharmaceutical
  supplies. For all hospitals it adds up to 150
  billion annually.
• The average inventory in US economy about 1.13
  trillion on 9.66 trillion of sales. About 430
  billion in manufacturing, 230 billion in
  wholesaler, 411 billion in retail.
• What happens when a company with a large Work In
  Process (WIP) and Finished Goods (FG) inventory
  finds a market demand shift to a new product? Two
  choices
• Fire-sell all WIP and FG inventories and then
  quickly introduce the new product ? Significant
  losses
• Finish all WIP inventory and sell all output
  before introducing the new product ? Delay and
  reduced market response time

3
Inventory Classified

• Inputs inventory
• Raw materials and Parts
• In-process inventory
• Parts and products that are being processed
• Parts and products to decouple operations (line
  balancing inventory).
• Parts and products to take advantage of
  Economies of Scale (batch inventory).
• Outputs inventory
• To meet anticipated customer demand (average
  inventory and safety stock).
• To smooth production while meeting seasonal
  demand (seasonal inventory).
• In transit to a final destination to fill the gap
  between production and demand lead times
  (pipeline inventory).

4
Inventory

• Poor inventory management hampers operations,
  diminishes customer satisfaction, and increases
  operating costs.
• A typical firm probably has tied in inventories
  about
• 30 percent of its Current Assets
• 90 percent of its Working Capital (Current Assets
  Current Liabilities)
• Understocking lost sales, dissatisfied
  customers.
• Overstocking tied up funds (financial costs),
  storage and safe keeping (physical cost), change
  in customer preferences (obsolescence cost).

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Periodic Inventory Counting Systems

• At the beginning of each period, the existing
  inventory level is identified and the additional
  required volume to satisfy the demand during the
  period is ordered.
• The quantity of order is variable but the timing
  of order is fixed.
• Re-Order Point (ROP) is defined in terms of time.

Physical count of items made at periodic
intervals. Disadvantage no information on
inventory between two counts. Advantage order
for several items are made at the same time.
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Perpetual Inventory Systems

• When inventory reaches ROP an order of EOQ
  (Economic Order Quantity) units is places.
• The quantity of order is fixed but the timing of
  order is variable.
• ROP is defined in terms of quantity (inventory on
  hand).

Keeps track of removals from inventory
continuously, thus monitoring current levels of
each item. A point-of-sales (POS) system record
items at the time of sale.
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A classification Approach ABC Analysis

• ABC Analysis in terms of dollars invested, profit
  potential, sales or usage volume, and stockout
  penalties. Perpetual for class A, Periodic for
  class C.

Group A Perpetual Group C Periodic
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The Basic Inventory Model Economic Order
Quantity

• Only one product
• Demand is known and is constant throughout the
  year
• Each order is received in a single delivery
• Lead time does not vary
• Two costs
• Ordering Costs Costs of ordering and receiving
  the order
• Holding or Carrying Costs Cost to carry an item
  in inventory for one year
• Unit cost of product is not incorporated because
  we assume it is fixed. It does not depends on the
  ordering policy.

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The Basic Inventory Model

• Annual demand for a product is 9600 units.
• D 9600
• Annual carrying cost per unit of product is 16.
• H 16
• Ordering cost per order is 75.
• S 75
• How much should we order each time to minimize
  our total cost?
• b) How many times should we order?
• c) What is the length of an order cycle (288
  working days/year)?
• d) What is the total cost?
• Do NOT worry if you do not get integer numbers.

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Ordering Cost
D Demand in units / year Q Order quantity in
units / order
Number of orders / year
S Order cost / order
Annual order cost
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Annual Ordering Cost
12
Annual Ordering Cost
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The Inventory Cycle
Quantity on hand
Inventory
Receive order
Time
When the quantity on hand is just sufficient to
satisfy demand in lead time, an order for EOQ is
placed At the instant that the inventory on hand
falls to zero, the order will be received
(Screencam tutorial on DVD)
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The Inventory Cycle
Inventory
Q Order quantity At the beginning of the period
we get Q units. At the end of the period we have
0 units.
15
Average Inventory / Period Average Inventory /
year
This is average inventory / period. Average
inventory / period is also known as Cycle
Inventory What is average inventory / year ?
16
Inventory Carrying Cost
Q Order quantity in units / order
Average inventory / year
H Inventory carrying cost / unit / year
Annual carrying cost
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Annual Carrying Cost
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Total Cost
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EOQ

• EOQ is at the intersection of the two costs.
• (Q/2)H (D/Q)S
• Q is the only unknown. If we solve it

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Back to the Original Questions
Annual demand for a product is 9600 units. D
9600 Annual carrying cost per unit of product is
16. H 16 Ordering cost per order is 75. S
75 a) How much should we order each time to
minimize our total cost? b) How many times should
we order? c) What is the length of an order cycle
(288 working days/year)? d) What is the total
cost?

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D 9600, H 16, S 75
What is the Optimal Order Quantity


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How Many Times Should We Order?

Annual demand for a product is 9600 units. D
9600 Economic Order Quantity is 300 units. EOQ
300 Each time we order EOQ. How many times
should we order per year? D/EOQ 9600/300 32
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What is the Length of an Order Cycle?

Working Days 288/year 9600 units are required
for 288 days. 300 units is enough for how many
days? (300/9600)(288) 9 days
24
What is the Optimal Total Cost

The total cost of any policy is computed as

The economic order quantity is 300.
This is optimal policy that minimizes total cost.
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Centura Health Hospital

• Centura Health Hospital processes a demand of
  31200 units of IV starter kits each year
  (D31200), and places an order of 6000 units at a
  time (Q6000). There is a cost of 130 each time
  an order is placed (S 130). Inventory carrying
  cost is 0.90 per unit per year (H 0.90).
  Assume 52 weeks per year.
• What is the average inventory?
• Average inventory Q/2 6000/2 3000
• What is the total annual carrying cost?
• Carrying cost H(Q/2) 0.930002700
• How many times do we order?
• 31200/6000 5.2
• What is total annual ordering cost?
• Total ordering cost S(D/Q)
• Ordering cost 130(5.2) 676

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Assignment 12a.1
A toy manufacturer uses approximately 32000
silicon chips annually. The Chips are used at a
steady rate during the 240 days a year that the
plant operates. Annual holding cost is 60 cents
per chip, and ordering cost is 24. Determine the
following a) How much should we order each time
to minimize our total cost? b) How many times
should we order? c) what is the length of an
order cycle (working days 240/year)? d) What is
the total cost?
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Assignment 12a.2

• Victor sells a line of upscale evening dresses in
  his boutique. He charges 300 per dress, and
  sales average 30 dresses per week. Currently,
  Vector orders 10 week supply at a time from the
  manufacturer. He pays 150 per dress, and it
  takes two weeks to receive each delivery. Victor
  estimates his administrative cost of placing each
  order at 225. His inventory charring cost
  including cost of capital, storage, and
  obsolescence is 20 of the purchasing cost.
  Assume 52 weeks per year.
• Compute Vectors total annual cost of inventory
  system (carrying plus ordering but excluding
  purchasing) under the current ordering policy?
• Without any EOQ computation, is this the optimal
  policy? Why?
• Compute Vectors total annual cost of inventory
  system (carrying plus ordering but excluding
  purchasing) under the optimal ordering policy?
• What is the ordering interval under optimal
  ordering policy?
• What is average inventory and inventory turns
  under optimal ordering policy? Inventory turn
  Demand divided by average inventory. Average
  inventory Max Inventory divided by 2. Average
  inventory is the same as cycle inventory.

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Assignment 12a.3

• Complete Computer (CC) is a retailer of computer
  equipment in Minneapolis with four retail
  outlets. Currently each outlet manages its
  ordering independently. Demand at each retail
  outlet averages 4,000 per week. Each unit of
  product costs 200, and CC has a holding cost of
  20 of the product cost per annum. The fixed cost
  of each order (administrative plus
  transportation) is 900. Assume 50 weeks per
  year. The holding cost will be the same in both
  decentralized and centralized ordering systems.
  The ordering cost in the centralized ordering is
  twice of the decentralized ordering system.
• Decentralized ordering If each outlet orders
  individually.
• Centralized ordering If all outlets order
  together as a single order.
• Compute EOQ in decentralized ordering
• Compute the cycle inventory for one outlet and
  for all outlets.
• Compute EOQ in the centralized ordering
• Compute the cycle inventory for all outlets and
  for one outlet
• Compute the total holding cost ordering cost
  (not including purchasing cost) for the
  decentralized policy
• Compute the total holding cost plus ordering cost
  for the centralized policy