Oct 26, 2014
Lecture 7 Inventory PlanningChapter 12: Operations Management - 5th Edition Roberta Russell & Bernard W. Taylor, III And Chapter 8: Operations Management Krajewski and Ritzman 6/e
What Is Inventory? Stock of items kept to meet future demand
Purpose of inventory management how many units to order when to order
Types of Inventory Raw materials
Purchased parts and supplies Work-in-process (partially completed) products
(WIP) Items being transported Tools and equipment
Inventory and Supply Chain Management Bullwhip effect Seasonal or cyclical demand Inventory provides independence from
vendors Take advantage of price discounts Inventory provides independence between stages and avoids work stop-pages or delays
Two Forms of Demand Dependent Demand for items used to produce final products Tires stored at a Goodyear plant are an example of a dependent demand item
Independent Demand for items used by external customers Cars, appliances, computers, and houses are examples of independent demand inventory
Inventory and Quality Management The ability to meet effectively internal
organisational demand or customer demand in a timely, efficient manner is referred to as the level of customer service. Customers usually perceive quality service as
availability of goods they want when they want them Inventory must be sufficient to provide high-quality customer service in TQM
Inventory Costs Carrying cost
cost of holding an item in inventory Ordering cost / Setup cost cost of replenishing inventory Shortage cost temporary or permanent loss of
sales when demand cannot be met
Carrying Costs Carrying costs can include the following items: Facility storage Material handling Labour Record keeping Borrowing to purchase inventory (loan from banks)
Product deterioration, spoilage, breakage, obsolescence,
pilferage Carrying cost may be shown as total or as percentage of the value of an item Carrying costs range from 10 to 40 percent of the value of a manufactured item
Inventory Control Systems An inventory system controls the level of inventory by
determining how much to order and when to order. There are two basic types of inventory systems:
Continuous or fixed-order-quantity system Periodic or fixed-time-period system
Continuous System Constant amount ordered when inventory
declines to predetermined level Inventory level is continuously monitored Order time may vary Also known as perpetual system
Periodic System Order placed for variable
amount after fixed passage of time Order size differs. O = T IP Also known as periodic review system
ABC Classification Class A 5 15 % of units 70 80 % of value Class B 30 % of units 15 % of value Class C 50 60 % of units 5 10 % of value
ABC Classification: ExamplePART1 2 3 4 5 6 7 8 9 10
UNIT COST$ 60 350 30 80 30 20 10 320 510 20
ANNUAL USAGE90 40 130 60 100 180 170 50 60 120
PART
TOTAL PART VALUE
% OF TOTAL % OF TOTAL UNIT COSTQUANTITY % CUMMULATIVE ANNUAL USAGE VALUE
9 8 2 1 4 3 6 5 10 7
9 $85,400 10
$30,600 1 16,000 2 14,000 3 5,400 4 4,800 5 3,900 3,600 6 3,000 7 2,400 8 1,700
35.9 $ 60 18.7 350 16.4 30 6.3 80 5.6 30 4.6 4.2 20 3.5 10 2.8 320 2.0
510 20
6.0 5.0 4.0 9.0 6.0 10.0 18.0 13.0 12.0 17.0
90 40 A 130 60 B 100 180 170 C 50 60 120
6.0 11.0 15.0 24.0 30.0 40.0 58.0 71.0 83.0 100.0
CLASS A B C
% OF TOTAL ITEMS VALUE 9, 8, 2 71.0 1, 4, 3 16.5 6, 5, 10, 7 12.5
% OF TOTAL QUANTITY 15.0 25.0 Example 10.1 60.0
Economic Order Quantity (EOQ) Models EOQ optimal order quantity that will minimize
total inventory costs Basic EOQ model
Production quantity model
Definitions Order Cycle: The time between the receipt of orders in an
inventory system Lead Time: The time required to receive the order after an order
is placed.
Inventory Order CycleOrder quantity, Q Inventory Level
Demand rate
Reorder point, R
0
Lead time Order Order placed receipt
Lead time Order Order placed receipt
Time
Assumptions of Basic EOQ ModelDemand is known with certainty and is constant over time 2. No shortages are allowed 3. Lead time for the receipt of orders is constant 4. Order quantity is received all at once1.
EOQ Cost ModelCo - cost of placing order Cc - annual per-unit carrying cost D - annual demand Q - order quantity CoD Q CcQ 2 CcQ 2
Annual ordering cost =Annual carrying cost = Total cost = CoD + Q
EOQ Cost ModelDeriving Qopt Proving equality of costs at optimal point CoD CcQ = Q 2 Q2 2CoD = Cc 2CoD Cc
Co D CcQ TC = + Q 2CoD Cc TC = + Q2 2 Q C0D Cc 0= + Q2 2 Qopt = 2CoD Cc
Qopt =
EOQ Cost Model (cont.)Annual cost ($) Slope = 0 Minimum total cost Carrying Cost = CcQ 2
Total Cost
Ordering Cost =
CoD Q
Optimal order Qopt
Order Quantity, Q
Example The e-Paint Store paint in its warehouse and
sells it online on its Internet Web site. The store stocks several brands of paint; however, its biggest seller is Sharman-Wilson Ironcoat paint. The company wants to determine the optimal order size and total inventory cost for Ironcoat paint given an estimated annual demand of 10,000 gallons of paint, an annual carrying cost of $0.75 per gallon, and an ordering cost of $150 per order. They would also like to know the number of orders that will be made annually and the time between
EOQ ExampleCc = $0.75 per yard Qopt = Qopt = Co = $150 D = 10,000 yards
2CoD Cc2(150)(10,000) (0.75)
CoD CcQ TCmin = + Q 2TCmin(150)(10,000) (0.75)(2,000) = + 2,000 2
Qopt = 2,000 yards
TCmin = $750 + $750 = $1,500Order cycle time = 311 days/(D/Qopt) = 311/5 = 62.2 store days
Orders per year = D/Qopt = 10,000/2,000 = 5 orders/year
Production Quantity Model An inventory system in which an order is
received gradually, as inventory is simultaneously being depleted AKA non-instantaneous receipt model assumption that Q is received all at once is relaxed
p - daily rate at which an order is received
over time, a.k.a. production rate d - daily rate at which inventory is demanded
Production Quantity Model (cont.)Inventory level Maximum inventory level Average inventory level
Q(1-d/p)
Q (1-d/p) 2
0 Order receipt period Begin End order order receipt receipt Time
Production Quantity Modelp = production rateMaximum inventory level = Q - Q d p
d = demand rate
=Q1- d pQ d Average inventory level = 12 p CoD CcQ d TC = Q + 2 1 - p
2CoD Qopt = d Cc 1 p
Example Assume that the e-Paint Store has its own
manufacturing facility in which it produces Ironcoat paint. The ordering cost, C0, is the cost of setting up the production process to make the paint. C0 = $150. Recall that Cc = $0.75 per gallon and D = 10,000 gallons per year. The manufacturing facility operates the same days the store is open (311 days) and produces 150 gallons of paint per day. Determine the optimal order size, total inventory cost, the length of time to receive an order, the number of orders per year, and the maximum inventory level.
Cc = $0.75 per yard Co = $150 d = 10,000/311 = 32.2 yards per day
D = 10,000 yards p = 150 yards per day
2CoD Qopt =Cc 1 - d p
2(150)(10,000)
=
32.2 0.75 1 150
= 2,256.8 yards
CoD CcQ d TC = Q + 2 1 - p
= $1,329
2,256.8 Q Production run = = = 15.05 days per order 150 p
Production Quantity Model: Example
Number of production runs =
10,000 D = = 4.43 runs/year 2,256.8 Q d p 32.2 150
Maximum inventory level = Q 1 -
= 2,256.8 1 -
= 1,772 yards
Reorder PointLevel of inventory at which a new order is placed
R = dLwhere d = demand rate per period L = lead time
Reorder Point: Example The ePaint Internet Store is open 311 days per
year. If annual demand is 10,000 gallons of Ironcoat paint and the lead time to receive an order is 10 days, determine the reorder point for paint. Demand = 10,000 yards/year Store open 311 days/year Daily demand = 10,000 / 311 = 32.154 yards/day Lead time = L = 10 days R = dL = (32.154)(10) = 321.54 yards
Safety StocksSafety stock: buffer added to on hand inventoryduring lead time Stockout :an inventory shortage Service level: probability that the inventory available during lead time will meet demand
Variable Demand with a Reorder PointQ Inventory level
Reorder point, R
0 LT Time LT
Reorder Point with a Safety StockInventory level
QReorder point, R
Safety Stock
0 LT Time LT
Reorder Point With Variable DemandR = dL + zd Lwhere d = average daily demand L = lead time d = the standard deviation of daily demand z = number of standard deviations corresponding to the service level probability zd L = safety stock
Reorder Point for a Service LevelProbability of meeting demand during lead time = service level
Probability of a stockout
Safety stock zd L dL Demand
R
Example For the e-Paint Internet Store , we will assume
that daily demand for Ironcoat paint is normally distributed with an average daily demand of 30 gallons and a standard deviation of 5 gallons of paint per day. The lead time for receiving a new order of paint is 10 days. Determine the reorder point and safety stock is the store wants a service level of 95% - that is, the probability of a stockout is 5%.
Reorder Point for Variable DemandThe carpet store wants a reorder point with a 95% service level and a 5% stockout probabilityd = 30 yards per day L = 10 days d = 5 yards per day For a 95% service level, z = 1.65 R = dL + z d L Safety stock = z d L = (1.65)(5)( 10)
= 30(10) + (1.65)(5)( 10)
= 326.1 yards
= 26.1 yards
Order Quantity for a Periodic Inventory SystemQ = d(tb + L) + zd where d tb L d zd = average demand rate = the fixed time between orders = lead time = standard deviation of demand tb + L - I
tb + L = safety stock I = inventory level
Example The KVS Pharmacy stocks a popular brand of
over-the-counter flu and cold medicine. The average demand for the medicine is 6 packages per day, with a standard deviation of 1.2 packages. A vendor for the pharmaceutical company checks KVSs stock every 60 days. During one visit the store had 8 packages in stock. The lead time to receive an order is 5 days. Determine the order size for this order period that will enable KVS to maintain a 95% service level.
Fixed-Period Model with Variable Demandd d tb L I z = 6 bottles per day = 1.2 bottles = 60 days = 5 days = 8 bottles = 1.65 (for a 95% service level) tb + L - I 60 + 5 - 8
Q = d(tb + L) + zd = 397.96 bottles
= (6)(60 + 5) + (1.65)(1.2)