Inventory BM317 Warehousing and Inventory Management Lecture 10 Inventory System – Defined used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be Cost trade-offs in Marketing LOGISTICS MARKETING Cost Trade-offs Required in a Logistics System Relationship Between Customer Service and Inventory Investment 0 400 800 1200 1600 2000 75 80 85 90 95 100 Service % Inventory Investment in units Selected Financial Data for Manufacturers, Wholesalers, and Retailers for 1997 ($Millions) Companies Sales Net Profits Net Profits as a Total Assets Inventory Investment Inventories as a Percent of Sales Percent of Assets Manufacturers Abbott Laboratories ,883 ,094 18% ,061 ,280 11% Borden, Inc. 1,488 221 15% 2,206 302 14% The Clorox Company 2,741 298 11% 3,030 212 7% Dresser Industries, Inc. 7,458 318 4% 5,099 972 19% Ford Motor Company 153,627 6,920 5% 279,097 5,468 2% General Electric Company 90,840 8,203 9% 304,012 5,895 2% General Mills 6,033 422 7% 3,861 389 10% Goodyear Tire & Rubber Co. 13,065 559 4% 9,917 1,835 19% Harris Corp. 3,939 133 3% 3,784 604 16% Honeywell Co. 8,028 471 6% 6,411 1,028 16% NCR Corp. 6,598 7 0.11% 5,293 489 9% Newell Co. 3,234 290 9% 3,944 625 16% Pfizer, Inc. 12,188 2,213 18% 15,336 1,773 12% Sara Lee Corp. 20,011 ( 523) -3% 10,989 2,882 26% Xerox Corp. 18,166 1,452 8% 27,732 2,792 10% Wholesalers and Retailers Baxter International 6,138 300 5% 8,707 1,208 14% Bergen Brunswig Corp. 11,661 8 2 1% 2,707 1,309 48% Dayton Hudson Corp. 27,757 751 3% 14,191 3,251 23% Fleming Companies, Inc. 15,372 2 5 0.16% 3,924 1,019 26% Kmart Corporation 32,183 249 1% 13,558 6,367 47% Nordstrom 4,852 186 4% 2,865 826 29% Sears, Roebuck & Company 41,296 1,188 3% 38,700 5,044 13% Supervalu Inc. 17,201 231 1% 4,093 1,116 27% Wal-Mart Stores, Inc. 117,958 3,526 3% 45,384 16,497 36% Winn-Dixie 13,219 204 2% 2,921 1,249 43% Note: Ending inventory figures are used for inventory investment. All figures are for 1997. Purposes of Inventory 1. 2. 3. 4. material delivery time 5. size 6. within the supply chain Finished goods inventory in field Finished goods inventory at plant Raw materials inventory In-process inventory Purposes of Holding Different Types of Inventory Types of Inventory Purpose of holding inventory Raw material inventory / Component Parts Reducing ordering costs or setup costs Work-in-process Reducing setup costs, reducing inter-dependencies between operations Finished products Reducing ordering costs or setup costs, allowing flexibility in production scheduling, protecting against uncertainites in demand Facilitating goods in service systems Reducing ordering costs or setup costs, protecting against uncertainites in supply & demand Independent vs. Dependent Demand Independent Demand (Demand for the final endproduct or demand not related to other items) Dependent Demand (Derived demand items for component parts, subassemblies, raw materials, etc) Finished product Component parts Inventory Costs Components of Inventory Carrying Costs Inventory carrying costs Inventory investment Insurance Taxes Obsolescence Pilferage Storage space costs Capital costs Inventory service costs Inventory risk costs Plant warehouses Public warehouses Rented warehouses Company-owned warehouses Damage Relocation costs Inventory Carrying Costs Two Major Decisions 1. 2. item? Six Types of Inventory 1. 2. 3. lead time 4. quantities discounts) 5. inventory before a season begins 6. specified period of time Inventory Systems sales representative) Fixed-Order Quantity Model throughout the period orders are allowed) Assumptions Basic Fixed-Order Quantity Model and Reorder Point Behavior R = Reorder point Q = Economic order quantity L = Lead time L L Q Q Q R Time Number of units on hand 1. You receive an order quantity Q. 2. Your start using them up over time. 3. When you reach down to a level of inventory of R, you place your next Q sized order. 4. The cycle then repeats. 200 400 0 Days 10 20 30 40 50 60 Inventory Order placed Order arrival Order placed Average cycle inventory A. Orderquantity of 400 units Order arrival The Effect of Reorder Quantity on Average Inventory Investment With Constant Demand and Lead Time Inventory Order placed Order arrival Average cycle inventory Days 10 20 30 40 50 60 0 100 200 B. Orderquantity of 200 units The Effect of Reorder Quantity on Average Inventory Investment With Constant Demand and Lead Time Average cycle inventory Order arrival Order placed C. Orderquantity of 600 units Days 10 20 30 40 50 60 Inventory 0 300 600 The Effect of Reorder Quantity on Average Inventory Investment With Constant Demand and Lead Time Cost Minimization Ordering Costs Holding Costs Order Quantity (Q) C OST Annual Cost of Items (DC) Total Cost QOPT By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Q By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Q Basic Fixed-Order Quantity (EOQ) Model Formula H 2 Q S + Q D TC = DC + Total Annual = Cost Annual Purchase Cost Annual Ordering Cost Annual Holding Cost + + TC=Total annual cost D =Demand C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory TC=Total annual cost D =Demand C =Cost per unit Q =Order quantity S =Cost of placing an order or setup cost R =Reorder point L =Lead time H=Annual holding and storage cost per unit of inventory Source: Chase, Aquilano, Jacobs, “Operations Management – For Competitive Advantage” Iran McGraw-Hill Order Quantity Number of Orders (D/Q) Ordering Cost S * (D/Q) Inventory Carrying Cost 1/2 Q * H Total Cost 40 60 80 100 120 140 160 200 300 400 120 80 60 48 40 35 30 24 18 12 $ 4,800 3,200 2,400 1,920 1,600 1,400 1,200 960 720 480 $ 500 750 1,000 1,250 1,500 1,750 2,000 2,500 3,750 5,000 $ 5,300 3,950 3,400 3,170 3,100 3,150 3,200 4,460 4,470 5,480 Cost Trade-offs Required to Determine the Most Economic Order Quantity Deriving the EOQ Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Q Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Q Q = 2DS H = 2(Annual Demand)(Order or Setup Cost) Annual Holding Cost Q = 2DS H = 2(Annual Demand)(Order or Setup Cost) Annual Holding Cost Reorder point, R = d L _ Reorder point, R = d L _ d = average daily demand (constant) L = Lead time (constant) _ We also need a reorder point to tell us when to place an order We also need a reorder point to tell us when to place an order EOQ Example Annual Demand = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order = Holding cost per unit per year = .50 Lead time = 7 days Cost per unit = Given the information below, what are the EOQ and reorder point? Given the information below, what are the EOQ and reorder point? EOQ Example – Solution Q = 2DS H = 2(1,000 )(10) 2.50 = 89.443 units or d = 1,000 units / year 365 days / year = 2.74 units / day Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _ 20 units In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units. In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units. Price-Break Model Formula Annual Holding Cost 2(Annual Demand)(Order or Setup Cost) = iC 2DS Q = Based on the same assumptions as the EOQ model, the price-break model has a similar Q i = percentage of unit cost attributed to carrying inventory C = cost per unit Since “C” changes for each price-break, the formula above will have to be used with each price-break cost value Price-Break Example A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of , a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units? A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of , a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units? Order Quantity(units) Price/unit($) 0 to 2,499 .20 2,500 to 3,999 1.00 4,000 or more .98 Price-Break Example Solution = 1,826 units 0.02(1.20) 2(10,000)( 4) = iC 2DS Q = Annual Demand (D)= 10,000 units Cost to place an order (S)= First, plug data into formula for each price-break value of “C” = 2,000 units 0.02(1.00) 2(10,000)( 4) = iC 2DS Q = = 2,020 units 0.02(0.98) 2(10,000)( 4) = iC 2DS Q = Carrying cost % of total cost (i)= 2% Cost per unit (C) = .20, .00, .98 Interval from 0 to 2499, the Qopt value is feasible Interval from 2500-3999, the Qopt value is not feasible Interval from 4000 & more, the Qopt value is not feasible Next, determine if the computed Q Since the feasible solution occurred in the first pricebreak, it means that all the other true Q at the beginnings of each price-break interval. Why? Since the feasible solution occurred in the first pricebreak, it means that all the other true Q at the beginnings of each price-break interval. Why? 0 1826 2500 4000 Order Quantity Total annual costs So the candidates for the pricebreaks are 1826, 2500, and 4000 units So the candidates for the pricebreaks are 1826, 2500, and 4000 units Because the total annual cost function is a “u” shaped function Because the total annual cost function is a “u” shaped function Price-Break Example Solution iC 2 Q S + Q D TC = DC + Next, we plug the true Q annual cost function to determine the total cost under each price-break Next, we plug the true Q annual cost function to determine the total cost under each price-break TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = ,043.82 TC(2500-3999)= ,041 TC(4000&more)= ,949.20 TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = ,043.82 TC(2500-3999)= ,041 TC(4000&more)= ,949.20 Finally, we select the least costly Q problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units Finally, we select the least costly Q problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units Price-Break Example Solution A.With variable demand Inventory Average cycle inventory Ss( afety tock 50) y Ave ra ge inve ntor (150) 200 100 8 10 20 30 40 { { Average Inventory Investment Under Conditions of Uncertainty B. With variable lead time Inventory Average cycle inventory y Ave ra ge inve ntor (140) 200 100 { Day Ss( afety tock 40) s Average Inventory Investment Under Conditions of Uncertainty C. With variable demand and lead time Inventory Average cycle inventory y Ave ra ge inve ntor (200) 200 100 { Day y Ss( afet 0 tock 10 ) { Average Inventory Investment Under Conditions of Uncertainty Fixed-Time Period Model with Safety Stock Formula I = current inventory level (includes items on order) = standard deviation of demand over the review and lead time z = the number of standard deviations for a specified service probabilit y d = forecast average daily demand L = lead time in days T = the number of days between reviews q = quantitiy to be ordered Where : q = d(T + L) + Z – I T+L T+L q Fixed-Time Period Model: Determining the Value of T+L d i 1 T+L d T+L d 2 = Since each day is independent and is constant, = (T + L) i 2 = T+L d i 1 T+L d T+L d 2 = Since each day is independent and is constant, = (T + L) i 2 = random events equals the square root of the sum of the variances Symptoms of Poor Inventory orders remaining constant. distribution centers and major inventory items. Ways to Reduce Inventory Levels carriers ABC Classification System • importance in terms of: 0 30 60 30 60 A B C % of $ Value % of Items So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 15 %, “B” items as next 35 %, and the lower 65% are the “C” items Relationship Between Customer Service and Inventory Investment 0 400 800 1200 1600 2000 75 80 85 90 95 100 Service % Inventory Investment in units Model of Consumer Reaction to a Repeated Stockout Customer 3 Lower 4 Other size 2 Same 1 Higher Another store 6 Ask here again 5 Special order Switch stores ? Substitute ? Switch brand ? Substitute ? Switch price ? No No Yes Yes Yes Yes No No Inventory Accuracy & Cycle Counting inventory records agree with physical count technique in which inventory is counted on a frequent basis rather than once or twice a year
Control Systems 1
Inventory is the stock of any item or resource
An inventory system is the set of policies and
s
To maintain independence of operations
To meet variation in product demand
To allow flexibility in production scheduling
To provide a safeguard for variation in raw
To take advantage of economic purchase-order
To act as a buffer between critical interfaces
Holding (or carrying) costs
Costs for storage, handling, insurance, etc
Setup (or production change) costs
Costs for arranging specific equipment setups, etc
Ordering costs
Costs of someone placing an order, etc
Shortage costs
Costs of canceling an order, etc
Capital
Inventory service
Storage space
Inventory risk
When to place an order for an item?
How many to order or to produce of this
Cycle Stock
is inventory required to meet demand under certainty
In-Transit Inventories
are items that are move from one location to another
Safety or Buffer Stock
is held in excess of cycle stock because of uncertainty in demand or
Speculative Stock
is inventory held for reasons other than satisfying current demand (e.g.
Seasonal Stock
is a form of speculative stock that involves the accumulation of
Dead Stock
is the set of items for which no demand had been registered for some
Fixed-Order Quantity Model
Event triggered (Example: running out of stock)
Fixed-Time Period Model
Time triggered (Example: Monthly sales call by
Demand for the product is constant and uniform
Lead time (time from ordering to receipt) is constant
Price per unit of product is constant
Inventory holding cost is based on average inventory
Ordering or setup costs are constant
All demands for the product will be satisfied (No back
opt inventory order point that minimizes total costs
opt inventory order point that minimizes total costs
opt
opt
OPT
OPT
OPT 90 units
OPT
opt formula:
OPT
OPT
OPT
opt values are feasible or not
opt values occur
opt values occur
opt values into the total cost
opt values into the total cost
opt, which is this
opt, which is this
Days
10 12 20 30 40
{
10 12 20 30 40
s 8
q == Averaee demand ++ Safety stock ––Inventory currently on hand
T+L
( )
( )
The standard deviation of a sequence of
Increasing numbers of back orders
Increasing dollar investment in inventory with back
High customer turnover rate.
Increasing number of orders being canceled.
Periodic lack of sufficient storage space.
Wide variance in inventory turnover among
Deteriorating relationships with intermediaries
Large quantities of obsolete items
Multi-level inventory planning – ABC analysis
Lead time analysis
Delivery time analysis – This may lead to a change in
Elimination of low turnover and/or obsolete items
Analysis of pack size and discount structure
Encouragement/automation of product substitution
Analysis of customer demand characteristics
Development of a formal sales plan and source demand
Items kept in inventory are not of equal
dollars invested
profit potential
sales or usage volume
stock-out penalties
Inventory accuracy refers to how well the
Cycle Counting is a physical inventory taking
Credit:ivythesis.typepad.com
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