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Managing Economies of Scale Cycle Inventory
Managing Economies of Scale
Cycle Inventory
Role of InventoryImprove Matching of Supply
and Demand
Improved Forecasting
Reduce Material Flow Time
Reduce Waiting Time
Reduce Buffer Inventory
Economies of ScaleSupply / Demand
VariabilitySeasonal
Variability
Cycle Inventory Safety InventoryFigure Error! No text of
Seasonal Inventory
Role of Cycle Inventory
Lot, or batch size = Q
Cycle inventory = Q/2
Inventory profile: plot of the inventory level over time
Average flow time = Avg inventory / Avg flow rate
= Q/(2D)D = demand per unit time
Cycle Inventory
Q = 1000 unitsD = 100 units/day
Cycle inventory = Q/2 = 1000/2 = 500 = Avg inventory level from cycle inventory
Avg flow time = Q/2D = 1000/(2)(100) = 5 days
Cycle Inventory
Adds to the time a unit spends in the supply chain
Lower cycle inventory is better because: Average flow time is lower Working capital requirements are lower Lower inventory holding costs
Role of Cycle Inventory
Held to take advantage of economies of scale
Supply chain costs influenced by lot size Material cost = C ($/unit) Fixed ordering cost = S ($/lot) Holding cost = H = hC
h = cost of holding $1 in inventory for one year (fraction of unit cost of product)
H = cost of holding 1 unit in inventory for one year
Role of Cycle Inventory
To purchase products in lot sizes that minimize total material, ordering, and holding costs
Each stage generally makes its own cycle inventory decisions
Exploiting Economies of Scale
3 typical situations:
Fixed cost incurred for each order
Supplier offers price discounts based on quantity
Supplier offers short-term discounts or holds trade promotions
Economies of Scaleto Exploit Fixed Costs
Lot sizing for a single product (EOQ)
Aggregating multiple products in a single order
Lot sizing with multiple products or customersLots are ordered and delivered independently for each product jointly for all products jointly for a subset of products
Lot sizing for a single product (EOQ)D: Annual demand S: Setup or Order CostC: Cost per unith: Holding cost per year as a fraction of
product costH: Holding cost per unit per yearQ: Lot Sizen: Ordering frequencyT: Reorder interval
Lot sizing for a single product
Number of orders per year = D/Q
Annual material cost = CD
Annual order cost = (D/Q)S
Annual holding cost = (Q/2)H = (Q/2)hC
Total annual cost = TC = CD + (D/Q)S +
(Q/2)hC
S
DhCn
hC
DSQ
hCH
2*
2*
Optimal Lot Size (EOQ)
EOQ ModelDemand for Deskpro computers at Bestbuy d = 1000 computers/monthCosts for retailer:Unit cost, C = $500Holding cost fraction, h = 0.2Fixed cost, S = $4,000/order
How many should the retailer order?
EOQ ModelQ* = Sqrt[(2)(12000)(4000)/(0.2)(500)] = 980
computers Cycle inventory = Q/2 = 490Average Flow time = Q/2D = 980/(2)(12000) = 0.041
year = 0.49 monthn* = 12.24Reorder interval, T = 0.98 month
Annual ordering and holding cost = = (12000/980)(4000) + (980/2)(0.2)(500) = $97,980
EOQ Model
In deciding optimal lot size, the tradeoff is between setup (order) cost and holding cost.
Order convenient lot size close to EOQ
If demand increases by k, optimal lot size and n increases by √k and flow time (for cycle inventory) reduces by √k
EOQ ModelSuppose lot size is reduced to Q=200 to
reduce flow time:Annual ordering and holding cost = = (12000/200)(4000) + (200/2)(0.2)(500) =
$250,000
Significantly higherTo make it economically feasible to reduce lot size, the fixed cost associated with each lot would have to be reduced
EOQ ModelIf desired lot size = Q* = 200 units, what
would S have to be?D = 12000 unitsC = $500h = 0.2Use EOQ equation and solve for S:S = [hC(Q*)2]/2D = [(0.2)(500)(200)2]/(2)
(12000) = $166.67
To reduce optimal lot size by a factor of k, the fixed order cost must be reduced by a factor of k2
Aggregating Multiple Productsin a Single Order
Transportation is a major fixed cost per order
Can combine shipments of different products from the same supplier same overall fixed cost shared over more than one product effective fixed cost is reduced for each
product lot size for each product can be reduced
Example
Suppose there are 4 computer products : Deskpro, Litepro, Medpro, and Heavpro
Demand for each is 1000 units per month
If each product is ordered separately: Q* = 980 units for each product Total cycle inventory = 4(Q/2) = (4)(980)/2
= 1960 units
Example
Aggregate orders of all four products: Combined Q* = 1960 units For each product: Q* = 1960/4 = 490 Cycle inventory for each product is reduced
to 490/2 = 245 Total cycle inventory = 1960/2 = 980 units Average flow time & inventory holding costs
will be reduced
Aggregating Multiple Productsin a Single Order
Can have single delivery from multiple suppliers or single truck delivering to multiple retailers Cross docking
Aggregating across products, retailers, or suppliers in a single order fixed ordering and transportation costs are
spread out allows for a reduction in lot size for individual
products Increase in product variety increases receiving/
loading costs ASN &/ or RFID can help
Lot Sizing with MultipleProducts or Customers
Fixed ordering cost is dependent at least in part on the variety associated with an order of multiple models
With an order of multiple models the fixed ordering cost has A portion related to transportation
(independent of variety) A portion related to loading and receiving
(not independent of variety)
Lot Sizing with MultipleProducts or Customers
To find lot sizes & ordering policy to minimize total cost
Three scenarios: Lots are ordered and delivered
independently for each product Lots are ordered and delivered jointly for
all products in each lot Lots are ordered and delivered jointly for
a selected subset of products
Lot Sizing with Multiple Products
Demand per year DL = 12,000; DM = 1,200; DH = 120
Common transportation cost, S = $4,000Product specific order cost sL = $1,000; sM = $1,000; sH = $1,000
Holding cost, h = 0.2Unit cost CL = $500; CM = $500; CH = $500
Delivery Options
No Aggregation: Each product
ordered separately
Complete Aggregation: All products
delivered on each truck
Tailored Aggregation: Selected
subsets of products on each truck
No Aggregation Litepro Medpro Heavypro
Demand per year
12,000 1,200 120
Fixed cost / order
$5,000 $5,000 $5,000
Optimal order size
1,095 346 110
Order frequency
11.0 / year 3.5 / year 1.1 / year
Annual cost $109,544 $34,642 $10,954
Total cost = $155,140
Complete Aggregation
S* = S + sL + sM + sH
= 4000+1000+1000+1000 = $7000
n* = Sqrt[(DLhCL+ DMhCM+ DHhCH)/2S*]
= 9.75
QL = DL/n* = 12000/9.75 = 1230
QM = DM/n* = 1200/9.75 = 123
QH = DH/n* = 120/9.75 = 12.3
Cycle inventory = Q/2
Complete AggregationLitepro Medpro Heavypro
Demand peryear
12,000 1,200 120
Orderfrequency
9.75/year 9.75/year 9.75/year
Optimalorder size
1,230 123 12.3
Annualholding cost
$61,512 $6,151 $615
Annual order cost = 9.75 × $7,000 = $68,250Annual total cost = $136,528
Aggregation with capacity constraint
Aggregating for products from 4 suppliers:
Truck capacity = 2500 units
Demand per product: Di = 10,000
Holding cost, h = 0.2
Unit cost per product Ci = $50
Common order cost S = $500
Supplier specific order cost si = $100
Aggregation with capacity constraint
S* = 500+100+100+100+100 = $900 per order
n* = Sqrt[(D1hC1+ D2hC2+ D3hC3 + D4hC4)/2S*]
= 14.91 (number of orders per year)
Q= 10,000/14.91 = 671 units per order from each supplier
Needs truck capacity = 4 X 671 = 2684 units
Order from each can be = 2500/4 = 625 units
Ordering frequency = 10,000 /625 = 16
Annual order cost per supplier increases from $3354 to $3600Annual holding cost per supplier decreases from $3355 to $3125
Tailored Aggregation Litepro Medpro Heavypro
Demand per year
12,000 1,200 120
Order frequency
11.47/year 5.74/year 2.29/year
Optimal order size
1,046 209 52
Annual holding cost
$52,307 $10,461 $2,615
Annual order cost = $65,383.5Annual total cost = $130,767
Aggregation
Allows firm to lower lot size without increasing cost
Use complete aggregation If product specific fixed cost is a small
fraction of joint fixed cost
Use tailored aggregation If product specific fixed cost is a large
fraction of joint fixed cost
Quantity Discounts
Lot size based All units Marginal unit
Volume based
Economies of Scale toExploit Quantity Discounts
Why quantity discounts? Price discrimination to maximize
supplier profits Coordination in the supply chain
How should buyer react?
What are appropriate discounting schemes?
All-Unit Quantity Discounts
Pricing schedule has specified quantity break points q0, q1, …, qr, where q0 = 0
If an order is placed that is at least as large as qi but smaller than qi+1, then each unit has an average unit cost of Ci
All-Unit Quantity Discounts
The unit cost generally decreases as the quantity increases, i.e., C0>C1>…>Cr
The objective for the company is to decide on a lot size that will minimize the sum of material, order, and holding costs
All-Unit Quantity Discount: Example
Order quantity Unit Price0- <5000 $3.005000- <10000 $2.9610000 or more $2.92
q0 = 0, q1 = 5000, q2 = 10000
C0 = $3.00, C1 = $2.96, C2 = $2.92
D = 120000 units/year, S = $100/lot,
h = 0.2
ExampleQ0 = Sqrt[2DS/h C0] = 6324 units
Since 6324 > q1 move to i = 1
Q1 = 6367 units
Since 5000<6367<10,000 set lot size = 6367 (get discounted price C1 )
TC1 = 358,969 (ordering+ holding+ material costs)
For i=2, Q2 = 6410 unitsSince 6410<10,000 set lot size = 10,000 (to get
discount price C2 )TC2 = 354520
Since TC is lowest for i=2, optimal order quantity = 10,000 units
Effects of Quantity Discounts
Retailers are encouraged to increase the size of their orders
Average inventory (cycle inventory) in the supply chain is increased
Average flow time is increased Is quantity discount an advantage in the
supply chain?
Value of Quantity Discounts
Improved coordination to increase supply chain profits Commodity products Products for which firms have market p
ower
Extraction of surplus through price discrimination
Commodity products: Example
D =10,000 / monthFor retailer:Fixed Order cost=100; C=$3; h=.2Q=6324Annual Order & holding cost=$3795For manufacturer:Order filling cost=$250; Production cost =$2/bottle ; h=.2Annual Order & holding cost=$6009Total SC cost=$9804
Commodity products: Example
Convince retailer to increase lot size to say 10,000 unitsImplications:
For retailer:Annual Order & holding cost =$1200+$3000
=$4200Cost increases by $(4200-3795) = $405For manufacturer:Annual Order & holding cost=$(3000+2000) =
$5000Cost decreases by $(6009-5000) = $1009
Total SC cost decreases by=$(9804-9200) =$604
Commodity products: Example
Why should retailer agree?
Give just enough discount to offset his increased ordering & holding costs
Cost increased by 405 for 120000 unitsDiscount to be given per unit
= 405 / 120000 =0.003375New C= 3- 0.003375 = $2.996625
Products for which firms have market power: Example
Final Demand D=360,000 – 60,000pProduction cost of manufacturer: $2
per unit
How much manufacturer charges?How much retailer charges?What is the optimal price for SC?
Double Marginalization
Products for which firms have market power: Example
Pricing schemes for manufacturer:2-part tariff Charge an upfront fee Plus material cost
Volume-based quantity discount Price such that retailer buys total
volume sold when two stages coordinate pricing
Quantity Discounts
Lot size based Commodity products Manufacturers have large fixed costs Maximize SC profits Increase cycle inventory
Volume based Firm has market power Manufacturer passes some fixed cost to
retailer Better even when we consider inventory
(ordering & holding costs)
Short-Term Discounting: Trade PromotionsPrice discounts for a limited period of time may require specific actions from retailers, such
as displays, advertising, etc.
Key goals from a manufacturer’s perspective: Induce retailers to use price discounts, displays,
advertising to increase sales Shift inventory from the manufacturer to the
retailer and customer Defend a brand against competition
Goals are not always achieved by a trade promotion
Short-Term Discounting: Trade Promotions
What is the impact on the behavior of the retailer and on the performance of supply chain?
Retailer options in response to a promotion Pass through some or all of the promotion to
customers to spur sales
Purchase in greater quantity during promotion period to take advantage of temporary price reduction, but pass through very little of savings to customers Forward buy
Short-Term Discounting
Forward buy Increase demand variability Increase inventory Increase flow time Decrease SC profits
Retailers optimal response?
Weekly Consumption ofChicken Noodle Soup
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Consumption
Weekly Shipments ofChicken Noodle Soup
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ShipmentsConsumption
Short Term Discounting
Q*: Normal order quantity
C: Normal unit costd: Short term
discountD: Annual demandh: Cost of holding
$1 per yearQd: Short term order
quantity
dC
C
hdC
dD QQ
d
-+
)-(=
*
Forward buy = Qd - Q*
Short-Term Discounting
Costs retailer considers Material Holding Order
Assumptions Discount offered only once Retailer takes no action to influence
customer demand Analyze a period over which demand is
an integer multiple of Q*
Short Term Discounts:Forward Buying
Annual demand D = 120,000 Normal cost C = $3 per bottleDiscount per tube d = $0.15 ; Holding cost h =
0.2
Normal order size Q* = 6,324 bottles Cycle inventory =3162 bottlesAverage Flow Time = 0.3162 months
Qd = 38,236Forward buy = 38,236 - 6,324 = 31,912 bottles
Cycle inventory =19118 bottlesAverage Flow Time = 1.9118 months
Trade Promotions
Major contributor to bullwhip effect
Retailers total cost decreases
Manufacturer justified when Excess inventory Smooth demand from peak to low demand
periods
Trade Promotions
Manufacturer revenue reduces if most product sold at discount
Supply chain Increase inventory Decrease revenue
Total profit decreases
Promotion Pass Throughto Consumers
Demand curve at retailer: 300,000 - 60,000pNormal price to retailer, CR = $3.00
Optimal retail price = $4.00 Customer demand = 60,000
Promotion discount = $0.15 Optimal retail price = $3.925 Customer demand = 64,500
Retailer only passes through half the promotion discount (0.075) and demand increases by 7.5%
Trade Promotions
Manufacturer takes actions to discourage forward buying EDLP Promotions for products with high
deal elasticity Scanner-based promotions
For sell-through, not sell-in items Not possible for weak brands
Managing Multi-EchelonCycle Inventory
Multi-Echelon SC Multiple stages, with many players at each
stage and one stage supplying another
Synchronize lot sizes at different stages Unnecessary cycle inventory eliminated
Cross-dock orders from customers who order less frequently some of the orders from customers that order
more frequently Use integer replenishment policy
Estimating Cycle Inventory-Related Costs in Practice
Inventory holding cost Cost of capital Obsolescence cost Handling cost Occupancy cost Miscellaneous costs
Estimating Cycle Inventory-Related Costs in Practice
Order cost Buyer time Transportation costs Receiving costs Other costs
