Managing Economies of Managing Economies of Scale in the Supply Chain: Scale in the Supply Chain: Cycle InventoryCycle Inventory

Role of Inventory in the Supply Role of Inventory in the Supply ChainChain

Improve Matching of Supplyand 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 InventoryRole of Cycle Inventoryin a Supply Chainin a Supply Chain

Lot, or batch size: quantity that a supply chain stage either produces or orders at a given time.

Cycle inventory is held primarily to take advantage of economies of scale in the supply chain and reduce cost within a supply chain.

Cycle inventory: average inventory that builds up in the supply chain because a supply chain stage either produces or purchases in lots that are larger than those demanded by the customer◦Q = lot or batch size of an order◦D = demand per unit time

Case of jeans at Jean Mart, a Case of jeans at Jean Mart, a department storedepartment store

Inventory profile: plot of the inventory level over time

It is assumed here that the demand is stable (while considering safety inventory, it is not so)

Cycle inventory = Q/2 (depends directly on lot size)

Average flow time = Average inventory / Average flow rate (Little’s Law) = average length of time that elapses between the time material enters the supply chain to the point at which it exits.

But, for any supply chain, average flow rate equals demand

Thus, average flow time from cycle inventory = Q/(2D)

Role of Cycle Inventory in a Supply Role of Cycle Inventory in a Supply ChainChainQ = 1000 unitsD = 100 units/dayIt takes 10 days for the entire lot to be soldCycle inventory = Q/2 = 1000/2 = 500 = Avg

inventory level from cycle inventoryAvg flow time = Q/2D = 1000/(2)(100) = 5 daysThus, jeans spend in the supply chain an average time

of 5 daysTherefore, cycle inventory adds 5 days to the time a

unit spends in the supply chainLower cycle inventory is better because:

◦ Average flow time is lower. The larger the cycle inventory, the longer is the lag time between when a product is produced and when it is sold. A lower level of cycle inventory is always desirable, because long time lags leave a firm vulnerable to demand changes in the marketplace.

◦ Working capital requirements are lower◦ Lower inventory holding costs

Role of Cycle InventoryRole of Cycle Inventoryin a Supply Chainin a Supply Chain

For this we first identify supply chain costs that are influenced by lot size.

Supply chain costs influenced by lot size:◦ Material cost = C (average price paid per unit purchased,

increasing lot size might result in availing of price discounts and thus reduce material cost , $ per unit)

◦ Fixed ordering cost = S (such as administrative cost, trucking cost, labour cost, all costs that do not vary with the size of the order but are incurred every time an order is placed, e.g., $400 per truck, if a lot of 100 pairs, transportation cost will be $4/pair, whereas 1000 pairs means $0.40/pair, thus increasing the lot size decreases the fixed ordering cost per unit purchased, $ per lot)

◦ Holding cost = H = hC (a combination of the cost of capital, cost of physically storing the inventory, and the cost that results from the product being obsolete, reducing lot size and cycle inventory, reduces the holding cost, H: $ per unit per year, h = cost of holding $1 in inventory for one year)

Role of Cycle InventoryRole of Cycle Inventoryin a Supply Chainin a Supply Chain

Primary role of cycle inventory is to allow different stages to purchase product in lot sizes that minimize the sum of material, ordering, and holding costs

Ideally, cycle inventory decisions should consider costs across the entire supply chain, but in practice, each stage generally makes its own supply chain decisions. This increases total cycle inventory and total costs in the supply chain

Economies of ScaleEconomies of Scaleto Exploit Fixed Coststo Exploit Fixed Costs

How do you decide whether to go shopping at a convenience store or at Sam’s Club?

When we need only a small quantity, we go to the nearby convenience store because the benefit of a low fixed cost outweighs the cost of the convenience store’s higher prices.

When we are buying a large quantity, however, we go to Sam’s Club (located far away), where the lower prices over the larger quantity purchased more than make up for the increase in fixed cost.

Economies of ScaleEconomies of Scaleto Exploit Fixed Costs: different waysto Exploit Fixed Costs: different ways

Lot sizing for a single product (EOQ)Aggregating multiple products in a single

orderLot sizing with multiple products or

customers◦Lots are ordered and delivered

independently for each product◦Lots are ordered and delivered jointly

for all products◦Lots are ordered and delivered jointly

for a subset of products

Lot sizing for a single product Lot sizing for a single product (EOQ)(EOQ)

The Purchasing Manager of Best Buy places a replenishment order for a new lot of Q number of HP computers. Including the cost of transportation, Best Buy incurs a fixed cost of $S per order.

The purchasing manager must decide on the number of computers to order from HP in a lot.

We assume the following inputs:

Economies of ScaleEconomies of Scaleto Exploit Fixed Coststo Exploit Fixed CostsAnnual demand = DC = cost per unitH = holding cost per year as a fraction of product costIf no discount is available, the holding cost per unit per

year, H = hCNumber of orders per year = D/QThree costs to decide on the lot size:Annual material cost = CD (purchase price is independent

of lot size)Annual order cost = (D/Q)SAnnual holding cost = (Q/2)H = (Q/2)hC (where average

inventory or cycle inventory = Q/2)Total annual cost = TC = CD + (D/Q)S + (Q/2)hC

Fixed Costs: Optimal Lot SizeFixed Costs: Optimal Lot Size

and Reorder Interval (EOQ)and Reorder Interval (EOQ) D: Annual demand D: Monthly demand = D/12S: Setup or Order CostC: Cost per unith: Holding cost per year as a

fraction of product costH: Holding cost per unit per yearQ: Lot Size (the optimal lot size

that minimizes total cost = Q*, known as Economic Order Quantity, EOQ)

T: Reorder intervaln* = optimal ordering frequencyAFT = average flow timeMaterial cost is constant and

therefore is not considered in this model DQAFT

DQDH

ST

S

DHn

H

DSQ

hCH

2/*

/*2

2*

2*

Example 1 Example 1 Demand, D = 12,000 computers per yeard = 1000 computers/monthUnit cost, C = $500Holding cost fraction, h = 0.2 (holding cost of 20%)Fixed cost, S = $4,000/orderQ* = Sqrt[(2)(12000)(4000)/(0.2)(500)] = 980

computers Cycle inventory = Q*/2 = 490Average flow time = average time each computer

spends in inventory before it is sold = Q*/2d = 980/(2)(1000) = 0.49 month

Reorder interval, T = 0.98 monthNo. of reorders per year = D/Q* = 12.24

Example 1 (continued)Example 1 (continued)

Annual ordering and holding cost = = (12000/980)(4000) + (980/2)(0.2)(500) = $97,980Suppose lot size is reduced to Q=200, which would reduce flow

time:Annual ordering and holding cost = = (12000/200)(4000) + (200/2)(0.2)(500) = $250,000To make it economically feasible to reduce lot size, the fixed cost

associated with each lot would have to be reduced. Thus, if the fixed cost associated with each lot is reduced to $1000, the optimal lot size reduces to 490.

Further, using a lot size of 1,100 (instead of 980), increases annual cost to $98,636. Even though the order size is more than 10% larger than the optimal order size Q*, the total cost increases by only 0.6%.

Thus, total ordering and holding costs are relatively stable around the EOQ, that is, relatively insensitive to Q around Q*.

Moreover, if demand increases by a factor k, the optimal lot size increases by a factor sqrt k. The number of orders placed per year should also increase by a factor sqrt k. However, flow time attributed to cycle inventory should decrease by a factor sqrt k.

Example 2 (Relationship between Example 2 (Relationship between desired lot size and order cost)desired lot size and order cost)

If desired lot size = Q* = 200 units, what would S haveto 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) = $166.67Thus, to reduce optimal lot size by a factor of k, the

fixed order cost must be reduced by a factor of k2

Key Points from EOQ ModelKey Points from EOQ Model

In deciding the optimal lot size, the tradeoff is between setup (order) cost and holding cost.

If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often. Cycle inventory (in days of demand) should decrease as demand increases.

If lot size is to be reduced, one has to reduce fixed order cost. To reduce lot size by a factor of 2, order cost has to be reduced by a factor of 4.

Example: Aggregating Multiple Products in Example: Aggregating Multiple Products in a Single Ordera Single Order Suppose there are 4 computer products in the previous

example: Deskpro, Litepro, Medpro, and Heavpro Assume 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

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◦ Thus, lot size for each product, average flow time,

inventory holding costs will be reduced

Aggregating Multiple ProductsAggregating Multiple Productsin a Single Orderin a Single Order

Transportation is a significant contributor to the fixed cost per order.

Can, therefore, possibly 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

Can also have a single delivery coming from multiple suppliers (allowing fixed transportation cost to be spread across multiple suppliers) or a single truck delivering to multiple retailers (allowing fixed transportation cost to be spread across multiple retailers).

Aggregating across products, retailers, or suppliers in a single order allows for a reduction in lot size for individual products because fixed ordering and transportation costs are now spread across multiple products, retailers, or suppliers.

Wal-Mart achieves the above through cross-docking, but we cannot ignore receiving or loading costs – importance of Advanced Shipping Notices (ASN) and RFID technology.

Three models of Store Manager: Best Buy with Three models of Store Manager: Best Buy with multiple models of computers (Litepro (L), multiple models of computers (Litepro (L), Medpro (M), and Heavypro (H))Medpro (M), and Heavypro (H))

If each product manager orders his model independently (no aggregation – high cost).

The product managers jointly order every product in each lot (weakness – low demand products are aggregated with high demand products in each order, resulting in high costs if the product-specific order costs for the low demand products is large).

Product managers order jointly but not every order contains every product; that is, each lot contains a selected subsets of the products.

Let us consider all the models.

Lot Sizing with MultipleLot Sizing with Multipleproducts or Customersproducts or Customers

In practice, the fixed ordering cost is dependent at least in part on the variety associated with an order of multiple models◦ A portion of the cost is related to transportation

(independent of variety)◦ A portion of the cost is related to loading and receiving

(not independent of variety) Three scenarios:

◦ Lots are ordered and delivered independently for each product

◦ Lots are ordered and delivered jointly for all three models◦ Lots are ordered and delivered jointly for a selected

subset of models

Lot Sizing with Multiple ProductsLot Sizing with Multiple ProductsDemand per year

◦ DL = 12,000; DM = 1,200; DH = 120Common transportation cost, S = $4,000Product specific order cost (for each

model ordered and delivered on the same truck, an additional fixed cost of $1000 is incurred for receiving and storage) ◦ sL = $1,000; sM = $1,000; sH = $1,000

Holding cost, h = 0.2Unit cost

◦ CL = $500; CM = $500; CH = $500

Delivery OptionsDelivery Options First model: No Aggregation: Each product ordered separately.

Because each model of the computer is ordered and delivered

independently, a separate truck delivers each model. Thus, a

fixed ordering cost of $4000 + $1000 = $5000 is incurred for

each product delivery. Annual ordering cost = ((S + sL) + (S + sM)

+ (S + sH)) x n (ordering frequency).

Second model: Complete Aggregation: All products delivered on

each truck. All three models are included each time an order is

placed. So the annual ordering cost here is (S* x n) = (S + sL + sM

+ sH) x n.

Third model: Tailored Aggregation: Lots are ordered and delivered

jointly for a selected subsets of the products on each truck

Aggregate across products, supply points or delivery points.

No Aggregation: Order Each Product No Aggregation: Order Each Product

IndependentlyIndependently 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

Cycle inventory 548 173 55

Annual holding cost

$54,772 $17,321 $5,477

Order frequency 11.0 / year 3.5 / year 1.1 / year

Annual ordering cost

$55,000 #17,500 $5,500

Average flow time

2.4 weeks 7.5 weeks 23.7 weeks

Annual cost $109,772 $34,821 $10,977

Total cost = $155,570

Aggregation: Order All Products JointlyAggregation: Order All Products Jointly

S* = S + sL + sM + sH = 4000+1000+1000+1000 = $7000

n* = Sqrt[(DLhCL+ DMhCM+ DHhCH)/2S*]= 9.75 (formula obtained by minimizing total annual

cost), where hCL = hCM = hCH = 20% of $500 = $100Annual order cost = 9.75 x $7000 = $68, 250QL = DL/n* = 12000/9.75 = 1230

QM = DM/n* = 1200/9.75 = 123

QH = DH/n* = 120/9.75 = 12.3Cycle inventory = Q/2 Average flow time (in weeks) = (Q/2)/(weekly

demand)

Complete Aggregation:Complete Aggregation:Order All Products JointlyOrder All Products Jointly

Litepro Medpro Heavypro

Demand per year (D)

12,000 1,200 120

Order frequency (n*)

9.75/year 9.75/year 9.75/year

Optimal order size (D/n*)

1,230 123 12.3

Cycle inventory 615 61.5 6.15 Annual holding cost

$61,512 $6,151 $615

Average flow time

2.67 weeks 2.67 weeks 2.67 weeks

Annual order cost = 9.75 × $7,000 = $68,250Annual total cost = $136,528 (down from $155,570, by about 13 per cent)

Case of W.W. Grainger: Aggregating four Case of W.W. Grainger: Aggregating four suppliers (each supplier, one product) per trucksuppliers (each supplier, one product) per truck

Di = 10,000 h = 0.2 Ci = $50 Common order cost = S = $500 Supplier-specific order cost = $100 Combined order cost = S* = ($500+$100+$100+$100+

$100) =$900 n* = Sqrt[(Σ DihCi, i=1,..k)/2S*] = 14.91 (k = 4 here) Annual order cost per supplier = 14.91 x (900/4) =

$3,354 Quantity ordered from each supplier = Q =

10,000/14.91 = 671 units per order Annual holding cost per supplier =(h CiQ)/2 =

(0.2x50x671)/2 = $3,355

Thus, total capacity per truck = 4 x 671 = 2,684

Case of W.W. Grainger: Aggregating four Case of W.W. Grainger: Aggregating four suppliers (each supplier, one product) per truck: suppliers (each supplier, one product) per truck: Introducing Capacity constraintIntroducing Capacity constraint

Compare the total load for the optimal n* with truck capacity. If the optimal load exceeds the truck capacity, n* is increased until the load equals the truck capacity. Further, by applying the formula n* = Sqrt[(SUM DihCi, i=1,..k)/2S*] for different values of k, we can also find the optimal number of items or suppliers to be aggregated in a single delivery.

Thus, if truck capacity limit is 2500 units, the order frequency must be increased to ensure that the order quantity from each supplier is 2,500/4 = 625.

Thus, W.W. Grainger should increase the order frequency to 10,000/625 = 16.

This would increase the annual cost order cost per supplier to $3,600 and decrease the annual holding cost per supplier to #3,125.

Tailored aggregationTailored aggregationThe first step is to identify the product that is to

be ordered most frequently, assuming each product is ordered independently.

For each successive product, we then identify orders in which it is included. Assumption: each product is included in the order at regular intervals.

Once we have identified the most frequently ordered model, for each successive product i, we identify the frequency mi, where model i is ordered every mi deliveries.

Each product i has an annual demand Di, a unit cost Ci, and a product specific order cost si. The common order cost is S.

Using the same Best Buy data, product managers have decided to order jointly, but to be selective about which models they include in each order.

Calculations: Tailored aggregationCalculations: Tailored aggregation

nL = sqrt ((DLhCL)/2(S+ sL)) = 11.0; similarly, nM = 3.5 and nH = 1.1 (L is most frequently ordered model, 11 times a year). (Put 1bar).

The frequency with which M and H are included in L order are given as follows:

nM = sqrt ((DMhCM/2 sM)) = 7.7 and nH = 2.4 (Put 2 bars)

mM = nL/ nM (2 bars) = 11.0/7.7 = 1.4 (= 2) and similarly, mH = 4.5 (= 5)

Therefore, L is included in every order, M in every 2nd order and H in every 5th order.

Recalculate nL = n = sqrt ((DLhCLmL + DMhCM mM + DHhCH mH)/2(S + sL/mL + sM/ mM + sH/ mH)) = 11.47

Calculations: Tailored aggregationCalculations: Tailored aggregation

Thus, recalculated nM = 11.47/2 = 5.74/year and nH = 11.47/5 = 2.29/year

Thus, L will be ordered 11.47 times, L, 5.74 times, and H, 2.29 times/year.

The annual holding cost of this policy = (((DL/2 nL) hCL) + ((DM/2 nM) hCM) + ((DH/2 nH) hCH) = $65,385.5

The annual order cost = nS + nL sL + nM sM + nH sH, (n = nL)

For each, order size = D/n, cycle inventory = D/2n

Total (annual order + holding) cost = $130,767

Lessons from AggregationLessons from Aggregation Aggregation allows a firm to lower lot size without

increasing cost Complete aggregation is effective if product specific fixed

cost is a small fraction of joint fixed cost (all customers, all products, all trips).

Tailored aggregation is effective if product specific fixed cost is a large fraction of joint fixed cost. Here, larger customers get more frequent deliveries. Tailored aggregation differentiates between high volume and low volume items, orders low volume items less frequently, and is suitable when product specific order cost is high. For instance, the total cost in the last example was $130,767. Tailored aggregation results in a cost reduction of $5,761 (about 4%) compared to the joint ordering of all models. The cost reduction results because each model specific fixed cost of $1,000 is not incurred with every order.

On the transportation end, the product-specific order costs can be reduced by locating supply points or delivery points close to one another.

Economies of Scale toEconomies of Scale toExploit Quantity DiscountsExploit Quantity Discounts

All-unit quantity discountsMarginal unit quantity discountsWhy quantity discounts?

◦ Improved coordination to increase total supply chain profits. A supply chain is coordinated if the decision the retailer and supplier make maximize total supply chain profits. However, in reality, each stage has a separate owner and considers its own costs in an effort to maximize its own profit. Thus, the question is how can a manufacturer use appropriate quantity discount to ensure that coordination results even if the retailer is acting to maximize its own profits?

◦ Price discrimination to maximize supplier profits through extraction of surplus

Quantity DiscountsQuantity DiscountsCommodity products - Lot size based: a discount is

lot-sized based if the pricing schedule offers discounts based on the quantity ordered in a single lot. ◦ All units◦ Marginal unit, also known as multi-block tariffs. In

this case, the pricing schedule contains specified break points q0, q1, q2, …qr. If an order size of q is placed, the first q1-q0 units are priced at C0, the next q2-q1 are priced at C1, and so on, C0>C1>C2…

Products with demand curve - Volume based: a discount is volume-based if the discount is based on the total quantity purchased over a given period, regardless of the number of lots purchased over that period.

How should buyer react? What are appropriate discounting schemes?

All-Unit Quantity DiscountsAll-Unit Quantity DiscountsPricing 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

The unit cost generally decreases as the quantity increases, i.e., C0>C1>…>Cr

The objective for the company (a retailer in our example) is to decide on a lot size that will minimize the sum of material, order, and holding costs

All-Unit Quantity Discount Procedure (different All-Unit Quantity Discount Procedure (different from what is in the textbook)from what is in the textbook)

Step 1: Calculate the EOQ for the lowest price. If it is feasible (i.e., this order quantity is in the range for that price), then stop. This is the optimal lot size. Calculate TC for this lot size.

Step 2: If the EOQ is not feasible, calculate the TC for this price and the smallest quantity for that price.

Step 3: Calculate the EOQ for the next lowest price. If it is feasible, stop and calculate the TC for that quantity and price.

Step 4: Compare the TC for Steps 2 and 3. Choose the quantity corresponding to the lowest TC.

Step 5: If the EOQ in Step 3 is not feasible, repeat Steps 2, 3, and 4 until a feasible EOQ is found.

All-Unit Quantity Discounts: ExampleAll-Unit Quantity Discounts: Example

Cost/Unit

$3$2.96

$2.92

Order Quantity

5,000 10,000

Order Quantity

5,000 10,000

Total Material Cost

All-Unit Quantity Discount: ExampleAll-Unit Quantity Discount: Example

Order quantity Unit Price0-5000 $3.005001-10000 $2.96Over 10000 $2.92

q0 = 0, q1 = 5001, q2 = 10001

C0 = $3.00, C1 = $2.96, C2 = $2.92D = 120000 units/year, S = $100/lot, h

= 0.2

All-Unit Quantity Discount: ExampleAll-Unit Quantity Discount: ExampleStep 1: Calculate Q2* = Sqrt[(2DS)/hC2] = Sqrt[(2)(120000)(100)/(0.2)(2.92)] = 6410Not feasible (6410 < 10001)Calculate TC2 using C2 = $2.92 and q2 = 10001

TC2 = (120000/10001)(100)+(10001/2)(0.2)(2.92)+(120000)(2.92)

= $354,520Step 2: Calculate Q1* = Sqrt[(2DS)/hC1]=Sqrt[(2)(120000)(100)/(0.2)(2.96)] = 6367Feasible (5000<6367<10000) StopTC1 = (120000/6367)(100)+(6367/2)(0.2)

(2.96)+(120000)(2.96)= $358,969TC2 < TC1 The optimal order quantity Q* is q2 =

10001

All-Unit Quantity DiscountsAll-Unit Quantity Discounts

If all units are sold for $3 (no discount), Q0* = 6,324 units. Since 6,324>5000, we should set q1 = 5001 for getting it at $2.96 per unit, and TC0 = $359,080. However, the optimal quantity to order is 10,001 with discounts. Thus, the quantity discount is an incentive to order more.

Suppose fixed order cost were reduced to $4 (from $100)◦ Without discount, Q0* would be reduced to 1265 units, that is,

if fixed cost of ordering is reduced, lot size reduces sharply. ◦ With discount, optimal lot size would still be 10001 units◦ Thus, the average inventory (flow time) increases.

What is the effect of such a discount schedule?◦ 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 an all-unit quantity discount an advantage in the supply

chain?

All unit quantity discount vs. marginal All unit quantity discount vs. marginal unit quantity discountunit quantity discount

◦The marginal unit quantity discount results in a larger lot size than an all-unit quantity discount.

◦As the lot size is increased beyond the last break point, the material cost continues to decline.

◦Quantity discounts often contribute more to cycle inventory.

◦So, why quantity discounts?

Why Quantity Discounts?Why Quantity Discounts?

Improved coordination in the supply chain◦Commodity products: for commodity

products such as milk, a competitive market exists, and costs are driven down to the product’s marginal cost. In this case, the market sets the price and the firm’s objective is to lower costs.

◦Products with demand curve 2-part tariffs Volume discounts

Commodity products caseCommodity products caseA retail company DO sells a commodity product

(vitamins). Do incurs a fixed order placement, transportation, and receiving cost of $100 every time it places an order with the manufacturer, plus a holding cost of 20%. The manufacturer charges $3 per bottle of vitamins.

Every time DO places an order, the manufacturer has to process, pack, and ship the order. The manufacturer incurs a fixed order filling cost of $250, production cost of $2 per bottle, plus a holding cost of 20%.

Coordination forCoordination forCommodity ProductsCommodity Products

D = 120,000 bottles/year SR = $100, hR = 0.2, CR = $3 SS = $250, hS = 0.2, CS = $2Retailer’s (DO) optimal lot size (EOQ) = 6,324 bottles. Annual

holding + ordering costs of Retailer = $3,795; Annual order cost at manufacturer = (120,000/6,324) x 250 = $4,744, annual holding cost of supplier = (6,324/2) x 2 x 0.2 = $1,265, thus total supplier cost = $6,009

Therefore, supply chain cost = $3,795 + $6,009 = $9,804A lot size-based quantity discount is appropriate in this case.

When the lot size increases, manufacturer’s cost relatively decreases due to large lot size, but order and holding costs (cycle inventory increases) increase for the retailer although the total supply chain cost also decreases. Therefore, the manufacturer must induce the retailer to buy in larger quantity, by sharing some benefits with the retailer.

Q* for the manufacturer = sqrt ((2 x 120,000 x 250)/0.2 x 2)) = 9,165. Thus, if the supplier offers each bottle for $2.9978 for all orders in lots of 9,165 or more. The manufacturer’s and the total supply chain profit increases by $638, by offering quantity discount of $264, when DO has an incentive to order in lots of 9,165.

Coordination forCoordination forCommodity ProductsCommodity Products

What can the supplier do to decrease supply chain costs?◦ Coordinated lot size: 9,165; Retailer cost = $4,059;

Supplier cost = $5,106; Supply chain cost = $9,165 Effective pricing schemes

◦ All-unit quantity discount $3 for lots below 9,165 $2.9978 for lots of 9,165 or more

◦ Pass some fixed cost to retailer (enough that he raises order size from 6,324 to 9,165)

On the contrary, for a low enough set-up or order cost (fixed cost per order reduces from $250 to $100), the manufacturer gains very little from using a lot size-based quantity discount; it makes sense for him to eliminate all quantity discounts. This brings out the importance of marketing and sales on the one hand, and operations, on the other hand, working in close coordination.

Quantity Discounts WhenQuantity Discounts WhenFirm Has Market PowerFirm Has Market PowerA new vitamin pill whose properties are highly

valued has been introduced into the market by the manufacturer. It can be thus be argued that the price at which DO sells this drug influences demand. Assume that the annual demand faced by DO is given by the demand curve 360,000 – 60,000p, where p is the price DO sells this drug. The manufacturer incurs a cost CS = $2 per bottle.

The manufacturer must decide what to charge DO, and DO, in turn, must decide on the price to charge the customer.

Quantity Discounts WhenQuantity Discounts WhenFirm Has Market PowerFirm Has Market Power

No inventory related costs Demand curve

360,000 - 60,000p

What are the optimal prices and profits in the following situations?◦ The two stages coordinate the pricing decision

Price = $4, Profit = $240,000, Demand = 120,000◦ The two stages make the pricing decision

independently Price = $5, Profit = $180,000, Demand = 60,000

Quantity Discounts WhenQuantity Discounts WhenFirm Has Market PowerFirm Has Market Power Independent decision-making: it is optimal

for DO to sell the drug at $5 per bottle (= p) and for the manufacturer to charge CR = $4 per bottle .

Total market demand = 360,000 – 60,000p = 60,000

ProfitR = p(360,000 – 60,000p) - (360,000 – 60,000p) x $4

= ($5 x 60,000) – ($4 x $60,000) = $60,000ProfitM = ($4 x 60,000) – ($2 x 60,000) =

$120,000Thus, the total supply chain profit in this

case = $60,000 + $120,000 = $180,000

Double marginalizationDouble marginalization

If the two stages coordinate pricing, p = $4, and let CR = $3.25 per bottle, market demand is 120,000, the total supply chain profit = 120,000 x ($4 - $2) = $240,000 = ProfitR + ProfitM = (120,000 x (4 – 3.25)) + (120,000 x (3.25-2))

We can thus realize that if each stage sets its price independently, the supply chain thus loses $240,000 - $180,000 = $60,000 in profit.

This phenomenon is referred to as double marginalization. Double marginalization leads to a loss of profit because the

supply chain margin is divided between two stages but each stage makes its decision considering only its local margin.

There are two pricing schemes that the manufacturer may use to achieve the coordinated solution and maximize supply chain profits even though the retailer firm DO acts in a way that maximizes its own profit: two-part tariff and volume-based quantity discounts.

Two-Part TariffsTwo-Part Tariffs

Design a two-part tariff that achieves the coordinated solution: the manufacturer charges its entire profit as an up-front franchise fee and then sells to the retailer at its cost price.

In the case here, the manufacturer charges DO a franchise fee of $180,000 (its profit) and material cost of CS = CR = $2 per bottle. DO maximizes its profit if p = $4 per bottle. It has annual sales of 360,000 – 60,000p = 120,000 and profits of $60,000 = ([120,000 x $4] – [(120,000 x 2) + 180,000)]).

Volume DiscountsVolume DiscountsDesign a volume discount scheme that achieves the

coordinated solution. We recall that 120,000 bottles are sold per year when the supply chain is coordinated.

The manufacturer must offer DO a volume discount to encourage DO to purchase this quantity. The manufacturer thus offers a price CR = $4 per bottle if the quantity purchased by DO is less than 120,000 and CR = $3.50 per bottle if the volume is 120,000 or higher.

It is then optimal for DO to order 120,000 units and offer them at $4 per bottle to the customers. The total profit earned by DO is (360,000-60,000p) x (p – CR) = $60,000.

The total profit earned by the manufacturer is 120,000 x (CR - $2) = $180,000, the total supply chain profit remaining unchanged.

Impact of inventory costsImpact of inventory costs◦ For products for which a firm has market

power, lot size-based discounts are not optimal for the supply chain even in the presence of inventory costs (order and holding).

◦ In such a setting, a two-part tariff or volume-based discount, with the supplier passing on some fixed costs with above pricing to the retailer, is needed for the supply chain to be coordinated and maximize profits, given the assumption that customer demand decreases when the retailer increases price.

Lessons from Discounting SchemesLessons from Discounting Schemes Lot size-based discounts increase lot size and cycle

inventory in the supply chain. Lot size-based discounts are justified to achieve

coordination for commodity products. Lot-sized discounts are based on quantity purchased per lot, not the rate of purchase.

Volume-based discounts are based on the rate of purchase or volume purchased on average per year or month.

Volume-based discounts are compatible with small lots that reduce cycle inventory.

Lot size-based discounts make sense only when the manufacturer incurs a very high fixed cost per order.

Volume based discounts with some fixed cost passed on to retailer are more effective in general◦ Volume based discounts are better over rolling

horizon, for instance, each week the manufacturer may offer DO the volume discount based on sales over the last 12 weeks.

Short-Term Discounting: Trade Short-Term Discounting: Trade PromotionsPromotions

Trade promotions are price discounts for a limited period of time (also may require specific actions from retailers, such as displays, advertising, etc.)

Key goals for promotions 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

What is the impact on the behavior of the retailer and on the performance of the supply chain?

Retailer has two primary 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

Short-Term Discounting: Trade PromotionsShort-Term Discounting: Trade Promotions

The first action lowers the price of the product for the end customer, leading to increased purchases and thus increased sales for the entire supply chain.

The second action does not increase purchases by the customer but increases the amount of inventory held at the retailer increasing the cycle inventory and the flow time within the supply chain.

A forward buy occurs in the latter case helping reduce the retailer’s cost of goods after the promotion ends but it usually increases demand variability and can decrease supply chain profitability.