1. Product Availability

2. Level of product availability
Also referred as customer service level.
Is measured using the cycle service level or fill rate.
Is high to improve the responsiveness and attract customers.
But high level requires large inventories.
These large inventories tend to raise cost for SC.
Therefore, SC needs to balance between level of inventory and cost of inventory.

3. Factors affecting optimal level of product availability
Before understanding factors consider one example of a storekeeper who sells jacket.
He buys the stock for entire season’s supply of jacket before start of selling season.
High level of product availability requires large number of jackets.
It is likely to satisfy all demands.
However, it results in a large number of unsold jackets at the end of season.

4. Example…
On the other hand, low level of product availability results in few unsold jackets.
In this scenario, a loss of potential customers has to bear.
Must balance the loss from having too many unsold jackets and lost profit from turning away customers.

5. Mattel, Inc. & Toys ‘R Us
Mattel was hurt last year by inventory cutbacks at Toys ‘R Us, and officials are also eager to avoid a repeat of the 1998 Thanksgiving weekend. Mattel had expected to ship a lot of merchandise after the weekend, but retailers, wary of excess inventory, stopped ordering from Mattel. That led the company to report a $500 million sales shortfall in the last weeks of the year ... For the crucial holiday selling season this year, Mattel said it will require retailers to place their full orders before Thanksgiving. And, for the first time, the company will no longer take reorders in December, Ms. Barad said. This will enable Mattel to tailor production more closely to demand and avoid building inventory for orders that don't come.
- Wall Street Journal, Feb. 18, 1999

6. Key Questions
How much should Toys ‘R Us order given demand uncertainty?
How much should Mattel order?
Will Mattel’s action help or hurt profitability?
What actions can improve supply chain profitability?

7. Importance of the Level of Product Availability
Product availability measured by cycle service level or fill rate
Also referred to as the customer service level
Product availability affects supply chain responsiveness
Trade-off:
High levels of product availability  increased responsiveness and higher revenues
High levels of product availability  increased inventory levels and higher costs
Product availability is related to profit objectives, and strategic and competitive issues (e.g., Nordstrom, power plants, supermarkets, e- commerce retailers)
What is the level of fill rate or cycle service level that will result in maximum supply chain profits?

8. Factors Affecting the Optimal Level of Product Availability
Cost of overstocking
Cost of understocking
Possible scenarios
Seasonal items with a single order in a season
One-time orders in the presence of quantity discounts
Continuously stocked items
Demand during stockout is backlogged
Demand during stockout is lost

9. Cost of overstocking = C0 of understocking = Cu
Is the loss incurred by a firm for each unsold unit at the end of selling season.
of understocking = Cu
Is the margin lost by a firm for each lost sale from current and future sales if customer does not return.
Two factors that affect optimal level of product availability.
Cost of overstocking
Cost of understocking

10. Optimal level of product availability
Makes sense in the context of demand uncertainty.
Firms have forecast a consensus estimate of demand without any measure of uncertainty.
Now they have better appreciation for uncertainty.
Incorporation of uncertainty and optimal level of product availability can increase profit.

11. Example Demand distribution for jackets Demand Di (*100) Probability
Cumulative probability of demand being Di or less
probability of demand being greater then Di 4
0.01
0.99 5
0.02
0.03
0.97 6
0.04
0.07
0.93 7
0.08
0.15
0.85 8
0.09
0.24
0.76 9
0.11
0.35
0.65 10
0.16
0.51
0.49 11
0.20
0.71
0.29 12
0.82
0.18 13
0. 10
0.92 14
0.96 15
0.98 16 17
1.00
0.00

12. Example Expected profit from ordering a thousands of jacket =$49,900
Potential outcome to buy 100 more jackets
If extra 100 are sold, then profit=$5,500
If 100 units are send to outlet, then loss=$500
From table, there is 0.49 probability that demand is or higher and a 0.51 probability that demand will be 1000 or less.
Expected profit=$5,500Xprob[Demand≥1,100]
-$500Xprob[Demand<1,100]
=$5,500* *0.51=$2,440
Expected profit from ordering 1,100 is 5% greater than that of ordering 1,000.

13. Optimal cycle service level for seasonal items
Focus on seasonal product where leftover items must be disposed at the end of season.
Input:
C0: cost of overstocking = c-s
Cu: cost of understocking =p-c
CSL*=optimal cycle service level
O*=corresponding optimal order size
CSL*=probability that demand during season will be at or below O*.

14. Optimal cycle service level for seasonal items
Rise in quantity from O* to O*+1 is with probability 1-CSL*
Expected profit of purchasing extra unit= (1-CSL*)(p-c)
If additional unit remains unsold if demand is below O*
Expected cost of purchasing cost of extra unit=CSL*(c- s)
Expected marginal contribution of raising the order size from O* to O*+1=(1-CSL*)(p-c)- CSL*(c-s)

15. Optimal cycle service level for seasonal items
Expected marginal cost=0
CSL*=probability (demand≤O*)= (p-c)/(p-s)
C0/(Cu+C0)=1/{1+(C0/Cu)}
Optimal CSL* is referred as critical fractile
If demand during season is normally distributed with mean µ and standard deviation σ, optimal order quantity
O*=F-1(CSL*, µ, σ)
Expected profit=
Fs is the standard normal cumulative distribution function and fs is the standard normal density function

16. Desired cycle service level for continuously stocked items
Focus on products such as detergent that are ordered repeatedly.
Organization uses safety inventory to increase the level of safety inventory to avoid stocking out.
Left over detergent can be sold in next cycle.
However, holding cost is incurred form one cycle to next cycle.
Two extreme scenarios
All demands that arises when the product is out of stock is backlogged and filled later
All demand arising when product is out of stock is lost.

17. When Demand during stockout is backlogged
No demand is lost, minimizing costs is equivalent to maximizing profit.
When store is out of stock, discount of Cu is provided to each customer.
Ensures that each customer will return.
Increase in safety inventory satisfies more orders resulting in less backlogs
Cost of holding inventory increases.
Level of safety inventory that minimizes backlogs and holding cost??
Optimal cycle service level
CSL*=1-(HQ/DCu)

18. Example
Input
Q=400 gallons, ROP= 300 gallons, D=100 gallons, σD=20, unit cost=$3, holding cost as a fraction of cost h=0.2, cost of holding one unit for one year=0.6 Lead time =2 weeks
Cost of stocking out?? If all unfilled demand is backlogged and carried over to next cycle.

19. Solution Mean demand over lead time DL=DL=200 gallons
Standard deviation of demand in lead time
CSL=F(ROP, DL, σL) =F(300, 200, 28.3)
CSL=NORMDIST(300, 200, 28.3, 1)=0.9998
Imputed cost of stocking out Cu=HQ/(1- CSL)Dyear=0.6*400/0.0002*5,200=230.8 per gallon

20. When Demand during stock out is lost
Optimal cycle service level CSL*
CSL*=1-HQ/(HQ+DCu)
Cu is the cost of loosing one unit of demand during stockout period.

21. Managerial levers to improve SC profitability
Focus on actions that can be taken to improve the SC profitability
Two obvious managerial levers
Increasing the salvage value of each unit increases profitability.
Decreasing the margin lost from a stockout increases profitability.
Strategies to
Increase to salvage value include selling outlet stores so that left units are not merely discarded.
To decrease the margin lost in a stockout include arranging the backup sourcing so that customers are not lost forever.

22. Importance of the Ratio of cost of overstocking and understocking
If this gets smaller, optimal level of product availability increases.

23. Another lever Is to reduction of demand uncertainty.
By this, better supply and demand can be matched by reducing over and understocking.
Means to reduce demand uncertainty.
Improved forecasting
Quick response
Postponement
Tailored sourcing

24. Improving forecast Helps the demand planning information systems.
Can help a firm to increase its profitability while decreasing excess inventory overstock and sales lost due to understocking.

25. Improved Forecasts Improved forecasts result in reduced uncertainty
Less uncertainty (lower sR) results in either:
Lower levels of safety inventory (and costs) for the same level of product availability, or
Higher product availability for the same level of safety inventory, or
Both lower levels of safety inventory and higher levels of product availability
An increase in forecast accuracy decreases both the overstocked and understocked quantity and increases a firm’s profits.

26. Impact of Improving Forecasts (Example)
Demand: Normally distributed with a mean of R = 350 and standard deviation of R = 100 Purchase price = $100 Retail price = $250 Disposal value = $85 Holding cost for season = $5 How many units should be ordered as R changes?
Note:
Cost of understocking = = $150
Cost of overstocking = = $20
p = 150/(150+20) = 0.88
Order size = 426

27. Impact of Improving Forecasts

28. Quick response
Is the set of actions a supply chain takes that leads in the reduction of lead time.
Decrease in lead time results in increase in forecast accuracy.
This allows them to better match with the demand and increase in profitability.
Typically, buyers are able to make accurate forecasts once they have observed demand in first or second week in season.

29. Quick Response Set of actions taken by managers to reduce lead time
Reduced lead time results in improved forecasts
Typical example of quick response is multiple orders in one season for retail items (such as fashion clothing)
For example, a buyer can usually make very accurate forecasts after the first week or two in a season
Multiple orders are only possible if the lead time is reduced – otherwise there wouldn’t be enough time to get the later orders before the season ends
Benefits:
Lower order quantities  less inventory, same product availability
Less overstock
Higher profits
If quick response allows multiple orders in the season, profits increase and the overstock quantity decreases.

30. Example Selling season is of 14 weeks.
Replenishment time is 25 to 30 weeks.
Difficult for a buyer to make a accurate forecast of demand this far in advance.
This results in high demand uncertainty, leading the buyer in too many or too less units each year.
Consider a case where replenishment time can reduce upto 6 weeks.
Its results in entire seasons purchase in two orders.

31. Variation of profit and inventories with forecast accuracy
Expected over stock
Expected profit
Standard deviation of forecast error
Expected understock

32. Quick Response: Multiple Orders Per Season
Ordering shawls at a department store
Selling season = 14 weeks
Cost per handbag = $40
Sale price = $150
Disposal price = $30
Holding cost = $2 per week
Expected weekly demand = 20
SD of weekly demand = 15

33. Comparison of two policies
A single order must arrive at the beginning of the season to cover the entire seasons demand.
Two orders are placed in the season, one arriving at the beginning of the season and other arriving at the beginning of the eight week.
Now consider two instances
One where buyers forecast accuracy does not improve for the second order and where it improves and the SD can be reduced.

34. Comparison
Single order: consists of a quantity ordered at the beginning of season.
Two orders: consists of initial order quantity for first seven weeks followed by an order upto level for the second week.
Second round quantity should account for sales during the first week and inventory remaining.
The quantity ordered in second round it the difference between order up-to-level and inventory remaining after first week.

35. Consequences of being able to place a second order
The expected total quantity ordered during the season with two orders is less than that with a single order for the same cycle service level.
The average overstock to be disposed of at the end of the sales season is less if two orders are allowed.
The profits are higher when a second order is allowed during the sales season.
Total quantity is broken up into multiple smaller orders, the buyer is better able to match supply and demand and increase profitability.

36. Impact of Quick Response

37. Forecast Improves for Second Order (SD=3 Instead of 15)

38. Postponement
Delay of product differentiation until closer to the time of the sale of the product
All activities prior to product differentiation require aggregate forecasts more accurate than individual product forecasts
Individual product forecasts are needed close to the time of sale – demand is known with better accuracy (lower uncertainty)
Results in a better match of supply and demand
Valuable in e-commerce – time lag between when an order is placed and when customer receives the order (this delay is expected by the customer and can be used for postponement)
Higher profits, better match of supply and demand
Postponement allows a firm to increase profits and better match supply and demand if the firm produces a large variety of products whose demand is not positively correlated and is of about the same size.

39. Postponement
Refers to the delay of product differentiation until closer to the sale of product.
Aggregate forecasts are more accurate then individual product forecasts.
Individual forecasts are required close to the time of sale when demand is known with greater accuracy.
Allows a SC to better match SC demand.

40. Postponement… A powerful managerial tool to increase profitability.
However, while using it production cost would be higher than the case where there is no postponement.
Is valuable to for a firm that sells a large variety of products with demand.

41. Value of Postponement: Benetton
For each color
Mean demand = 1,000; SD = 500
For each garment
Sale price = $50
Salvage value = $10
Production cost using Option 1 (long lead time) = $20
Production cost using Option 2 (uncolored thread) = $22
What is the value of postponement?
Expected profit increases from $94,576 to $98,092

42. Value of Postponement with Dominant Product
Color with dominant demand: Mean = 3,100, SD = 800
Other three colors: Mean = 300, SD = 200
Expected profit without postponement = $102,205
Expected profit with postponement = $99,872

43. Tailored postponement
A firm uses production with postponement to satisfy a part of demand with the rest being satisfied without it.
Produces higher profits then when no postponements is used or all are produced using postponement.
A firm produces a portion of demand which is uncertain, postponement significantly improves the forecasts accuracy.
Thus, allows a firm to increase its profitability by only postponing the uncertain part of the demand and producing the predictable part at a lower cost without postponement.

44. Tailored Postponement: Benetton
Produce Q1 units for each color using Option 1 and QA units (aggregate) using Option 2
Results:
Q1 = 800
QA = 1,550
Profit = $104,603
Tailored postponement allows a firm to increase profits by postponing differentiation only for products with the most uncertain demand; products with more predictable demand are produced at lower cost without postponement

45. Tailored Sourcing A firm uses a combination of two supply sources
One is lower cost but is unable to deal with uncertainty well
The other is more flexible, and can therefore deal with uncertainty, but is higher cost
The two sources must focus on different capabilities
Depends on being able to have one source that faces very low uncertainty and can therefore reduce costs
Increase profits, better match supply and demand

46. Tailored sourcing Firms uses a combination of two supply sources
Focusing on cost but unable to handle the uncertainty.
Focusing on flexibility to handle uncertainty but at higher cost.
But, to be effective, having supply sources where one serves as the backup to other is not sufficient.
The first should be required to supply the predictable portion of demand.
The second should be responsive and be required to supply the uncertain portion of demand.
Allows to better match supply and demand and increase of profit.

47. Tailored sourcing…
Value depends on the reduction in cost that can be achieved.
Small benefit— it may not be ideal.
May be volume based or product based depending on source depending on the source of uncertainty.

48. Volume based
Tailored sourcing, the predictable part of a product’s demand is produced at an efficient facility.
Should be considered by firms that have moved a lot of their production overseas to take advantage of lower costs.
In this condition source with shorter lead time is more profitable even if he is more expensive.

49. Product based
Low volume product with uncertain demand are obtained from a flexible source while high volume product with less demand uncertainty are obtained form an efficient source.
New products have a very uncertain demand while well established products have more stable demand.
May be implemented with a flexible facility focusing on new products and efficient facilities focusing on well established products.

50. Tailored Sourcing Sourcing alternatives
Low cost, long lead time supplier
Cost = $245, Lead time = 9 weeks
High cost, short lead time supplier
Cost = $250, Lead time = 1 week

51. Tailored Sourcing Strategies

52. Tailored Sourcing: Multiple Sourcing Sites

53. Dual Sourcing Strategies

54. Multiple product order Decrease the order size Allocating the products
Setting Product Availability for Multiple Products under Capacity Constraints
Single product order
Multiple product order
Decrease the order size
Allocating the products
When ordering multiple products under a limited supply capacity, the allocation of capacity to products should be based on their expected marginal contribution to profits.
This approach allocates a relatively higher fraction of capacity to products that have a high margin relative to their cost of overstocking.

55. Setting Optimal Levels of Product Availability in Practice
Use an analytical framework to increase profits
Beware of preset levels of availability
Use approximate costs because profit- maximizing solutions are very robust
Estimate a range for the cost of stocking out
Ensure levels of product availability fit with the strategy