11

Practice Final

John H. Vande Vate

Spring 2006

22

Question 1

• In class we described how a model that holds inventory of incoming supplies to buffer the supply chain from variations in customer demand.

33

Question 1

• Under the model, the supplier normally ships the same quantity every day. When inventory rises to S, the model recommends curtailing shipments until it falls to Q and when inventory falls to 0, the model recommends expediting shipments or sending an unusually large shipment to bring inventory levels back up to q.

44

Question 1Consider the special case in which:

a. there is no inventory holding cost (h = 0)

b. because of space limitations, the maximum inventory level S for the part cannot exceed a given level M

c. the fixed costs of expediting and curtailing shipments are equal (K = L > 0)

d. There are no variable costs for expediting and curtailing shipments (k = l = 0)

55

Question 1

 

What is the optimal strategy in this special case?

S =

Q =

q =

66

Answer

• S = M• Q = q = M/2• Reasoning: Inventory is free, so we are only

concerned with running into the bounds 0 and M, which we want to do as infrequently as possible. Since there are no variable costs to expedite and curtail, when we do expedite, we should expedite as much as we can to prevent having to expedite or curtail again. Symmetry leads us to Q = q = M/2

77

Question 2

• We argued in class that, under a periodic review regime, increasing the frequency of shipments generally reduces total inventory and expediting costs. We made this argument assuming that the costs of increasing frequency were negligible.

•  

88

Question 2

• Suppose– inventory carrying costs are h = $100 per item

per year– ordering costs are c = $1,000 per shipment – Demand over time is relatively constant at D

= 200,000 per year– The average lead time is 4 weeks with a

standard deviation of 2 days.

• If we intend to hold safety stock constant regardless of the frequency of orders, how frequently should we order?

99

Solution

• The lead time information is a red herring. It’s irrelevant as we have decided to hold safety stock constant.

• This becomes a simple EOQ type problem with n, the number of times to order as the variable. The total cost formula is

• hD/2n + cn

• The solution is n = SQRT(hD/2c) = 100

1010

Question 3

• We receive a shipment from our supplier once each week. The lead time for those shipments is 4 weeks with a standard deviation of 2 days. Demand each day is normally distributed with mean 100 and standard deviation 10. How much safety stock should we hold to ensure that the chances of stocking out before a shipment (not the annual chances of stocking out) are only 2%?

1111

Solution

• Calculate the variance in demand during the lead time plus the order period. This is

(T+E[L]) D2 +D2

L2

• Careful with the units. Let’s work in days• T = 7 days• E[L] = 28 days• D = 100 units/day• D

2 = 100 units2/day• L

2 = 4 days2

1212

Solution

• So the variance is

(T+E[L]) D2 +D2

L2

• 35*100+40,000 = 43,500

• And the standard deviation is about 208.5 units

• We want to carry just over 2 standard deviations or about 417 items

1313

Question 4We ship products from Asia to Europe for sale to

customers and are interested in strategies that reduce the “avoidable” costs of supply.

A. Under a periodic review regime, which of the following strategies will help reduce pipeline (in-transit) inventories?

i. Increasing frequencyii. Improving forecast accuracyiii. Reducing the safety lead-timeiv. Moving our source for the products closer to

Europev. Changing to a faster mode of transportation

1414

Question 4

B. Under a periodic review regime, which of the following strategies will help reduce cycle inventories (on-hand inventory excluding safety stock)?

i. Increasing frequency

ii. Improving forecast accuracy

iii. Reducing the safety lead-time

iv. Moving our source for the products closer to Europe

v. Changing to a faster mode of transportation

1515

Question 4

C. Under a periodic review regime, which of the following strategies will allow us to reduce safety stock without compromising product availability?

i. Increasing frequencyii. Improving forecast accuracyiii. Reducing the safety lead-timeiv. Moving our source for the products closer to

Europev. Changing to a faster mode of transportation

 

1616

Solution

A. Under a periodic review regime, which of the following strategies will help reduce pipeline (in-transit) inventories?

i. Increasing frequency

ii. Improving forecast accuracy

iii. Reducing the safety lead-time

iv. Moving our source for the products closer to Europe

v. Changing to a faster mode of transportation

1717

Question 4B. Under a periodic review regime, which of

the following strategies will help reduce cycle inventories (on-hand inventory excluding safety stock)?

i. Increasing frequencyii. Improving forecast accuracy iii. Reducing the safety lead-timeiv. Moving our source for the products closer to

Europev. Changing to a faster mode of transportation

Only the first of these is direct. The rest are secondary effects achieved through improved forecast accuracy. We might argue that these only affected safety stock

1818

Question 4

C. Under a periodic review regime, which of the following strategies will allow us to reduce safety stock without compromising product availability?

i. Increasing frequencyii. Improving forecast accuracyiii. Reducing the safety lead-timeiv. Moving our source for the products closer to

Europev. Changing to a faster mode of transportation

  We strongly suspect increasing frequency will reduce safety stock, but it is not always evident because we face the reduced risks more often.

1919

Issues Raised in Projects

• DaimlerChrysler Project– Which makes the most sense?– Front Suspension => Power Train => Assembly– Power Train => Front Suspension => Assembly– Power Train =>

Front Suspension =>

• The issues are:– Operating and Fixed Cost– Risk of shutting down assembly– Inventory– …

Assembly

2020

Risk of Shutting Down

• Where do we want the bottleneck?

• Important to note the relationships

Power train

Front Suspension

Assembly

Lost capacity at one process does NOT mean lost capacity

at another

Power Train

Front Suspension

Assembly

Power Train

Front Suspension

Assembly

What is the issue?

2121

Joint Replenishment

• Several parts from a single supplier• How often to ship and how much?• Assume every part on every truck• ci = unit cost of part I• Di = Annual demand for part I• N = number of joint shipments per year• T = cost of transportation per shipment• h = holding cost percentage • Total Cost = Ordering Costs + Inventory Costs

2222

Joint Replenishment

• Ordering Costs: T*N– N shipments at $T per shipment

• Inventory Costs:– Di/N items per shipment– ciDi/N value of a shipment– hciDi/2N (one-sided inventory cost)

• Total Cost– TN+sum (hciDi/2N) – N = sqrt(sum(hciDi/2)/T) – Qi = Di/N

2323

•The replenishment is scheduled to share the transportation cost among products from the same supplier.

•- Find the right demandDaily production x % Usage x Usage by BOM

- Compute EOQ and T respectively for different parts -- [step 1]:Round T to nearest power of two, minimal T*

Re-compute order quantity (Q=DT) and thus holding cost with reduced transportation cost (A)

•- [step 2]: Decrease T for all parts towards T*Re-compute order quantity (Q=DT) and thus holding cost with A unchanged

Supply Consolidation

2424

Team’s Approach

• Don’t have every part on every truck• Compute EOQ quantities for each part to get Ti,

the ideal time between shipments for each part• Take the smallest of these as T* • Trucks run that frequently• Other parts don’t get on every truck. Make them

regular– Round Ti to one of 2T*, 4T*, 8T*…– I.e, gets on every other truck, every 4th truck, …– Step 2?

2525

Newgistics Case

• Economics

• Pulling from RDU has three effects– Cost of pulling from RDU– Savings in postal costs to BMC– Reduced volume picked up from BMC and so

(perhaps) truck costs

• Hard part:– Estimate cost of pulling from RDU

2626

Estimating RDU Costs

• Carrier bags packages charges by bag based on weight

• This charge is not $A/bag + $B/lb so…

• This charge does include a fixed component per bag so….

Cost of Avg weight bag is

not Avg cost of a bag

The cost per package (inferred) rises as the

volume at the RDU drops

2727

The Optimization• What happens at 1 BMC has no impact on what

happens at another – the problem separates• Variables:

– How many trucks to the BMC– Whether of not to pull from each RDU

• The objective is:– RDU pickup cost +– Postal cost to BMC +– Truck cost from BMW

• Constraints are:– Enough trucks to meet frequency requirements at BMC– Enough trucks to meet volume requirements at BMC

2828

Question

• For you to think about:

• How could you solve this problem if you did not have access to an optimization application?

2929

BMW Projects

• Frequency Project– Current Approach: Assumed transport costs across

Atlantic are similar (turned out not true)• Optimize on the basis of lead-time

• Simulate to determine– Total cost

– Best split of shipments across routes

• Interesting question: – Good model of total cost where variables are routes

used and the quantities shipped on each

3030

Ship-to-Average

• Ship-to-Forecast – Places orders with regular frequency– But the order quantities change– Goal: Maintain regular inventory

3131

Inventory

• On-hand inventory* with ship-to-forecast: – constant level?

0

200

400

600

800

1000

1200

1400

1600

1 11 21 31 41 51 61 71 81 91 101 111

days

OH

I

*) Data of engine #7781905-00, high runner

3232

Ship-to-Average

• Increasing frequency– reduces relevant level of forecast accuracy– Increases shipment volatility

3333

Forecast error

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%

Day Week Month Quarter

Use forecast accuracy over longer

period of time!

Use forecast accuracy over longer

period of time!

Use forecast accuracy over longer

period of time!

• Why try to chase the daily forecast?%

3434

Demand Variability*

0

20

40

60

80

100

120

140

160

180

1 11 21 31 41 51 61 71 81 91 101 111

days

dem

and

Standard Deviation:42/dayMean Demand:

78/day

*) Data of engine #7781905-00, high runner

3535

Ship-to-Average

• Reduces the variability in the order quantities

• Does not raise the total avoidable cost

• Simplifies the process

3636

Shipment Comparison

ship-to-forecast

ship-to-average

(shipment adjustment: 66%)

(shipment adjustment: 14%)

300

400

500

600

700

800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

weekssh

ipm

ents

300

400

500

600

700

800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51

weeks

ship

men

ts= shipment quantity changes more than 10% compared to

previous one

Shipment adjustments happen in 14% of all

shipmentsGoal #2 achieved!

3737

Summary Table

55.83%

-5.36%

-0.45%

7783354-00HIGH

29.60%

+15.22%

-3.87%

1552166-00LOW

48.84%

14.00%

-1.67%

6753862-00LOW

21.79%

60.45%

-0.94%

7759119-00LOW

56.04%

0.00%

-3.85%

7781903-00LOW

51.46%-16.32%32.22%47.11%Shipment changes

57.71%+461.28

%77.14%

+25.25%

Air cost

-0.56%-5.70%-6.47%-0.36%Total avoidable cost

7781905-00HIGH

6762958-00HIGH

6756673-00HIGH

1092396-00HIGHPart #

3838

• I will think of some clever questions

3939

Shelter First

• Design a shelter and a logistics network to deliver it – Immediate (2-3 days)– Temporary

• Change in thinking– Old thinking: Framework agreements with

suppliers– Source from low cost countries – Often poorly served by international carriers

4040

Current Thinking

Before Disaster• Supplier to Pre-positioned stock

• $’s are driver. • Use ocean and ground

After Disaster• Warehouses to Staging Area

• Time is the driver• Use Commercial Air freight

• Staging Area to Beneficiaries• If feasible, airdrop• If not, boats, helicopters, small trucks, animal carts…

Warehouse Staging Area Beneficiaries

(Disaster Zone)

500 to 2000 miles

~ 100 milesSupplier

4141

Response Time

Mobilization and Procurement

(21 days)

Current Timeline

Long Haul Transit

(1-2 day)

Last “100-Mile”

(1-2 day)

Delivery to Beneficiaries

(7 days)

Proposed Timeline

Mobilization

(3 days)

4242

Challenges

• Limited space available on commercial aircraft on short-notice basis

• Charters appear to offer potential solution• Design requirements of the shelter must be more

focused on the goal– Immediate (smaller and lighter)– Temporary (so smaller and lighter may be ok)

• Questions: Models to balance pre-positioned stocks vs expensive air freight in an environment of tight budgets and volatile demand.

4343

Milliken Domestic and XYZ

• Freight Consolidation– Where are the opportunities?

• Volume• Sensitivity to distance

– What are the economics?• Very hard to estimate LTL rates on lanes we don’t use

– What Supply/Demand? • Model each customer/supplier or aggregate?

– Volatility and Service• Model uses average volumes through consolidation, actual volumes

fluctuate• Both a frequency and a volume component to truck costs

– Optimization limitation (other)• Fooling the fixed costs

4444

Milliken Asia

• Model of total costs based on number and location of DCs

• How is this different than BMW Frequency project? (Claim: It’s harder)

• Data issues– Too much required, too little available– Demand! What other approaches?

• Safety Stock: How to calculate from historical order information

4545

Projects

• I hope you have gotten meaningful feedback from me and your sponsor on your projects. If not. See me.

• Pleased with level of work. Always possible to do more, better, …

• Get me your files! Organized• Assessment of contributions (any form)• If you want to participate in Summer Special

Topics Course get a Request for Approval of Special Projects form from Pam or Valarie for me to sign

4646

Exam

• Scheduled for 11:30 – 2:20 Friday May 5

• Flexible about dates

• Can’t hurt your grade