supply chain hw

ISYE 4210 / 6600

Design and Analysis of Supply Chains

Homework Assignment #7

Chaoqun Deng 661249767

1. Discuss how air, rail, water and truck transportation differ on the following dimensions:

cost, speed and volume.

Regarding cost, air is most expensive while rail, truck and water are cheap.

Regarding speed, air is quickest while rail, truck and water are slow.

Regarding volume, air carries low volume while rail, truck and water carry high volume.

2. By offering a buyback contract to the retailer, with a properly chosen buyback price, a

manufacturer can increase the retailers order quantity. Explain why.

Manufacturer agree to buy back any excess stock at retailer at price of b per unit,

Where sOD

Thus, retailer orders more under the buyback contract than in decentralized supply chain without buyback.

3. Explain what is meant by aligning incentives in a supply chain. What are some of the

factors that make aligning incentives difficult?

A supply chain works well if its companies' incentives are aligned-that is, if the risks, costs, and

rewards of doing business are distributed fairly across the network (Narayanan and Raman, 2004,

p96).

There are several factors that make aligning incentives difficult: firstly, when companies cannot

observe other firms' actions, they find it hard to persuade those firms to do their best for the

CarolineSticky Note10/10




supply network; secondly, it's difficult to align interests when one company has information or

knowledge that others in the supply chain don't; thirdly, incentive schemes are often badly

designed (Narayanan and Raman, 2004).

4. Do exercise 2 in Chapter 14 of the Chopra and Meindl textbook. Hint: The point of this

exercise is to evaluate the change in facility, inventory and transportation costs as a result

of using different warehouse locations. To answer this question, you should evaluate the

costs for the following three options: (1) One warehouse is built in either the eastern or

western zone (by symmetry, the costs will be the same in both cases); (2) One warehouse is

built in the central zone; and (3) A warehouse is built in each of the three zones. In

performing your analysis, note that the average weekly demand for each region is given as

50,000. This is the average number of books demanded each week, not the average number

of orders. Since orders contain 4 books (on average), the average number of orders per

week for each zone is just 50,000/4. For each of the three options to be evaluated, you will

need to calculate five different types of costs: transportation cost, cycle inventory costs,

safety inventory costs, fixed costs for the warehouse and operating costs for the warehouse.

Each of these costs should be calculated on a weekly basis and then summed to get the total

cost per week. For the cycle and safety inventory holding costs, you will find it easier to

calculate the annual holding cost and then divide by 52 weeks per year. For the safety

inventory costs, notice that Books-on-Line uses a periodic review policy in which they order

once per week. For the cycle inventory costs, notice that the average order size is equal to

the average demand per week. In the equation provided for the fixed cost of the warehouse,

x is the capacity, which can be calculated as 1.5 * (order size plus safety stock). In the

equation given for the warehouse operating cost, y is the average number of books shipped

per week.

(1) One warehouse is built in either the eastern or western zone (by symmetry, the costs will be

the same in both cases)

--Transportation Cost Per week:

The average number of orders per week for each zone is 50000/4=12500

12500*(2+3+4)= 112500

--For cycle inventory and safety inventory Cost :

Total Cycle Inventory per week per region

50000/2=25000

Total Safety Inventory per week per region

58154/52=1118.35

Thus, across three regions, the cycle and safety inventory holding cost per week

(25000+1118.35)*3*10*0.25=195887.6

Fixed Cost of the warehouse per week

200,000+1.5* ( 50000+1118.35)*3=200,000+230,032.57=430,032.57430,033

Warehouse Operating Cost

0.01*50000*3=1500

Total Cost per week:

112500+195887.6+430032.57+1500=739,920,17739,920

(2) One warehouse is built in the central zone

Input Data (given data is in yellow)

Average demand per week D 50000

Standard deviation of demand per week s_D 25000

Lead time in weeks L 1

Review time in weeks T 1

For a given desired cycle service level

find associated required reorder point

Desired cycle service level CSL 99.70%

Average demand during lead time + review period D_L+T = (L+T) D 100000

Standard deviation of demand during lead time + review period s_L+T= sqrt(L+T) s_D 35355.3

Safety stock factor z = normsinv(CSL) 1.64

Safety stock ss = z s_L+T 58154

Order up to level OUL = D_L+T + ss 158154

CarolineSticky NoteWeekly cost of this option = Transport cost + facility cost + cost of inventory = $112,500 + $13,027 + $1,500 + $3,606 + $8,090= $138,722

CarolineSticky NoteSafety inventory = normsinv(CSL)**25000 = normsinv(0.997)**25000 = 168,267

--Transportation Cost Per week:


12500*(3+2+3)= 100,000

--For cycle inventory and safety inventory Cost :


50000/2=25000


58154/52=1118.35

Thus, across three regions, the cycle and safety inventory holding cost per week

(25000+1118.35)*3*10*0.25=195887.6

Fixed Cost of the warehouse per week

200,000+1.5* (50000+1118.35)*3=200,000+230,032.57=430,032.57430,033

Warehouse Operating Cost

0.01*50000*3=1500


100,000+195887.6+430032.57+1500=727,420,17727,420

(3) A warehouse is built in each of the three zones

Transportation Cost Per week:


12500*(2+2+2)=75,000

For one warehouse:

--For cycle inventory and safety inventory Cost For one warehouse :


50000/2=25000

CarolineSticky NoteWeekly cost of this option = Transport cost + facility cost + cost of inventory = $100,000 + $13,027 + $1,500 + $3,606 + $8,090 = $126,222

CarolineSticky NoteSafety inventory = normsinv(CSL)**25000 = normsinv(0.997)**25000 = 168,267


58154/52=1118.35

Thus, the cycle and safety inventory holding cost per week

(25000+1118.35)**10*0.25=65,295.87 ,

Fixed Cost of the warehouse per week for one warehouse

200,000+1.5* (50000+1118.35)=276,677.52276,678

Warehouse Operating Cost for one warehouse

0.01*50000=500

For three warehouses :

3*(65295.87+276,677.52+500) =1,027,420.17


100,000+1,027,420.17=1,127,420.171,127,420

Thus, transportation can be increased when inventory is aggregated. The facility cost could be increased

when inventory is not aggregated.

According to the comparison, the total cost for option 2 is the lowest. Thus, we choose to build a

warehouse in the central zone.

5. Do exercises 1 and 3 in Chapter 15 of the Chopra and Meindl textbook. For these two

problems, do the order quantity calculations by hand, i.e., write out the equations used to

find, co, cu and O*, using Excel only to look up the appropriate z value for the Normal

distribution. For the remaining parts of the problems (e.g., calculating profits, etc.), you

will need to use Excel.

Exercise 1

E1-Question a:

D=20000, = 5000

= = 24 12 = 12

= = 12 3 = 9

Pr(d ) =

+ 0=

12

12 + 9= 0.57

CarolineSticky NoteAnswer: Total cost for building warehouse in each location is best.

CarolineSticky NoteSafety inventory = normsinv(CSL)**25000 = normsinv(.997)**25000 = 97,149

CarolineSticky NoteWeekly cost of this option = 3*(Transport cost + facility cost + cost of inventory at each warehouse)= 3*($25,000 + $8,091 + $500 + $1,202 + $6,599)= $124,174


z = NormsInv(0.57) = 0.18

= + = 20000 + 0.18 5000 = 20900

Thus, Barnes & Nobel should order 20900 books. The expected profit for Barnes & Nobel is $198,784

It expects to sell 2477 books at a discount.

E1-Question b:

The profit for pulisher is $229,901

E1- Question c:

D=20000, = 5000

Production cost per unit v $1

Wholesale price per unit c $12

Retail price per unit p $24

Salvage value per unit s $3

Cost of understocking Cu = p-c $12

Cost of overstocking Co = c-s $9

Optimal cycle service level CSL = Cu/(Cu+Co) 0.57

Optimal z value z = NormsInv(CSL) 0.18

Optimal order quantity O_D = D + z s_D 20900

Expected overstock E[OS] 2477

Expected understock E[US] 1577

Expected profit for retailer(p-c) x D - Co E[OS]

- Cu E[US]$198,784

Expected profit for supplier (c-v) x O_D $229,901

Expected profit for system (retailer

+ supplier)$428,685

Decentralized Solution - Retailer Chooses Order Quantity

CarolineSticky NoteGood.


= = 24 12 = 12

= = 12 5 = 7

Pr(d ) =

+ 0=

12

12 + 7= 0.63

z = NormsInv(0.63) = 0.34

= + = 20000 + 0.34 5000 = 21700

Thus, under this plan, Barnes & Noble will order 21680 books.

The expected profit for Barnes & Noble will be $204,181





Buyback price b $5

Cost of understocking Cu = p-c $12

Cost of overstocking Co = c-b $7



Optimal order quantity O_B = D + z s_D 21680



Expected profit for retailer(p-c) x D - Co E[OS]

- Cu E[US]$204,181

Expected profit for supplier(c-v) x O_B

- (b-s) x E[OS]$232,589


+ supplier)$436,770

Decentralized Solution - Retailer Chooses Order Quantity - With Buyback

CarolineSticky NoteCheck values to solution. Your Co should be $4, causing your other values to be wrong.

2946 books are expected to be unsold.

The expected profit for publisher is $232,589

No Refund Refund Plan

Retailer Profits $198,784 $204,181

Supplier Profits $229,901 $232,589

Total SC Pofits $428,685 $436,770

Compare this two options, the buyback contract will increase both the profits of retaliers and

suppliers. Thus, the pulisher should choose this refund plan.

Exercise 3

D=5000, = 2000

= (1 ) = (1 0.35) 15 3 = 6.75

= = 3 1 = 2

Pr(d ) =

+ 0=

6.75

6.75 + 2= 0.77

z = NormsInv(0.77) = 0.74

= + = 5000 + 0.74 2000 = 6480

CarolineSticky NoteCorrect.


a.Thus, Topgun order 6487 CDs

b. 1752 CDs Topguns should expect to sell at a discount.

c. The expected profits for Topgun are $28,455

d. The expected profits for Studio are $ 31,344

e. The results are as follows:





Revenue sharing percentage f 0.35

Cost of understocking Cu = (1-f)p-c $6.75







expected sales E[Sales] 4735

Expected profit for retailer((1-f)*p-c) x D - Co

E[OS] - Cu E[US]$28,455


+f*p*E[sales]$31,344


+ supplier)$59,799

Decentralized Solution - Retailer Chooses Order Quantity -Revenue Sharing


Thus, Topgun order 7230 CDs

2363 CDs Topguns should expect to sell at a discount.

The expected profits for Topgun are $29,514

The expected profits for Studio are $ 31,391





Revenue sharing percentage f 0.43

Cost of understocking Cu = (1-f)p-c $6.55







expected sales E[Sales] 4867

Expected profit for retailer((1-f)*p-c) x D - Co

E[OS] - Cu E[US]$29,514


+f*p*E[sales]$31,391


+ supplier)$60,905

Decentralized Solution - Retailer Chooses Order Quantity -Revenue Sharing



Input Data

Product 1 2 3 4 5

Mean demand for season, D 20000 14000 3000 3000 3000

Standard deviation of demand for season, s 2000 2000 2000 2000 2000

Variance of demand for season, s 2 4000000 4000000 4000000 4000000 4000000

Sales price per unit, p $45 $45 $45 $45 $45

Salvage value per unit, s $5 $5 $5 $5 $5

Production cost per unit (without postponement), c $11 $11 $11 $11 $11

Production cost per unit (with postponement), c $12 $12 $12 $12 $12

Without Postponement (player 1 and player 2)

Product 1 2

Co = cost per unit overstock = c - s 6 6

Cu = cost per unit understock = p - c 34 34

CSL (no postponement) = Cu / (Cu + Co) 85% 85%

z = normsinv(CSL), no postponement 1.04 1.04

O* = D + z s_D for each product 22073 16073

Total inventory for all 2 products 38146

Expected overstock for each product 2228 2228

Expected understock for each product 155 155

Expected profit for product 1 and 2 $661,347 $457,347

Total profits $1,118,695

For Player 3, 4 and 5, I choose to use postponement

For Player 1 and 2, I choose to use the traditional approach

The reason is that player 3, 4 and 5 has more uncertain demand than player 1 and 2. We use postponement

only for products with most uncertain demand.

References:

Narayanan, V. G., & Raman, A. (2004). Aligning incentives in supply chains. Harvard business review,

82(11), 94-102.

With Postponement(player 3,4,and 5)

Mean aggregate demand = D_3 + D_4 + D_5 9000

Variance of aggregate demand = s^2_3 + s^2_4 + s^2_5 12000000

Standard deviation of aggregate demand = sqrt(variance) 3464

Co = cost per unit overstock = c - s $7

Cu = cost per unit understock = p - c $33

CSL (with postponement) = Cu / (Cu + Co) 83%

z = normsinv(CSL), with postponement 0.93

O* = mean + z x std dev, for aggregate demand 12238

Expected overstock 3564

Expected understock 326

Total expected profit for player 3 ,4 and 5 $261,281.61

Total expected profit for all players $1,379,976.21


CarolineSticky NoteCorrect.

25/25
