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Answers to Clfm OM Final-2011

Answers to Clfm OM Final-2011
Answers to Clfm OM Final-2011

Q1McDonald’s

The following figures are taken from the 2003 financial statements of McDonald’s and Wendy’s. Figures are in million dollars.

McDonald’s Wendy’s

Inventory$129.4 $ 54.4

Revenue17,140.5 3,148.9

Cost of goods sold11,943.7 1,634.6

Gross profit5,196.8 1,514.4

a. In 2003, what were McDonald’s inventory turns? What were Wendy’s inventory turns?

b. Suppose it costs both McDonald’s and Wendy’s $3 (COGS) per their value meal

offerings, each sold at the same price of $4. Assume that the cost of inventory for both companies is 30 percent a year. Approximately how much does McDonald’s save in inventory cost per value meal compared to that of Wendy’s? You may assume the inventory turns are independent of the price.

Q2 McKinley Consulting

McKinley is a strategy consulting firm that divides its consultants into three classes: associates, managers, and partners. The firm has been stable in size for the last 20 years, ignoring growth opportunities in the 90s, but also not suffering from a need to downsize in the financial recession. Specifically, there have been and are expected to be 200 associates,

60 managers, and 20 partners. The work environment at McKinley is rather competitive.

After four years o f working as an associate, a consultant goes “either up or out”; that is, becomes a manager or is dismisses from the company. Similarly, after six years, a manager either becomes a partner or is dismissed. The company recruits MBAs as associate consultants; no hires are made at the manager or partner level. A partner stays with the company for another 10 years (a total of 20 years with the company).

a. How many new MBA graduates does McKinley have to hire every year?

b. What are the odds that a new hire at McKinley will become partner (as opposed to being

dismissed after 4 years or 10 years)?

Answers:

We have the following information available from the question:

(a) We can use Little’s law to find the flow rate for associate consultants:

Inventory=Flow Rate * Flow Time; 200 consultants=Flow Rate * 4 years; thus, the flow rate is 50 consultants per year, which need to be recruited to keep the firm in its current size (note: while there are also 50 consultants leaving the associate level, this says nothing about how many of them are dismissed vs how many of them are promoted to Manager level).

(b) We can perform a similar analysis at the manager level, which indicates that the

flow rate there is 10 consultants. In order to have 10 consultants as a flow rate at the manager level, we need to promote 10 associates to manager level (remember, the firm is not recruiting to the higher ranks from the outside). Hence, every year, we dismiss

40 associates and promote 10 associates to the manager level (the odds at that level are

20%)

Now, consider the partner level. The flow rate there is 2 consultants per year (obtained via the same calculations as before). Thus, from the 10 manager cases we evaluate every year, 8 are dismissed and 2 are promoted to partner (the odds at that level are thereby also 20%).

In order to find the odds of a new hire to become partner, we need to multiply the promotion probabilities: 0.2*0.2=0.04. Thus, a new hire has a 4% chance of making it to partner.

Q3 Cranberries

International Cranberry Uncooperative (ICU) is a competitor to the National Cranberry Cooperative (NCC). At ICU, barrels of cranberries arrive on trucks at a rate of 150 barrels per hour and are processed continuously at a rate of 100 barrels per hour. Trucks arrive at a uniform rate over eight hours, from 6:00 a.m. until 2:00 p.m. Assume the trucks are sufficiently small so that the delivery of cranberries can be treated as a continuous inflow.

The first truck arrives at 6:00 a.m. and unloads immediately, so processing begins at 6:00

a.m. The bins at ICU can hold up to 200 barrels of cranberries before overflowing. If a truck

arrives and the bins are full, the truck must wait until there is room in the bins.

a. What is the maximum number of barrels of cranberries that are waiting on the trucks at

any given time?

b. At what time do the trucks stop waiting?

c. At what time do the bins become empty?

d. ICU is considering using seasonal workers in addition to their regular workforce to help

with the processing of cranberries. When the seasonal workers are working, the

processing rate increases to 125 barrels per hour. The seasonal workers would start

working at 10:00 a.m. and finish working when the trucks stop waiting. At what time

would ICU finish processing the cranberries using these seasonal workers? Answers:

Cranberries arrive at a rate of 150 barrels per hour. They get processed at a rate of 100 barrels per hour. Thus, inventory accumulates at a rate of 150-100=50 barrels per hour. This happens while trucks arrive, i.e. from 6am to 2pm. The highest inventory level thereby is 8h*50 barrels per hour=400 barrels. From these 400 barrels, 200 barrels are in the bins, the other 200 barrels are in trucks.

(a)200 barrels

(b)From 2pm onwards, no additional cranberries are received. Inventory gets depleted at a

rate of 100 barrels per hour. Thus, it will take 2h until the inventory level has dropped to 200 barrels, at which time all waiting cranberries can be stored in the bins (no more truck waiting)

(c)It will take another 2 hours until all the bins are empty

(d)Since the seasonal workers only start at 10:00am, the first 4 hours of the day we

accumulate 4hours * 50barrels per hour=200 barrels. For the remaining time that we receive incoming cranberries, our processing rate is higher (125 barrels per hour). Thus, inventory only accumulates at a rate of 25 (150-125 barrels per hour). Given that this happens over 4 hours, we get another 100 barrels in inventory. At 2pm, we thereby have 300 barrels in inventory. After 2pm, we receive no further cranberries, yet we initially process cranberries at a rate of 125 barrels per hour. Thus, it only takes 100 barrels / 125

barrels/hour=0.8 hours=48 minutes until all bins are empty. From then, we need another 2h until the bins are empty.

Q4 JCL Inc.

JCL Inc. is a major chip manufacturing firm that sells its products to computer manufacturers like Dell, Gateway etc. In simplified terms, chipmaking at JCL Inc. involves three basic operations: depositing, patterning and etching.

Depositing: Using Chemical Vapor Deposition (CVD) technology, an insulating material is deposited on the wafer surface, forming a thin layer of solid material on the chip.

Patterning: Photolithography projects a microscopic circuit pattern on the wafer surface which has a light-sensitive chemical like the emulsion on photographic film. It is repeated many times as each layer of the chip is built.

Etching: Etching removes selected material from the chip surface to create the device structures.

The following table lists the required processing times and set up times at each of the steps.

There is unlimited space for buffer inventory between these steps. Assume that the unit of production is a wafer, from which individual chips are cut at a later stage.

NOTE THAT A SET-UP CAN ONLY BEGIN ONCE THE BATCH HAS ARRIVED AT THE MACHINE.

a.What is the process capacity in units per hour with a batch size of 100 wafers?

b.For the current batch size of 100 wafers, how long would it take to produce 50 wafers?

Assume that the batch needs to stay together during deposition and patterning (i.e. the firm does not work with transfer batches that are less than the production batch). However, the

50 wafers can leave the process the moment all 50 wafers passed through the etching stage.

Recall that a set-up can only be started upon the arrival of the batch at the machine.

c.For what batch size is step 3 (etching) the bottleneck?

d.Suppose JCL Inc. came up with a new technology that eliminated the setup time for step 1

(deposition), but increased the activity time to 0.45 min/unit. What would be the batch size that you would choose so as to maximize the overall capacity of the process, assuming all units of a batch stay together for the entire process?

ANSWERS:

a. Capacity of a step is given by Batch Size/ (Set-Up-Time + Batch-Processing-Time).

Using this formula, the capacity of the three steps can be calculated as:

Deposition: 100/ (45+0.15*100) = 1.67 units/min = 100 units/hour

Patterning: 100/ (30+0.25*100) = 1.82 units/min = 109 units/hour

Etching: 100/ (20+0.2*100) = 2.5 units/min = 150 units/hour

Clearly the bottleneck is the “deposition” step and it determines process capacity.

b. Since the batch has to stay together in the first two steps, time taken is given by Deposition: 45 min + 0.15 min/unit * 100 units = 60 min

Patterning: 30 min + 0.25 min/unit * 100 units = 55 min

So the batch takes 115 min through the first two steps. At step 3, only 50 units need to be processed, and time taken is 20 min + 0.20 min/unit * 50 units = 30 min. Total time taken is hence 115 + 30 = 145 min = 2 hours 25 min

c. If batch size is B, then Activity time of step 3 is 20 + 0.20B which is always lesser than the activity time of step 2, 30 + 0.25B, for a positive value of B. Hence step 3 can never be the bottleneck.

d. Under the new technology, the process capacity of step 1 is no longer dependent on batch size and is = (1/ 0.45 min/unit) * (60 min/hr) = 133.33 units/hour. This is clearly the maximum overall process capacity that can be targeted.

Given that step 3 can never be the bottleneck, the maximum overall process capacity of 133.33 units/hour can be achieved by choosing a batch size for which step 1 is the bottleneck. So if B is the batch size for which step 1 is the bottleneck, then we have B/ (30 + 0.25B)>= 1/0.45. Solving for B, we get B>=150.

Q5 Millennium Liquors

Millennium Liquors is a wholesaler of sparkling wines. Their most popular product is the French Bete Noire 1989. Weekly demand is for 45 cases. Assume demand occurs over 50 weeks per year. The wine is shipped directly from France. Millennium’s annual cost of capital is 15 percent, which also includes all other inventory-related costs. Below are relevant data on the costs of shipping and handling. These costs include the usual ordering and handling costs, plus the cost of refrigeration, which includes a fixed component (mainly depreciation of the cooling equipment) and a variable component that depends on the number of cases in inventory.

?Cost per case: $120

?Shipping cost (for any size shipment): $290

?Cost of labor to place and process an order: $10

?Cost of labor to place cases into warehouse: $2/case

?Cost of labor to pick case when sold: $2/case

?Fixed cost for refrigeration: $75/week

?Variable cost for refrigeration: $3/case/week

a. Calculate the weekly holding cost for one case of wine.

b. Use the EOQ model to find the number of cases per order and the average number of orders per year.

c. Currently orders are placed by calling France and then following up with a letter. Millennium and its supplier may switch to a simple ordering system using the Internet. The new system will require much less labor. What would be the impact of this system on the ordering pattern?

Answers:

Note: cost of labor for placing and picking up cases can be ignored

Fixed cost of refrigeration can be ignored

Variable cost of refrigeration is $3 per case and week

(a) weekly holding cost 0.3%/week * 120 $/case = 0.36 $/week

Now we add the $3 per case and week for the refrigeration and we get a total cost of $3.36 (b) EOQ=64.8936

.345*300*2 cases per order (c) We would get slightly lower ordering costs, which results in more frequent orders and lower inventory

Q6 Philly Barber Shops

Newt Philly needs to decide where to get a haircut. He has narrowed the choice down to two local hair salons – Large Hair Salon (LHS) and Small Hair Cutters (SHC).

During busy periods, a new customer walks into LHS every 15 minutes (with a standard deviation of 15 minutes). At SHC, a customer walks in every hour (with a standard deviation of 1 hour). LHS has a staff of 4 barbers, while SHC has 1 barber. A typical service time at either salon lasts 30 minutes (with a standard deviation of 30 minutes).

a. If Newt walks into LHS during a busy period, how long must he wait in line before he can see a barber? (Only include the waiting time, not any service time)

b. If Newt goes to SHC, how long must he wait in line before his haircut starts?

c. Assume that it takes Newt 10 minutes to leave work and walk to LHS and 10 minutes to walk back (i.e. each way of the walk takes 10 minutes). How long will he need to leave work for to get a haircut at LHS?

d. LHS will buy out SHC. LHS will then close SHC’s op erations and serve all customers, including existing SHC customers, at the LHS location only. Assuming that the previous traffic of SHC customers now flows to the LHS location, what is the new inter-arrival time at LHS?

e. To accommodate the new flow rate, LHS now staffs one additional barber (to increase the headcount to 5). Is the new waiting time at LHS less than or greater than the waiting time

of LHS before the merger? (Assume that the coefficient of variation of customer inter-arrival times is 1). Justify your answer.

Answers:

Q7 Teddy Bower Parkas

Teddy Bower is an outdoor clothing and accessories chain that purchases a line of parkas at $10 each from its Asian supplier, TeddySports. Unfortunately, at the time of order placement, demand is still uncertain. Teddy Bower forecasts that its demand is normally distributed with mean of 2,100 and standard deviation of 1,200. Teddy Bower sells these parkas at $22 each. Unsold parkas have little salvage value; Teddy Bower simply gives them away to a charity.

a. What is the probability this parka turns out to be a “dog,” defined as a product that sells

less than half of the forecast?

b. How many parkas should Teddy Bower buy from TeddySports to maximize expected

profit?

c. If Teddy Bower wishes to ensure a 98.5 percent fill rate, how many parkas should it

order?

d. If Teddy Bower wishes to ensure a 98.5 percent in-stock probability, how many parkas

should it order?

For parts e through g, assume Teddy Bower orders 3,000 parkas.

e. Evaluate Teddy Bower’s expected profit.

f. Evaluate Teddy Bower’s fill rate.

g. Evaluate Teddy Bower’s stockout probability

Answers

a) The parka sells less than half of the forecast if demand is 2100/2 = 1050 or fewer units. Normalize the quantity 1050: ().88.01200/21001050-=-=z From the Standard Normal Distribution Function Table, 1894.0)88.0(=-Φ, which implies there is a 18.9% probability that the parka will be a dog.

b) To determine the profit maximizing order quantity, begin with the underage cost,

121022=-=u C , and the overage cost, .10010=-=o C The critical ratio is 5455.0)1210/(12=+. We see from the Standard Normal Distribution Function Table that 5438.0)11.0(=Φ and 5478.0)12.0(=Φ, so we choose 12.0=z . Convert that z-statistic back into an order quantity, .244,2120012.02100=?+=?+=σμz Q

c) To hit the target fill rate of 98.5% we need to evaluate the target lost sales:

()(/)(1(2100/1200)(1-0.985)0.0263L z Fill rate)μσ=?-=?=

From the Standard Normal Loss Function Table we see that 0267.0)54.1(=L and 0261.0)55.1(=L , so we choose z = 1.55. Convert to Q : 3960120055.12100=?+=Q .

d) To hit the target in-stock probability of 98.5%, we need to find the z-statistic such that 9850.0)(=Φz . We see from the Standard Normal Distribution Function Table that 9850.0)17.2(=Φ, so we choose 2.17z =. Convert to Q : 4704120017.22100=?+=Q .

e) If 3000 parkas are ordered then the corresponding z -statistic is

()75.01200/21003000=-. Now look up expected lost sales with the Standard Normal distribution in the Standard Normal Loss Function Table : 1312.0)75.0(=L . Convert that lost sales into the expected lost sales with the actual demand distribution: 4.1571312.01200)(=?=?z L σ. Expected sales = expected demand – expected lost sales = 2100 – 157.4 = 1942.6. Expected left over inventory = 3000 – 1942.6 = 1057.4. Finally,

()()22101942.61001057.4

12,737

Expected profit =-?--?=

f)The fill rate equals expected sales divided by expected demand = 1942.6 / 2100 =

92.5%.

g)The stock out probability is %

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Q8 Toyota Definitions

Please write the letter corresponding to the most appropriate example or definition from choices (a – k below) on the blank line next to each word below.

a) Examples of this include: workers having to make unnecessary movements (i.e. excessive

reaching or walking to get tools or parts), working on parts that are defective and idle time.

b) A system that enables a line worker to signal that he or she needs assistance from his or her

supervisor, for example in the case of a defect. Used to implement the Jidoka principle.

c) A brainstorming technique that helps structure the process of identifying underlying causes

of an (usually undesirable) outcome

d) A problem solving technique that consists of collecting data about different types of

problems that occurred over the past month (for example, paint scratches, defective seats, damaged trim, dents, electrical wiring defects, etc.) and then prioritizing resources to work on the few problems that had the highest frequencies.

e) As an example of this philosophy, workers in the Toshiba case had notebooks at their work

stations that they used to jot down improvement ideas.

f) A method that controls the amount of work-in-process inventory.

g) A system to detect when a significant change in the process has occurred (assignable cause),

that should be investigated and (if undesirable) removed.

h) Example: Floppy disc drives designed such that users cannot insert a disc if the disc is

upside down.

i) If an automotive assembly plant used this technique, the adjacent cars on an assembly line

would be mixed models (e.g. Model A with sunroof, Model A without sunroof, Model B, Model B with sunroof), in proportions equal to customer demand.

j) Making production problems visible and stopping production upon detection of defects

k) Moving flow units through the system in batches

Please only add ONE LETTER to each of the following terms:

Kanban ____

Heijunka ____

Poka-Yoke ____

Andon cord ____ Kaizen ____ Ishikawa ____ Jidoka ____

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