Deck 3: Flow-Time Analysis and Inventory Analysis

Question 1

The "Steal a Deal" gift shop specializes in heavily discounted merchandise for the holiday season. The store prices are so appealing that lines of people queue up in the early AM hours in front of the store doors in order to secure a place in the line.On the morning after Thanksgiving, one of the busiest days of the year, the store opened its doors at 8:00AM. At that time there were 120 customers already waiting in line. From 8:00AM to 10:00AM, new customers arrive at the rate of 5 per minute. After 10:00AM, the rate reduces to 2 per minute. The store admits customers at the rate of 4 per minute.
a. Jacob plans to arrive to the store at 9:00AM. How long should he expect to wait?
b. Rachel does not want to wait more than 15 minutes. When should she show up?

Answer 1

At 8:00Am, 120 customers are waiting
From 8:00 to 10:00AM, line increase by 1 customer per minute
From 10:00 to 12:00PM, line decrease by 2 customers per minute
a. At 9:00 the line is 180. Jacob will wait 180/4 = 45 minutes
b. To wait 15 minutes, the line has to be at most 15*4 = 60. Rachel must show up after 11:30AM

Question 2

EZS is a small fast food outlet located in midtown Manhattan and serving mainly the corporate clientele. EZS' main fare is a freshly prepared, customizable line of sandwiches. It is supplemented with an assortment of drinks, light salads, seasonal fruit and snacks. The restaurant is open 10:00AM to 10:00PM, but the peak demand is during lunch hours, 11:30 to 2:00PM.A customer joining the line makes a sandwich selection by consulting the billboard, marks her selection on a customized form, and hands the form to one of several assemblers who produce the sandwich. The customer does not wait for the sandwich to be assembled, but proceeds directly down the line to select additional items onto her tray. Next, the customer proceeds to pay at the cash register. Finally, (after the payment is completed) she collects her prepared sandwich at a designated location. Selecting the sandwich and marking the form takes 45 seconds. Assembling the sandwich requires 90 seconds. Selecting additional items takes 60 seconds. Paying at the cash register requires 40 seconds. Collecting the prepared sandwich requires 20 seconds. The restaurant employs 2 cash registers and 6 sandwich assemblers, and one person to disburse the prepared sandwiches.
a. Draw a process map
b. What is the theoretical flow time of the process?
c. What is the capacity of the process
d. During rush hour, demand exceeds capacity and long lines form. Does it make sense to add a sandwich assembler?

Answer 2

a.
b. The critical path is the top one, = 45 +60 + 40 +20 = 165 sec
c. Capacity per minute:
Assembly: 6*60/90 = 4
Cash register 2*60/40 = 3
Disburse 1*60/20= 3 (assuming time to collect = time to disburse)
d. No. Assembler is not a bottleneck

Question 3

A temp work service maintains an "inventory" of 200 computer specialists who are assigned to various customers on a short term basis. The typical tour of duty lasts for 7 weeks, and the period between assignments typically lasts for 3 weeks. Assume 50 weeks per year.
a. On average, how many specialists start on a new assignment each week?
b. On average, how many specialists are idle (between assignments)?

Answer 3

a. The flow time of entire process is 3+7 = 10 weeks
Inventory is 200
Therefore R= I/t = 200/10 = 20 per week
b. The flow time of "idle" is 3 weeks
The throughput is 20 per week
Therefore I=R*T= 20*3 = 60
Alternative way % of idle time 3/10= 30%. Thus 30% of staff will be idle on average, ( 30% of 200 = 60)

Question 4

A company's income statement for FY06 contains the following information (in $ Million): It is estimated that 20% of COGS and 10% of SGA&A are Throughput Cost (vary with throughput), and the rest are Capacity Cost ( fixed with respect to throughput). The throughput is 100,000 units per year.
a. What will be the increase in profit if throughput increases by 1%?

Question 5

Complete Computer (CC) is a retailer of computer equipment in Minneapolis with four retail outlets. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 4,000 units per week. Each unit costs $200 and CC has a holding cost of 20%. The fixed cost of each order (administrative + transportation) is $900. Assume 50 weeks in a year.

-Given that each outlet orders independently and gets its own delivery, the optimal order size at each outlet is [SHOW WORK]

A) 424
B) 3,000
C) 6,000
D) 42,426
E) None of the above

Question 6

Complete Computer (CC) is a retailer of computer equipment in Minneapolis with four retail outlets. Currently each outlet manages its ordering independently. Demand at each retail outlet averages 4,000 units per week. Each unit costs $200 and CC has a holding cost of 20%. The fixed cost of each order (administrative + transportation) is $900. Assume 50 weeks in a year.

-CC is thinking of centralizing purchasing (for all four outlets). In this setting, CC will place a single order (for all outlets) with the supplier. The supplier will deliver the order on a common truck to a transit point. Since individual requirements are identical across outlets, the total order is split equally and shipped to the retailers from this transit point. This entire operation has increased the fixed cost of placing an order to $1,800. If CC manages ordering optimally in the new setting, average inventory in the CC system (across all four outlets) can be expected to

A) Increase
B) Decrease
C) Remain unchanged