1. Seattle Wireless(SW), a wireless phone carrier, has a retail store at the Bellevue Mall, which is in charge of Sales for new services and maintenance and assistance to existing account holders. Arrivals to the store are Poisson with an average rate of 6 customers per hour. Approximately, 80% of the arrivals are Sales related and the rest are Maintenance of the existing account holders. Customers join a queue and are served on a First-Come-First-Served basis. Currently, the store has one agent who handles all customers (sales and maintenance of existing accounts). The time an agent spends with a customer is exponentially distributed with a mean of 6 minutes. A detailed study shows that around 40% of the potential new sales customers decide to get the wireless service (the rest leave the store after talking to the agent). SW pays those customers who open a new account $100 if they wait more than 2 minutes in line.
a) Identify the queueing system associated with the operation and find the average total hourly cost of the queue operation.
b) SW management is considering the creation of two separate lines, one for each of the customer types (sales and maintenance).In this configuration, the service times for each queue will remain as before (exponential with a mean of 6 minutes) but an additional agent must be hired. To make this two-line configuration more cost-effective (lower average total cost) than the original configuration, what is the maximum wage ($/hour) to pay the additional agent (Show all your work)
2. The production process of a product consists of 3 stages depicted below:
Each production stage is processed on a special machine type, M1, M2 and M3, respectively. Currently, the firm has one machine at each stage. Monthly demand for the end product is 122 units and the contribution margin from each unit sold is $150. Below is a summary of all relevant information on the machines:
|
Machine
|
M1
|
M2
|
M3
|
|
MONTHLY PRODUCTION RATE
|
45
|
40
|
65
|
|
COST
|
$200,000
|
$50,000
|
$60,000
|
Assuming that investments continue in perpetuity and the nominal cost of capital is 12% per year compounded monthly, and there are no limits in buffers in between machines, answer the following questions (In your analysis, ignore inventory costs and exclude the cost of existing machines in your calculations.):
a) Find the Average Throughput of the current process and the average monthly profit (alternatively you can calculate the Present Value of the Profit)
b) Suppose the firm is considering adding capacity at the stage of the process if needed. If a machine is purchased at the bottleneck stage, find the discounted monthly profit (or the Present Value of the Profit) and the resulting throughput rate. Should the firm undertake this capacity addition?
c) Using the concept of Theory of Constraints, how many additional machines at each stage (if any) should be bought if the goal is to maximize the discounted monthly profit (or the Present value of the profit). What is the resulting throughput rate associated with this decision.
3. A local electronic store provides customers with walk-in service to repair their flat screen TVs of various technologies (LCD, LED, Plasma, etc.). When an item arrives, store technicians perform basic tests at the test shop (station 1)and decide which rework shop to send for repair. Cleaning shop (station 2) is responsible for providing minor cosmetic repair work such as cleaning. Rework shop (station 3) provides moderate repair work such as replacing power supply unit of the panel. Due to its current limited capability, the store is not capable of fixing more serious damage and can only send customers away for some cases.
On average, flat screen set arrives the store at a rate of ten per hour. After testing at station 1, 20% of the units, which are seriously damaged and cannot be fixed, must leave the store. 50% of the units, which only need minor repair, will be sent to station 2. The remaining 30% will be sent to station 3. Usually, it takes an average of 20 minutes per unit at station 1, 10 minutes at station 2, 50 minutes at station 3. On average, 5 flat screen sets wait in front of station 1, 3 in front of station 2, and 5 in front of station 3. Assuming that the process is stable, answer the following questions:
a) On average, how long does a flat screen set stay in the shop?
b) What is the average number of flat screen sets in the store?
4. AMD movie complex in downtown Seattle has two staff working independently in his/her own window at the ticket office. Approximately, 40% of the arrivals holds AMD membership card, and the rest is general public customers. Currently, all customers form a single line (feeder line system), and it is estimated that the pattern of arrivals to the ticket office are Poisson with a mean of 50 per hour. The time a customer spends at the ticket window with a staff is exponentially distributed with a mean of 1.44 minutes. AMD estimates the waiting cost in a queue for member and general customers at $3 and $0.1 per minute, respectively.
a) Identify the queuing system associated with the operation and find the average total cost per hour of the operation. What is the average throughput of the system?
b) Suppose the management is considering a proposal to create two separate lines, one for member, and another for general public customers. In this situation, each line will have one staff that will serve their respective customers. Assume that the service times stay as before. Identify the queuing system associated with this configuration, find the average total hourly cost associated with this configuration, and conclude whether or not management should adopt this proposal
5. A local shrimp company processes and packages shrimp for sale to wholesale seafood distributors. The shrimp are transported to the main plant by trucks that carry 1,000 lbs. of shrimp. Once the continuous flow processing of the shrimp begins, no inventory is allowed at any point in the process due to spoilage and all of the shrimp must be processed within 12 hours to prevent spoilage.
The processing begins at the sorter, where the trucks dump the shrimp onto a conveyer belt that feeds into the sorter, which can sort up to 500 lbs. per hour. The shrimp then proceed to the desheller, which can process shrimp at a rate of 400 lbs. per hour. However, after 3 hours and 45 minutes of processing, the desheller must be stopped for 15 minutes to clean out empty shrimp shells that have accumulated. The veins of the shrimp are then removed in the deveining area at a maximum rate of 360 lbs. per hour. Finally, the shrimp proceed to the washing area, where they are processed at 750 lbs. per hour.
Note: All unit weights given are in "final processed shrimp". You do NOT need to account for the weight of the waste in the deshelling area. The plant operates continuously for 12 hours per day beginning at 8.00 am. Finally, there is a negligible time to fill the system in the morning
a) What is the daily process capacity of the desheller (in isolation from the other processes)?
b) What is the daily process capacity of the deveiner (in isolation from the other processes)?
c) What is the daily process capacity of the processing plant?
d) If five trucks arrive one morning at 8.00 am, what is the total number of pounds of shrimp that must be wasted?