Esercitazioni svolte - Programmazione e controllo della produzione

Q2.2 Baggage check-in of a small airline

Consider the baggage check-in of a small airline. Check-in data indicate that from 9 a.m. to 10 a.m., 255 passengers checked in. Moreover, based on counting the number of passengers waiting in line, airport management found that the average number of passengers waiting for check-in was 35. How long did the average passenger have to wait in line?

Q2.3 Manufacturing company producing medical devices

A manufacturing company producing medical devices reported $60,000,000 in sales over the last year. At the end of the same year, the company had $20,000,000 worth of inventory of ready-to-ship devices.

a. Inventory turnover

Assuming that units in inventory are valued (based on COGS) at $1,000 per unit and are sold for $2,000 per unit, how fast does the company turn its inventory? The company uses a 25 percent per year cost of inventory. That is, for the hypothetical case that one unit of $1,000 would sit exactly one year in inventory, the company charges its operations division a $250 inventory cost.

b. Per unit inventory cost

What—in absolute terms—is the per unit inventory cost for a product that costs $1,000?

Q2.5 LaVilla village in the Italian Alps

LaVilla is a village in the Italian Alps. Given its enormous popularity among Swiss, German, Austrian, and Italian skiers, all of its beds are always booked in the winter season and there are, on average, 1,200 skiers in the village. On average, skiers stay in LaVilla for 10 days.

a. New skier arrivals

How many new skiers are arriving—on average—in LaVilla every day?

b. Percentage change in revenues

A study done by the largest hotel in the village has shown that skiers spend on average $50 per person on the first day and $30 per person on each additional day in local restaurants. The study also forecasts that—due to increased hotel prices—the average length of stay for the 2003/2004 season will be reduced to five days. What will be the percentage change in revenues of local restaurants compared to last year (when skiers still stayed for 10 days)? Assume that hotels continue to be fully booked!

Q2.6 Flow rate on the highway

While driving home for the holidays, you can’t seem to get Little’s Law out of your mind. You note that your average speed of travel is about 60 miles per hour. Moreover, the traffic report from the WXPN traffic chopper states that there is an average of 24 cars going in your direction on a one-quarter mile part of the highway. What is the flow rate of the highway (going in your direction) in cars per hour?

Q2.7 Strohrmann bakery production process

Strohrmann, a large-scale bakery in Pennsylvania, is laying out a new production process for their packaged bread, which they sell to several grocery chains. It takes 12 minutes to bake the bread. How large an oven is required so that the company is able to produce 4,000 units of bread per hour (measured in the number of units that can be baked simultaneously)?

Q3.1 Process with three resources

Consider a process consisting of three resources: What is the bottleneck? What is the process capacity? What is the flow rate if demand is eight units per hour? What is the utilization of each resource if demand is eight units per hour?

Q3.2 Process with five resources

Consider a process consisting of five resources that are operated eight hours per day. The process works on three different products, A, B, and C:

Demand for the three different products is as follows: product A, 40 units per day; product B, 50 units per day; and product C, 60 units per day.

Bottleneck and flow rate

What is the bottleneck? What is the flow rate for each flow unit assuming that demand must be served in the mix described above (i.e., for every four units of A, there are five units of B and six units of C)?

Q3.3 International Cranberry Uncooperative (ICU)

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 there 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. Maximum barrels waiting

What is the maximum number of barrels of cranberries that are waiting on the trucks at any given time?

b. Trucks stop waiting

At what time do the trucks stop waiting?

c. Bins empty time

At what time do the bins become empty?

d. Processing with seasonal workers

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?

Q3.6 VF Accounting Firm

VF is a small accounting firm supporting wealthy individuals in their preparation of annual income tax statements. Every December, VF sends out a short survey to their customers, asking for the information required for preparing the tax statements. Based on 24 years of experience, VF categorizes their cases into the following groups:

• Group 1 (new customers, easy): 15 percent of cases
• Group 2 (new customers, complex): 5 percent of cases
• Group 3 (repeat customers, easy): 50 percent of cases
• Group 4 (repeat customers, complex): 30 percent of cases

Here, “easy” versus “complex” refers to the complexity of the customer’s earning situation. In order to prepare the income tax statement, VF needs to complete the following set of activities. Processing times (and even which activities need to be carried out) depend on which group a tax statement falls into. All of the following processing times are expressed in minutes per income tax statement. The activities are carried out by the following three persons:

• Administrative support person: filing and writing.
• Senior accountant (who is also the owner): initial meeting, review by senior accountant.
• Junior accountant: preparation.

Assume that all three persons work eight hours per day and 20 days a month. For the following questions, assume the product mix as described above. Assume that there are 50 income tax statements arriving each month.

a. Bottleneck identification

Which of the three persons is the bottleneck?

b. Utilization of personnel

What is the (implied) utilization of the senior accountant? The junior accountant? The administrative support person?

c. Profitability analysis

You have been asked to analyze which of the four product groups is the most profitable. Which factors would influence the answer to this?

d. Process capacity change

How would the process capacity of VF change if a new word processing system would reduce the time to write the income tax statements by 50 percent?

Q3.5 Bagel store production process

Consider a bagel store selling three types of bagels that are produced according to the process flow diagram outlined below. We assume the demand is 180 bagels a day, of which there are 30 grilled veggie, 110 veggie only, and 40 cream cheese. Assume that the workday is 10 hours long and each resource is staffed with one worker.

a. Bottleneck identification

Where in the process is the bottleneck?

b. Hourly production capacity

How many units can the process produce within one hour, assuming the product mix has to remain constant?

Q3.9 Airport check-in process

Kim Opim, an enthusiastic student, is on her flight over from Philadelphia (PHL) to Paris. Kim reflects upon how her educational experiences from her operations courses could help explain the long wait time that she experienced before she could enter the departure area of Terminal A at PHL. As an airline representative explained to Kim, there are four types of travelers in Terminal A:

• Experienced short-distance travelers: These passengers check in online and do not speak with any agent nor do they take any time at the kiosks.
• Experienced long-distance travelers: These passengers spend 3 minutes with an agent.
• Inexperienced short-distance travelers: These passengers spend 2 minutes at a kiosk; however, they do not require the attention of an agent.
• Inexperienced long-distance travelers: These passengers need to talk 5 minutes with an agent.

After a passenger checks in online, or talks with an agent, or uses a kiosk, the passenger must pass through security, where they need 0.5 minutes independent of their type. From historical data, the airport is able to estimate the arrival rates of the different customer types at Terminal A of Philadelphia International:

• Experienced short-distance travelers: 100 per hour
• Experienced long-distance travelers: 80 per hour
• Inexperienced short-distance travelers: 80 per hour
• Inexperienced long-distance travelers: 40 per hour

At this terminal, there are four security check stations, six agents, and three electronic kiosks. Passengers arrive uniformly from 4 p.m. to 8 p.m., with the entire system empty prior to 4 p.m. (the “midafternoon lull”) and no customers arrive after 8 p.m. All workers must stay on duty until the last passenger is entirely through the system (e.g., has passed through security).

a. Implied utilization levels

What are the levels of implied utilization at each resource?

b. Departure time of last passenger

At what time has the last passenger gone through the system? Note: If passengers of one type have to wait for a resource, passengers that do not require service at the resource can pass by the waiting passengers!

c. Kim's wait time

Kim, an experienced long-distance traveler, arrived at 6 p.m. at the airport and attempted to move through the check-in process as quickly as she could. How long did she have to wait before she was checked at security?

d. Educational program impact

The airline considers showing an educational program that would provide information about the airport’s check-in procedures. Passenger surveys indicate that 80 percent of the inexperienced passengers (short or long distance) would subsequently act as experienced passengers (i.e., the new arrival rates would be 164 experienced short-distance, 112 experienced long-distance, 16 inexperienced short-distance, and 8 inexperienced long-distance [passengers/hour]). At what time has the last passenger gone through the system?

Q4.2 Assignment of tasks on a conveyor-paced assembly line

Consider the following six tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task:

a. Current line capacity

What is the capacity of the current line?

b. Maximizing capacity with adjacent operations

Now assume that tasks are allocated to maximize capacity of the line, subject to the conditions that (1) a worker can only perform two adjacent operations and (2) all tasks need to be done in their numerical order. What is the capacity of this line now?

c. Maximizing capacity with any order of tasks

Now assume that tasks are allocated to maximize capacity of the line and that tasks can be performed in any order. What is the maximum capacity that can be achieved?

Q4.3 PowerToys Inc. production process

PowerToys Inc. produces a small remote-controlled toy truck on a conveyor belt with nine stations. Each station has, under the current process layout, one worker assigned to it. Stations and processing times are summarized in the following table:

a. Bottleneck identification

What is the bottleneck in this process?

b. Assembly line capacity

What is the capacity, in toy trucks per hour, of the assembly line?

c. Direct labor cost with current process

What is the direct labor cost for the toy truck with the current process if each worker receives $15/hour, expressed in dollars per toy truck?

d. Direct labor cost with work cell

What would be the direct labor cost for the toy truck if work would be organized in a work cell; that is, one worker performs all tasks? Assume that the processing times would remain unchanged (i.e., there are no specialization gains).

e. Worker utilization at station 2

What is the utilization of the worker in station 2?

f. Assignment of tasks with reduced staffing

Because of a drastically reduced forecast, the plant management has decided to cut staffing from nine to six workers per shift. Assume that (i) the nine tasks in the preceding table cannot be divided; (ii) the nine tasks are assigned to the six workers in the most efficient way possible; and (iii) if one worker is in charge of two tasks, the tasks have to be adjacent (i.e., one worker cannot work on tasks 1 and 3, unless the worker also does task 2).

How would you assign the nine tasks to the six workers?

g. New capacity of the line

What is the new capacity of the line (in toy trucks per hour)?

Q4.6 Production of Yoggo soft drink

A small, privately owned Asian company is producing a private-label soft drink, Yoggo. A machine-paced line puts the soft drinks into plastic...