Reference no: EM13667539

Problem 1: Process Analysis 

The company Furniture Face Lift refinishes old wood furniture. Their process for refinishing chairs has 8 workers and 4 stations. Each chair starts at the Stripping station, then goes to Priming, then to Painting and finally to Inspection. Where there are multiple workers within a station, each worker works independently on his/her own chair. Assume inventory buffers are allowed between each station.

Station Staffing Processing time (hours per chair per worker)
Stripping 3 2.5
Priming 2 1.5
Painting 2 1.75
Inspection 1 0.8

a) What is the maximum number of chairs per hour that can be produced? Assume they start the day with inventory at each station to work on.

Process Capacity (chairs/hour) __

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b) Suppose at the start of the day there is no inventory of chairs in the shop. That is, there are no chairs within any of the stations or between them in any buffer. A truck loaded with 15 chairs arrives. How many hours will it take Furniture Face Lift to complete these 15 chairs?

Throughput Time (hours) ___

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c) Suppose now that each worker is trained to do all tasks and each worker works on a chair from start to finish, i.e., each worker does Stripping, Priming, Painting and Inspection. What is the maximum capacity of the process in chairs per hour?

Process Capacity (chairs/hour) _______

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Problem 2: More Process Analysis 

The White Tooth Device Company is a manufacturer of high-end electric toothbrushes. For each toothbrush, there is a sequence of assembly steps performed by five workers. Each worker does two tasks. Inventory buffers are allowed between workers.

Worker Task Time (seconds)
A T1 40
A T2 25
B T3 20
B T4 15
C T5 10
C T6 15
D T7 10
D T8 20
E T9 25
E T10 35

a) What is the capacity of this process in toothbrushes per hour?

Process Capacity (toothbrushes/hour) _________

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b) Suppose two workers are hired, F and G, and they take the same time to complete tasks as the current five workers. F and G can be assigned to work on the same pair of tasks as one of the current workers. For example, F could be assigned tasks T1 and T2 (just like worker A) while G is assigned T5 and T6 (just like worker C). They cannot be assigned tasks that are currently assigned to two workers. For example, F cannot be assigned to tasks T2 and T3 (because they are currently being done by workers A and B). What is the capacity in toothbrushes per hour of this process with workers F and G included?

Process Capacity (toothbrushes/hour) _______

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c) Return to the case with 5 workers. Suppose the assignment of tasks to workers can change but the sequence of tasks must remain the same, workers must be assigned to consecutive tasks, and each task can be assigned to only one worker. For example, worker A could do tasks T1-T3 (because they are consecutive) but cannot be assigned T1, T2 and T4. If worker A is assigned to tasks T1-T3, then worker B's first task must be T4 (worker B cannot also be assigned to task T3). Because a U-shaped line is used, tasks T1 and T10 can actually be considered consecutive tasks - worker A could be assigned tasks T10, T1 and T2. What tasks should be assigned to each worker in order to maximize the capacity of the process? What is the resulting process capacity in toothbrushes per hour?

Assignment of Tasks to Workers _______ ______ _______ _______ _______
A B C D E
(3 points)

Process Capacity (toothbrushes/hour) ___________

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Problem 3: Batching

Sarah's Organic Soap Company makes four kinds of organic liquid soap- "regular", "lavender", "citrus" and "tea tree". Demand for the four scents is 150, 120, 75 and 55 kgs per hour respectively. Sarah's production process can produce any soap at the rate of 450 kgs per hour but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn't produce any soap. Sarah wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand and (iii) minimizes the amount of inventory held.

a) How many kgs of "regular" should Sarah produce before switching over to another scent?

Batch Size (kgs) ___________

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b) Sarah needs to purchase organic Palm oil to make her soaps. She needs 1,000 kgs of Palm oil per day on average. The supplier charges a $60 delivery fee per order (which is independent of the order size) and $4.75 per kg. Sarah's annual holding cost is 25%. Assume 52 weeks per year and 5 days per week. If Sarah wants to minimize inventory holding and ordering costs, how much Palm oil should she purchase with each order (in kgs)?

Optimal Order Quantity (kgs) _________

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c) Sarah's supplier is willing to sell Palm oil at a 5% discount if she purchases 10,000 kgs at a time. If she were to purchase 10,000 kgs per order what would be her average inventory holding and delivery fees per day? (Note, do NOT include Sarah's purchasing costs per day, which would be 1000 * 4.75 * 95%.)

Cost per Day ($) ___________

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Problem 4: Queuing 

Pharma Dev develops and markets new technological products to be used in health care. The development of a new product operates as follows: when a new technology meets the requisite market potential, a new patent is filed. Patents are granted for a period of 12 years starting from the date of issue. Once the patent is filed, the new technology is developed at one of its three independent development centers, and is then launched to the market. Each product is developed at only one center, and each center can only develop a single patented technology at a time.

On average, Pharma Dev files a new patent every 5 months (with standard deviation of 5 months). The average development process lasts 12 months (with standard deviation of 24 months).

a) What is the utilization of Pharma Dev's development facilities?

Utilization _________

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b) How long does it take for the average technology from filing a patent to the start of the development process?

Average Waiting Time (months) _______

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c) How many years of patent life remain on average when a product is launched to the market?

Remaining Patent Time (months) ___________

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d) On average how many patented products are undergoing development or waiting to be developed?

Inventory (products) _____________

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Pharma Dev is considering leasing an additional development center to shorten the time to market of patented products. If this center is used in addition to the three centers, by how will the total time-to-market (waiting time plus development time) of a patented product change?

Change in Time-to-Market (months) ___________
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e) After a product is launched to the market, it generates gross margins of US$40 million per year of patent life. After the patent expires, the product generates no gross margins. By how much would leasing the new facility increase Pharma Dev's average total annual gross margins?

Increase in Average Annual Gross Margin ($)

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Problem 5: Newsboy Model
Betty Cooker runs a bakery in San Francisco that specializes in her famous Black Forest cakes. These cakes come with four kinds of frostings-Vanilla, Chocolate, Raspberry and Devilicious. She estimates that the daily demand for each type of cake is independent and normally distributed with mean 50 and standard deviation 20. Each customer wants to buy exactly one cake. Customers who favor a particular type of frosting will not buy any other if their preferred frosting is out of stock. Every day in the morning, Betty Cooker and her team of bakers prepare a fresh batch of the cakes for sale that day. Her costs to bake and top each cake are $5. Each cake sells for $15. Betty's Bakery prides itself on its fresh assortment, so cakes not sold by the end of that day are given away to a soup kitchen for the homeless.

a) Suppose Betty wants to bake enough cakes so that she can be 97.5% sure that she can satisfy the demand for all of her customers. How many cakes with Devilicious frosting should she prepare daily in the morning? What is the associated expected profit?

Quantity ________________

Expected Profit _______________

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b) Suppose Betty wants to bake enough cakes so that she can satisfy 97.5% of her customers' demand. How many cakes with Devilicious frosting should she prepare daily in the morning? What is the associated expected profit?

Quantity ________________

Expected Profit _______________

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c) How many cakes with Devilicious frosting should Betty prepare daily in the morning if her objective is to maximize expected profit? What is the associated expected profit?

Quantity ________________

Expected Profit _______________
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Problem 6: Risk Pooling

The Sweater Factory stocks specialty cashmere sweaters that carry the University of Georgia logo. The company started this line to sell to two local firms (Firm A and Firm B) who use these items as gifts for senior executives and important customers. The sweaters are available in two colors, with red sweaters made exclusively for Firm A and black sweaters made exclusively for Firm B. Both red and black sweaters cost c = $20 per unit, but red sweaters sell for p = $50, while black sweater are priced at p = $30. The sweaters have no value after the selling season, i.e., v = $0 for both colors. Because of long lead times, the Sweater Factory must order well in advance of the selling season.

Before placing an order for red and black sweaters, you call on your contacts at Firm A and Firm B. Neither of these contacts can tell you how many units their firm will ultimately order, but the contact at Firm A states that there is a 50% chance that they will want 50 units and a 50% chance they will want 100. Similarly, the contact at Firm B states that there is a 50% chance that they will want 100 units and a 50% chance they will want 200. No other quantities are considered possible.

a. How many units of red sweaters should be ordered to maximize expected profit? What is the associated expected profit?

Number of Units of Red Sweaters to Order _________

Expected Profit __________

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b. How many units of black sweaters should be ordered to maximize expected profit? What is the associated expected profit?

Number of Units of Black Sweaters to Order _________

Expected Profit ___________

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c. The manufacturer of this line of sweater advises you that you may order sweaters uncolored. The advantage of an uncolored sweater is that it can be dyed by a local supplier during the selling season, allowing it to satisfy demand for red sweaters if necessary or black sweaters otherwise. The downside is the added cost - the cost to the Sweater Factory to deliver an uncolored sweater is $20, but it costs another $1 to dye the sweater (note that the latter cost is only incurred if the sweater is sold. Given this alternative, how many red, black, and uncolored sweaters should be ordered to maximize expected profit? What is the associated expected profit?

Number of Units of Red Sweaters to Order ________

Number of Units of Black Sweaters to Order _________

Number of Units of Uncolored Sweaters to Order _________

Expected Profit _________

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Problem 7: Supply Chain Coordination

A supplier manufactures a product at cost m = $50 and sells it to a retailer at wholesale price c = $150. The retailer sells this product to consumers at retail price p = $250. The replenishment lead time for this product is long relative to the selling season, so the retailer only has one opportunity to stock the product. Demand for the product is normally distributed with a mean of 1200 units and a standard deviation of 500 units. Units unsold at the end of the season are salvaged at price v = $20.

a. How many units of the product should the retailer order to maximize its expected profit? What is the associated retailer's expected profit and the supplier's expected profit?

Number of Units to Order _____________

Retailer's Expected Profit _____________

Supplier's Expected Profit _____________

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b. How many units of the product should the retailer order to maximize total supply chain expected profit? What is the associated retailer's expected profit and the supplier's expected profit?

Number of Units to Order _____________

Retailer's Expected Profit _____________

Supplier's Expected Profit _____________

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c. To motivate the retailer to buy more product, the supplier offers the following deal: the wholesale price is reduced to c = $70, but the retailer must pay the supplier an additional $100 for every unit that it sells. The supplier is also willing to buy back units that the retailer is unable to sell at buyback price b. These units are then salvaged by the supplier. What value of b should the supplier offer to maximize total supply chain expected profit? What is the associated retailer's expected profit and the supplier's expected profit?

Optimal Buyback Price _____________

Retailer's Expected Profit _____________

Supplier's Expected Profit _____________

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