Question 1:
a. Give an example each of a functional product and an innovative product.
b. Characterize functional/innovative products by choosing the appropriate adjective from the last column.
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Product Characteristic
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Functional Product
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Innovative Product
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Choose From
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Lifecycle length
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Long/Short
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Contribution margin
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High/Low
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Product variety
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Lot/Little
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Forecast errors
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Large/Small
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Stockout rates
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High/Low
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Forced end-of-season markdowns
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Frequent/Rare
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Order lead time
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Long/Short
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c. It is claimed that a supply chain has two functions: a physical function, and a market mediation function. Explain what these terms mean.
d. Supply chains are generally of two types: physically efficient supply chains, and market responsive supply chains. What type of supply chain would be suitable for a functional product? Why?
Question 2
The boardwalk on the Paradise City beach is 4 miles long with mile markers at 0, 1, 2, 3, and 4 miles, There are 100 customers at each mile marker and each customer's demand for ice cream is given by the function: D = 24 - 4d, where d = distance between customer and nearest ice cream vendor.
There are two ice cream vendors (A and B) and they are currently located at mile markers 1 and 2 as shown above.
a. Find out the demand at each vendor and total demand for the system.
b. Are these the best locations of the vendors from the system's point of view? If not, suggest better locations for the vendors. What is the total system demand now?
c. Compute how much and to whom an incentive should be offered so that the vendors relocate to the optimal locations from the system's point of view? (Assume one unit of ice cream generates $1.50 in profit.)
Question 3
RFC Bearings has just entered the U.S .market. It has three major DCs in the Atlanta, Boston, and Chicago areas.
Annual demand served by each DC is estimated to be:
Atlanta 10,000 Boston 20,000 Chicago 15,000
Four plants (Memphis, Philadelphia, Toledo) supply the DCs. Per-unit transportation costs and plant capacities are given in the following table:
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Plant Location
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Distribution Center
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Plant
Capacity
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Atlanta
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Boston
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Chicago
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Memphis
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$3
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9
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7
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30,000
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Philadelphia
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5
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2
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4
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35,000
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Toledo
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6
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6
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2
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35,000
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a. Using the notation:
XMA = Qty shipped from Memphis to Atlanta
XMB = Qty shipped from Memphis to Boston, etc.,
write down a model that will determine the optimal demand allocation (i.e. minimize transportation costs.)
b. Suppose now that the three locations (Memphis, Philadelphia, Toledo) are potential locations, i.e., each plant would only be constructed if it improves overall cost (i.e., transportation plus plant fixed costs). The data is repeated here with the (annualized) plant fixed costs shown additionally.
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Plant Location
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Distribution Center
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Plant
Capacity
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Annualized
Fixed Costs
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Atlanta
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Boston
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Chicago
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Memphis
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$3
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9
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7
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30,000
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$50,000
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Philadelphia
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5
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2
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4
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35,000
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45,000
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Toledo
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6
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6
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2
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35,000
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48,000
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What changes would you make to the model in part (a) so that we can determine the optimal locations of the plants as well as the optimal demand allocation (i.e. minimize both transportation as well as fixed costs).
[Do not attempt to solve this model-you are only asked to write down the algebraic model, i.e. objective function and constraints. Also, this question has nothing to do with Excel.]
Question 4
Consider the following data pertaining to a distribution center.
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Parameter
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Value
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Mean Weekly Demand
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100
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Standard Deviation of Weekly Demand
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30
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Lead Time
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2 Weeks
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# of weeks in year
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50
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Ordering cost: $50 /order
Holding cost: $4 /unit /week (This is H, not hc - see eq. (11.2), p. 273 of text.)
Cycle service level: 97%
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Measure
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Computation
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order quantity
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cycle inventory
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safety inventory
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reorder level
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number of orders per year
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annual inventory holding cost
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Question 5
Suppose the 100 retail stores of a supermarket chain have identical weekly demand for a product (mean 200, standard deviation 120). There is zero correlation between the retailers' demands. The lead time to replenish each retail store is 4 weeks. A cycle service level of 95% is desired.
a. If each retail store maintains its own dedicated warehouse, how much safety stock is needed at each store?
b. What is the total safety stock across all stores?
c. It is now proposed to have a central DC servicing all 100 retailers. The lead time to replenish the DC is the same (4 weeks). How much safety stock is needed at the DC to maintain the same cycle service level?
d. If annual inventory holding cost is $50/unit/year, how much money was saved as a result of the decrease in the safety stock?
Question 6
AspenWear, a retailer of ski wear needs to place an order for the Mirabelle, a designer ski jacket for the high-end market. The jacket retails for $600 and costs AspenWear $250 from a source in China. Due to fickle customer tastes, any surplus jackets at the end of the ski season cannot be carried over to the next season but must be disposed of. A bargain discounter has offered to buy these jackets at $150 each. Also, because of the long lead times involved in sourcing from China, there is realistically only one opportunity to place an order during each season (in November of each year so that the jackets will be ready by the following August). From past history, AspenWear believes that demand for the Mirabelle can be represented by a normal distribution with mean 6000 and standard deviation 3600.
a. Compute the order quantity that will maximize AspenWear's expected profit.
b. Compute the following performance measures for the above order quantity: expected sales, expected overstock, and expected profit.
Question 7
A movie studio sells the latest movie on DVD to Blockbuster at $10 per DVD. The marginal production cost for the movie studio is $2 per DVD. Blockbuster prices each DVD at $25 to its customers. DVD s are kept on the regular rack for a one-month period, after which they are discounted down to $3. Blockbuster places a single order for DVDs. Their current forecast is that sales will be normally distributed, with a mean of 50,000 and a standard deviation of 30,000.
a. How many DVDs should Blockbuster order? What is its expected profit?
b. What is the profit that the studio makes given Blockbuster's actions?
c. The studio is offering Blockbuster a deal: They will sell the DVD to blockbuster at $5 each in return for a 65-35 split of the revenue (65% to Blockbuster). Should Blockbuster agree to this deal?