The Exam Is to Be Done Individually, Without Collaboration with Anyone Else

ISyE 6203 Spring 2005 Exam 2 Vande Vate

Instructions

You have 90 minutes to complete the exam. Watch your time. If you are having difficulty with a question, you might wish to pass over it and return to it later if you have enough time at the end of the exam.

Be sure to put your name on your exam. Show your work – that will allow me to award partial credit. Make sure your answers are legible and clearly marked.

The exam is open book: you may use any notes or text material. The exam is to be done individually, without collaboration with anyone else. 1. (25 points) A major retailer works a third-party logistics firm (3PL) to consolidate and coordinate shipments from several regional suppliers to its stores nation- wide. The suppliers ship goods to the 3PL’s regional consolidation facility in full truckloads. At the consolidation facility, the 3PL unloads the suppliers’ trucks, sorts the goods and loads them onto trucks destined to regional distribution centers (RDCs). The retailer operates 10 regional distribution centers across the country.

Each supplier ships goods to the consolidation facility in 53ft trailers with a cubic capacity of approximately 3,900 cubic feet. At the consolidation facility, workers unload in-bound trucks from suppliers, sort the goods by destination and stage them for shipment to the RDCs. Whenever an out-bound load will fill a trailer, an empty trailer is called in, loaded and dispatched.

Five major suppliers ship to the consolidation facility. The following table shows the cubic feet each supplier ships to the consolidation facility, how those volumes are allocated among the different RDCs and the total cost of the goods each supplier provides on an annual basis.

Cubic feet per year from each supplier to each RDC RDC\Supplier 1 2 3 4 5 Total 1 45,990 7,987 367,608 82,764 660,654 1,165,003 2 559,208 309,125 306,180 1,836 167,440 1,343,789 3 118,668 428,200 528,581 606,882 232,470 1,914,801 4 231,868 247,766 30,134 268,398 22,491 800,657 5 646,196 198,856 334,359 340,912 75,854 1,596,177 6 293,040 268,970 35,644 333,840 34,008 965,502 7 636,320 26,384 143,521 38,114 95,690 940,029 8 81,286 45,838 461,168 327,516 114,576 1,030,384 9 185,318 274,832 57,323 171,648 85,488 774,609 10 636,075 94,146 87,696 428,352 927,673 2,173,942 Total 3,433,969 1,902,104 2,352,214 2,600,262 2,416,344 12,704,893 Total Value $ 35,903,088 $84,898,342 $ 73,485,270 $238,093,925 $ 25,170,922 $457,551,547 a. Provide an estimate of the average cubic feet of inventory in the consolidation facility. Be sure to explain your estimate.

The facility should have on average approximately ½ a truck load of inventory for each destination it serves. Since it serves 10 RDCs it will have 5 truckloads of inventory on average or about 19,500 cubic feet of inventory.

b. Provide an estimate of the average capital tied up in inventory at the consolidation facility. Be sure to explain your estimate.

Dividing the total value of the goods by their total volume yields an average value density of around $36/cubic foot. So the average value of inventory should be around $36*19,500 = $702,000.

c. The transit time from the supplier 1 to the consolidation facility is 8 hours. The transit time from the consolidation facility to RDC 9 is 48 hours. Provide an estimate of how long it takes products from supplier 1 to reach RDC 9 on average. Assume the operations run 24 hours a day, 365 days per year. Be sure to explain your estimate.

While the goods spend only 56 hours in transit, they also spend some time waiting at the consolidation facility. Since we send 198 = 774,609/3,900 trucks to RDC 9 each year. Hence, the average headway, or time between departures to RDC 9 is about 1.84 days or 44 hours. Some goods arrive at the start of this headway and some arrive at the end, so on average it is safe to estimate that goods spend about 22 hours waiting for the trailer to fill. Thus, the total time is about 78 hours. 2. (25 points) A company manufactures 3 models of a high value electronics product for distribution to customers in the US. The products are currently produced in Xiamen and shipped to Los Angeles for distribution. The product costs us roughly $200 per unit. We sell about 400,000 units annually. To fly the product from Xiamen takes 2 days and costs $7.50 per unit. To ship the product by ocean takes 20 days and costs $0.50 per unit. Our inventory holding charge is 25% per year. d. Should we ship this product by air or by ocean? Explain your answer.

Use Ocean. We sell about 1,100 units per day so 20 days of pipeline inventory is 22,000 units or about $4,400,000 at 25% that’s about $1,100,000 in pipeline inventory carrying costs and about 400,000*$0.25 = $100,000 in transportation annually.

If we used air, the pipeline inventory would drop to one tenth the value by sea or $110,000 while the transportation costs would increase 15 fold to $1,500,000. e. Customers for this product are very demanding and will not wait for delivery. Anytime an order is placed for a product in Los Angeles and the exact model is not available, the company loses the sale to a competitor. Consequently, management has decided to maintain a 98% fill rate by holding 2 standard deviations in lead-time demand in safety stock. The manufacturer has been exploring a postponement strategy that consists of shipping undifferentiated modules to Los Angeles and transforming them into the different models there. This strategy does not change the manufacturing costs in Xiamen at all, but does add $0.25 per unit in manufacturing costs in Los Angeles. This activity is provided by a third party and so there are no appreciable fixed costs involved in the postponement strategy. Should the manufacturer employ the postponement strategy and, if so, for which models? The following information may prove helpful. Be sure to explain your answer.

Model Annual Sales (units) Std. Dev. In Lead-time Demand (units) 1 100,000 1000 2 100,000 400 3 200,000 20

There are three options to consider: 1. Do not use the postponement strategy 2. Use the postponement strategy for everything 3. Use the postponement strategy for everything except model 3.

If we do not use the postponement strategy at all, we carry 2000 units of model 1 2000 units of model 2 and 40 units of model 3 as safety stock The total cost of holding this stock is $200*4040*.25 = $202,000 annually

If we use the postponement strategy for everything, we will pay $100,000 just for manufacturing in Los Angeles, but our safety stock will drop to something like 2828 units. Which will cost more than $141,000 to hold.

If we use the postponement strategy just for models 1 and 2, we will pay $50,000 for manufacturing in Los Angeles and our safety stock for these two items will drop from 4,000 units to something like 2828 units. Saving 1172 units of safety stock is worth about $50*1172 = $58,600. So it’s a tough call. We should probably study the relationship between the two models’ demands more closely to determine whether they are positively or negatively correlated. The decision would also depend on the balance between the added complexity and the added flexibility. 3. (25 points) In this case we sell fashion products that are produced in Europe and shipped to customers in the US for sale. The product costs us roughly $500 per unit. To fly the product from Austria takes 2 days and costs $7.50 per unit. To ship the product by ocean takes 20 days and costs $0.50 per unit. There is less competition for our product so customers are willing to wait a few days if we are out of stock – long enough for us to fly more product over. If we bring too much to market however, we can only sell the excess by discounting the selling price to $475. Our forecasts suggest demand is likely to be 10,000 units, but since we are not confident in our forecasts, we take demand to be normally distributed with mean 10,000 and standard deviation 1,000, i.e., N(10000, 1000). Describe how we should decide how much to bring to the US by ship.

The risk the last item faces is the $25 loss should we fail to sell it and the $7.00 should we need to expedite it. So, clearly there is a much greater risk involved in shipping too much. We want to ship so that there’s a 25/32 chance demand is greater than what we ship. i.e., we should ship about 9,223 units by ocean. This last step may require tools not available to everyone, so it is fine to say that you would choose the amount so that the cumulative probability to that point was 7/32 or about .22 4. (25 points) Container ships travel along routes or rotations. For example Hapag Lloyd’s Europe – Asia Loop A follows the rotation: Southampton – Rotterdam – Hamburg – Le Havre – Singapore –Kobe – Nagoya – Tokyo – Shimizu – Singapore and back to Southampton.

Intermediate stops at ports tend to make transits longer and less reliable. So, we are only willing to use a rotation to move containers from point A to point B if the rotation includes at most two stops between these two ports. For example, we would use Hapag Lloyd’s Europe – Asia route A to move containers from Shimizu to Southampton (as this involves only one intermediate stop in Singapore), or from Tokyo to Southampton (because that would require only two intermediate stops in Shimizu and Singapore), but we would not use it from Le Havre to Tokyo because that requires three intermediate stops.

Give a set of rotations: Rotation 1, Rotation 2, … Rotation r and a set of origin- destination pairs: o-d 1, o-d 2, o-d 3, …o-d n formulate a linear mixed integer model to find a smallest set of rotations that we can use to service all the origin – destination pairs.

Use the spreadsheet on the next page to illustrate your model. Identify the objective, variables, constraints and formulas here:

The cells B17:F20 are 1 if the origin – destination pair can be served by the rotation and 0 otherwise.

The cell G17 includes the formula =SUMPRODUCT(B17:F17, B21:F21) . This counts the number of times the selected rotations serve the origin – destination pair Singapore – Hamburg.

Similarly for G18, G19 and G20.

The cell G21 holds the formula =SUM(B21:F21), the number of rotations we selected.

This is the objective function.

The decision variables are B21:F21. These are binary and indicate whether or not we choose the rotation.

The only other constraint is that G17:G20 >= 1, i.e., that each origin-destination pair is served by at least one of the rotations we chose. A B C D E F G H I 1 Rotations Lanes 2 1 2 3 4 5 Origin Destination 3 Kobe Shanghai Shekou Pusan Shanghai Singapore Hamburg 4 Nagoya Ningbo Yantian Shanghai Xiamen Yantian Hong Kong 5 Tokyo Keelung Hong Kong Hong Kong Yantian Singapore Rotterdam 6 Shimizu Chiwan Singapore Singapore Hong Kong Singapore Southampton 7 Singapore Port Kelang Rotterdam Port Kelang Singapore 8 Southampton Constanza Hamburg Le Havre Southampton 9 Rotterdam Istanbul Southampton Rotterdam Hamburg 10 Hamburg Damietta Antwerp Rotterdam 11 Le Havre Bremerhaven 12 13 14 15 Rotation 16 1 2 3 4 5 Total Origin Destination 17 0 0 1 0 1 =SUMPRODUCT(B17:F17, B21:F21) Singapore Hamburg 18 0 0 1 0 1 =SUMPRODUCT(B18:F18, B21:F21) Yantian Hong Kong 19 1 0 1 1 1 =SUMPRODUCT(B19:F19, B21:F21) Singapore Rotterdam 20 1 0 1 0 1 =SUMPRODUCT(B20:F20, B21:F21) Singapore Southampton 21 =SUM(B21:F21) 22 23 24 25 26 27 28 29