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Arts N Crafts Industries manufacturers high-end light fixtures, which it sells internationally. The company is responsible for paying for shipping its product to a distributor located in Atlanta, Georgia. Due to the high cost of shipping, the company is considering shipping its products unassembled, but will include detailed assembly instructions in each package. By shipping unassembled products, Arts N Crafts will be able to shrink the size of its cartons and thereby increase the number of products per pallet from 16 (4 rows of 4) to 25 (5 rows of 5). Note that this change will not appreciably increase each product’s 8-pound shipping weight. Furthermore, since individual fixtures will be packed more tightly, they will be less susceptible to damage and easier to handle. Thus, the company expects the freight class to decrease from 85 to 70. Currently the company ships 400 units per week. a. Using Table 15.2, assess the impact of the proposed change in packaging on weekly shipping cost. b. How will your analysis change if demand for the product increases to 500 units per week?

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Helping Harvest is a food bank in the Greater Miami area that collects food donations from local grocery stores and transports them back to a distribution center for sorting and transfer to local food kitchens that feed needy clients. Tight budgets and environmental concerns require that both fuel and driver resources be used sparingly. Thus, Mr. Vivek, Helping Harvest’s general manager, would like to ensure that collection vehicles are routed most efficiently. The table below provides the driving distance in miles among the depot (the distribution center from where truck begins and ends its route) and the five stores that donate food. From/To Depot Store A Store B Store C Store D Store E Depot – 10 24 60 40 26 Store A 10 – 34 46 35 44 Store B 24 34 – 48 20 15 Store C 60 46 48 – 15 35 Store D 40 35 20 15 – 12 Store E 26 44 15 35 12 – Currently, the Helping Harvest truck travels the following route Depot–Store A–Store B–Store C–Store D–Store E–Depot. a. Use the NN heuristics to find a shorter route and calculate the savings in miles traveled per day. b. The manager at Store B would like the Helping Harvest truck to pick up from her store as early as possible. How many miles does the constraint of visiting Store B first add to the route selected in part a?

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On Thursdays, Traxis Consolidated delivers liquid oxygen to its industrial customers in northern Michigan. The table below provides the driving time in minutes among all customers and the Traxis liquid oxygen depot location. From/To A (depot) B C D E F G H A (depot) – 73 65 47 84 32 29 23 B 73 – 38 56 78 30 27 51 C 65 38 – 69 54 57 67 45 D 47 56 69 – 43 61 33 52 E 84 78 54 43 – 37 46 62 F 32 30 57 61 37 – 35 47 G 29 27 67 33 46 35 – 18 H 23 51 45 52 62 47 18 – a. Currently, Traxis travels from the depot (A) to (F) to (G) to (D) to (E) to (H) to (B) to (C), then return b. Using the depot (A) as the beginning location, create a route using the NN heuristic. What is the total driving time using this route? c. Use the NN heuristic to calculate seven routes, each starting from one of Traxis’s customer’s locations. What are your conclusions

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Royal Seafood delivers fresh fin and shellfish to specialty grocery stores in the state of Oregon. The company packs a delivery truck in Corvallis and then drives in one single route to its five customers spread throughout the state. The distances in miles between all locations may be found in the table below. From/To Corvallis (A) Roseburg (B) Bend (C) Baker (D) Lakeview (E) Burns (F) Corvallis (A) – 225 234 233 169 189 Roseburg (B) 225 – 159 244 265 168 Bend (C) 234 159 – 253 246 197 Baker (D) 233 244 253 – 153 287 Lakeview (E) 169 265 246 153 – 171 Burns (F) 189 168 197 287 171 – a. Propose an efficient route by using the NN heuristic with Corvallis as the starting city. What is the total distance traveled? b. Use the NN heuristic to calculate five routes, each starting from one of Royal Seafood’s customer’s location. What is the best route for Royal Seafood?

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