Question

In: Operations Management

Sycamore Plastics (SP) is a manufacturer of polyethylene plastic pellets used as a raw material by...

Sycamore Plastics (SP) is a manufacturer of polyethylene plastic pellets used as a raw material by manufacturers of plastic goods around the U.S. SP currently operates four manufacturing centers in Philadelphia, PA; Atlanta, GA; St. Louis, MO; and Salt Lake City, UT. The plants have different capacities and production costs as indicated in the table below.

PLANT MAXIMUM CAPACITY
(× 100,000 LBS.)
PROD. COST
(PER 1,000 LBS.)
Philadelphia 7.5 $326.00
Atlanta 9.5 $278.00
St. Louis 12.5 $306.00
Salt Lake City 10.3 $251.00


     SP currently has six contract customers located in New York City; Birmingham, AL; Terre Haute, IN; Dallas, TX; Spokane, WA; and San Diego, CA. Transportation costs between the plants and various customers, as well as contracted demand from each customer, are shown in the table below.

TRANSPORT COSTS PER 1,000 LBS.
FROM/TO NYC BIRMINGHAM TERRE HAUTE DALLAS SPOKANE SAN DIEGO
Philadelphia $45 $52 $56 $62 $77 $80
Atlanta 55 42 58 59 79 77
St. Louis 57 60 50 54 64 65
Salt Lake City 72 71 67 57 57 55
Total Demand
(× 1,000 lbs.)
524 420 932 595 350 450


a. Create a solver model and find the optimal solution to help SP develop a distribution plan that will minimize costs to supply the customers’ demand. (Enter your answers in terms of cost per 1,000 lbs and shipment quantities per 1,000 lbs. Round your answers to the nearest whole number.)

CombinedCosts Per 1,000 lbs.
From/To NYC Birmingham Terre Haute Dallas Spokane San Diego
Philadelphia $ $ $ $ $ $
Atlanta
St. Louis
Salt Lake City
Solution (× 1,000 lbs.)
From/To NYC Birmingham Terre Haute Dallas Spokane San Diego
Philadelphia
Atlanta
St. Louis
Salt Lake City
Received
Total Costs
From/To NYC Birmingham Terre Haute Dallas Spokane San Diego
Philadelphia $ $ $ $ $ $
Atlanta
St. Louis
Salt Lake City
Total cost $

Solutions

Expert Solution

(a) Calculate combined costs by adding the production cost for each plant and transport cost from each plant to customers.

Combined Costs Per 1000 lbs.
FROM/TO NYC BIRMINGHAM TERRE HAUTE DALLAS SPOKANE SAN DIEGO
Philadelphia 371 378 382 388 403 406
Atlanta 333 320 336 337 357 355
St. Louis 363 366 356 360 370 371
Salt Lake City 323 322 318 308 308 306

Formulas:

B15 =SUM(B11:B14)   copy to B15:G15

H11 =SUM(B11:G11)   copy to H11:H15

B17 =SUMPRODUCT(B11:G14,B3:G6)

Total costs
FROM/TO NYC BIRMINGHAM TERRE HAUTE DALLAS SPOKANE SAN DIEGO
Philadelphia 15,211 0 0 0 0 0
Atlanta 160,839 134,400 0 15,839 0 0
St. Louis 0 0 331,792 114,480 0 0
Salt Lake City 0 0 0 70,840 107,800 137,700
Total Costs 1,088,901

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