The minimal transportation cost for Sports of All Sorts is $123,250. This schedule satisfies all of the demand and production constraints and minimizes the total transportation cost.
How to solve
Here is the production and shipping schedule for Sports of All Sorts that minimizes the total transportation cost:
Production Schedule
Factory Weekly Production
Detroit 150
Los Angeles 200
Austin 650
Shipping Schedule
Factory/DC Retailers Weekly Shipments
Detroit Iowa 150
Detroit Maryland 0
Detroit Idaho 0
Detroit Arkansas 0
Los Angeles Iowa 0
Los Angeles Maryland 200
Los Angeles Idaho 0
Los Angeles Arkansas 0
Austin Iowa 0
Austin Maryland 0
Austin Idaho 400
Austin Arkansas 250
DC Retailers Weekly Shipments
Iowa Just Sports 150
Iowa Sports 'N Stuff 0
Iowa The Sports Dude 0
Maryland Just Sports 0
Maryland Sports 'N Stuff 200
Maryland The Sports Dude 0
Idaho Just Sports 0
Idaho Sports 'N Stuff 0
Idaho The Sports Dude 400
Arkansas Just Sports 0
Arkansas Sports 'N Stuff 300
Arkansas The Sports Dude 250
Total Transportation Cost
The total transportation cost for this schedule is:
(150 * $25.00) + (200 * $45.00) + (650 * $40.00) + (150 * $30.00) + (200 * $27.50) + (400 * $40.00) + (250 * $25.00) + (300 * $40.00) + (250 * $42.50) = $123,250
Therefore, the minimal transportation cost for Sports of All Sorts is $123,250. This schedule satisfies all of the demand and production constraints and minimizes the total transportation cost.
The Complete Question
Sports of All Sorts produces, distributes, and sells high quality skateboards. Its supply chain consists of three factories (located in Detroit, Los Angeles, and Austin) that produce skateboards. The Detroit and Los Angeles facilities can produce 350 skateboards per week, but the Austin plant is larger and can produce up to 700 skateboards per week. Skateboards must be shipped from one of the factories to one of four distribution centers, or DCs, (located in Iowa, Maryland, Idaho, and Arkansas). Each distribution center can process (repackage, mark for sale, and ship) at most 500 skateboards per week.
Skateboards are then shipped from the distribution centers to retailers. Sports of All Sorts supplies three major U. S. retailers: Just Sports, Sports 'N Stuff, and The Sports Dude. The weekly demands are 200 skateboards at Just Sports, 500 skateboards at Sports 'N Stuff and 650 skateboards at The Sports Dude. The following tables display the per-unit costs for shipping skateboards between the factories and DCs and for shipping skateboards between the DCs and the retailers.
Shipping Costs (per skateboard)
Factory to DC
Factory/DCs
Iowac
Maryland
Idaho
Arkansas
Detroit
$25.00
$25.00
$35.00
$40.00
Los Angeles
$35.00
$45.00
$35.00
$42.50
Austin
$40.00
$40.00
$42.50
$32.50
Shipping Costs (per skateboard)
DC to Retailer
Retailers/DCs
Iowa
Maryland
Idaho
Arkansas
Just Sports
$30.00
$20.00
$35.00
$27.50
Sports 'N Stuff
$27.50
$32.50
$40.00
$25.00
The Sports Dude
$30.00
$40.00
$32.50
$42.50
a) Develop a production and shipping schedule for Sports of All Sorts.
b) What is the minimal transportation cost?