Joke Shop imports goods at three ports and distributes to four regional warehous
ID: 467381 • Letter: J
Question
Joke Shop imports goods at three ports and distributes to four regional warehouses across the United States.One of their products, a political joke book is manufactured around the world with shipments arriving in Boston (MA), New York (NY), and San Diego (CA).Each port received 5,000 boxes to be distributed during the month of August 2016.The Demand for product for the month of August requires shipments to be made to satisfy the following demand:
Tupelo , MS 5,000 boxes
Houston, TX3,000 boxes
Chicago, IL4,500 boxes
Orlando, FL 2,500 boxes
The Distribution costs are as follows:
City
Boston
New York
San Diego
Tupelo
10
8
12
Houston
12
10
6
Chicago
8
7
8
Orlando
6
5
14
Develop a Network representation of this problem
Determine the cost of shipping product and satisfying the demand of each warehouse.
Create an alternative distribution plan that will satisfy demand and reduce cost.
City
Boston
New York
San Diego
Tupelo
10
8
12
Houston
12
10
6
Chicago
8
7
8
Orlando
6
5
14
Explanation / Answer
Network Representation
LPP Model:
Decision Variables
Xij - no. of boxes distributed from port i to Distribution Centre j
Objective Function:
Minimize Total Cost = Xij * Cij
where Cij is per unit cost of transportation from Port i to Distribution centre j
Subject to Constraints:
Supply constraints,
Sum of boxes distributed from any port <= 5000 (no. of boxes received at each port)
Demand constraint,
Sum of boxes received at each distribution centre >= demand at the distribution centre
Solving the LPP porblem for Total Cost minimization, the solution is given below;
Total Cost of distribution = $109,000
Cost of distribution at distribution centres,
Tupelo: $40000
Houston: $18000
Chicago: $36000
Orlando: $15000
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