- Transportation Cost Per Car Sydney Brisbane Melbourne Perth Adelaide 100 200 120 220 150 Holden Motors Has Three Pl 1 (79.28 KiB) Viewed 135 times
Perth, and Adelaide (i.e., these are the supply points), and two
major distributors in Sydney and Brisbane (i.e., these are the
demand points). The quarterly capacities of three plants are 1000,
1300 and 1200 cars, and the demands at the distribution centres for
the same period are 2300 and 1400 cars. A trucking company
transports the cars from the plants to the distributors. The
transportation cost per car between the different routes are given
in the table above. A penalty is levied at the rate of $350 and
$300 for each undelivered car at Sydney and Brisbane, respectively.
Additionally, no deliveries are made from the Melbourne plant to
the Brisbane distribution centre. Formulate the Linear programming
(LP) model and find the optimal solution that minimizes the total
transportation cost. Let be the number of cars transported from
plant i to distributor j, where: i = 1: Melbourne i = 2: Perth i =
3: Adelaide j = 1: Sydney j = 2: Brisbane Let and be the amount of
shortages for the distribution centres in Sydney and Brisbane
respectively. The solution is:
Transportation cost per car Sydney Brisbane Melbourne Perth Adelaide $100 $200 $120 $220 $150 Holden Motors has three plants (producing cars) in Melbourne, Perth, and Adelaide (i.e., these are the supply points), and two major distributors in Sydney and Brisbane (i.e., these are the demand points). The quarterly capacities of three plants are 1000, 1300 and 1200 cars, and the demands at the distribution centres for the same period are 2300 and 1400 cars. A trucking company transports the cars from the plants to the distributors. The transportation cost per car between the different routes are given in the table above. A penalty is levied at the rate of $350 and $300 for each undelivered car at Sydney and Brisbane, respectively. Additionally, no deliveries are made from the Melbourne plant to the Brisbane distribution centre. Formulate the Linear programming (LP) model and find the optimal solution that minimizes the total transportation cost. Let Lijbe the number of cars transported from plant i to distributor j, where: i - 1: Melbourne i-2: Perth i -3: Adelaide j - 1: Sydney j-2: Brisbane Let A and A2 be the amount of shortages for the distribution centres in Sydney and Brisbane respectively. The solution is: