In: Operations Management
A manufacturer of nylon carpets produces rolls of carpeting at three factories and ships them to distributors in three locations The table below shows the capacities at the factories and the demands at the distributors for the next quarter, all given in thousands of rolls. Also shown are the unit transportation costs between each factory and each distributor, stated in cost per roll.
Factory/Distributor | Distributor 1 | Distributor 1 | Distributor 3 | Capacity |
Factory 1 | $14 | $11 | $17 | 40 |
Factory 2 | $15 | $16 | $12 | 50 |
Factory 3 | $13 | $19 | $18 | 60 |
Demand | 50 | 45 | 55 | thousands of rolls |
Using greedy heuristic, what is the total shipping cost?
For the above transportation problem we will us the least cost method to find the initially feasible solution ( greedy heuristic )
As we know :
Factory/Distributor | Distributor 1 | Distributor 2 | Distributor 3 | Capacity |
Factory 1 | $14 | $11 | $17 | 40 |
Factory 2 | $15 | $16 | $12 | 50 |
Factory 3 | $13 | $19 | $18 | 60 |
Demand | 50 | 45 | 55 | thousands of rolls |
Now we see that the least transportation cost in the above table is $ 11 from Factory 1 to Distributor 1 , so we trry to balance that demand
we get :
Factory/Distributor | Distributor 1 | Distributor 2 | Distributor 3 | Capacity |
Factory 1 | $14 | $11(40) | $17 | 0 |
Factory 2 | $15 | $16 | $12 | 50 |
Factory 3 | $13 | $19 | $18 | 60 |
Demand | 50 | 5 | 55 | thousands of rolls |
Note that capacity for Distributor 2 has become zero and demand remains 5 ( put the number of goods in bracket )
Next iteration find the next lowest cost after 11 $ i.e 12 $ and so on we carry out the iterations balancing out the demand and capacity in each case till we reach a point where demand and capacity are 0 .
Factory/Distributor | Distributor 1 | Distributor 2 | Distributor 3 | Capacity |
Factory 1 | $14 | $11(40) | $17 | 0 |
Factory 2 | $15 | $16 | $12(50) | 0 |
Factory 3 | $13(50) | $19(5) | $18(5) | 0 |
Demand | 0 | 0 | 0 | thousands of rolls |
Total cost using least cost method is : ($11*40 + $12*50 +$13*50 + $18*5)*1000 = (440+600+650+90)*1000 = 1780000 $