Lab Study Industrial

Consider the least-unit cost algorithm to find an initial solution for the transportation problem.

a) Write a Matlab function to implement the least unit cost algorithm. The steps of this algorithm are outlined below. Note that your function is only required to find an initial solution, not to solve the whole transportation problem.

Your function should take a capacity array C for the distribution centers, demand array D for the customers, and the cost matrix A as the inputs. Observe that, if there are m distribution centers and n customers, then C will be a 1xm array, D will be a 1xn array and A will be a mxn matrix. Your function should run according to the following steps of the algorithm and give a matrix R that shows the resulting transportation amounts between the distribution centers and the customers and the value TC that shows the total transportation cost with this policy, as the outputs. Note that R will also be a mxn matrix and TC will be a rational number.

Least Unit Cost Algorithm to find an initial solution:

1. Check if the total demand is equal to total supply. If they are equal, go to step 2.

If total capacity is greater than total demand, then update the demand array by adding a new element to that array with the value equal to the difference between the total capacity and the total demand. Also update the cost matrix A by adding a new column to the end of the matrix A with values equal to 0.

If total demand is greater than total capacity, then update the capacity array by adding a new element to that array with the value equal to the difference between the total demand and the total capacity. Also update the cost matrix A by adding a new row to matrix A with values equal to 0.

2. Select the lowest cost value in the matrix A and send as much as possible units through that route without violating the demand and capacity values for that route. Update your R matrix accordingly to show how many units that you send from which...