- Table 1 shows the cost, in pounds, of transporting one unit of stock from each of four supply points, \(\mathrm { A } , \mathrm { B } , \mathrm { C }\) and D , to each of four demand points, \(\mathrm { P } , \mathrm { Q } , \mathrm { R }\) and S . It also shows the stock held at each supply point and the stock required at each demand point. A minimum cost solution is required.
\begin{table}[h]
| P | Q | R | S | Supply |
| A | 15 | 14 | 17 | 11 | 23 |
| B | 10 | 9 | 16 | 12 | 42 |
| C | 11 | 13 | 8 | 10 | 18 |
| D | 15 | 13 | 16 | 17 | 19 |
| Demand | 25 | 45 | 12 | 20 | |
\captionsetup{labelformat=empty}
\caption{Table 1}
\end{table}
Table 2 shows an initial solution given by the north-west corner method.
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Table 2}
\end{table}
- Taking DQ as the entering cell, use the stepping-stone method to find an improved solution. Make your method clear.
- Perform one further iteration of the stepping-stone method to obtain an improved solution. You must make your method clear by stating the
- shadow costs
- improvement indices
- route
- entering cell and exiting cell.
- Determine whether the solution obtained from this second iteration is optimal, giving a reason for your answer.
- State the cost of the solution found in (b).