Consider a situation where a particular product is produced and placed in in-pro

Question

Consider a situation where a particular product is produced and placed in in-process inventory until it is needed in a subsequent production process. The number of units required in each of the next 3 months, the setup cost, and the regular-time unit production cost (in units of thousands of dollars) that would be incurred in each month are as follows: There currently is 1 unit in inventory, and we want to have 2 units in inventory at the end of 3 months. A maximum of 3 units can be produced on regular-time production in each month, although 1 additional unit can be produced on overtime at a cost that is 2 larger than the regular-time unit production cost. The holding cost is 2 per unit for each extra month that it is stored. Use dynamic programming to determine how many units should be produced in each month to minimize the total cost.

Explanation / Answer

units to be produced in each months can be computed by use of dynamic programming:

let C[i][j] denotes cost of production till ith month where jth units are produced till ith month.

then C[i][j] = min(C[i-1][j]+ holding cost,for k varying from 1 to j, C[i-1][j-k] +holding cost+ setupcost+regular-timeunitcost*k)

going by above formula we need to calculate C[3][2]

C[1][1] = 5+8=13

C[2][1] = min(C[1][1] + 2, 10+10 ) = 15

C[2][2] = min(C[1][1] + 2+10+10, C[1][0]+ 10+2*10) = 30 .. [both made in 2nd month]

C[3][1] = min(C[2][1]+2, 5+9) =14

C[3][2] = min(C[2][2]+2*2, 5+9*2, C[1][1]+ 2*2+5+9) = 23 .. [which means buiding 2 units in 3rd month is best suited]

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---