a company knows that the demand for it product during the next three months are:
month 1: 200 units
month 2: 300 units
month 3: 300 units
For each unit produce during month 1 and 2, a $10 variable cost is incurred; for each unit produced during month 3, a $12 variable cost is incurred. Inventory cost is $1.5 for each unit in stock at the end of the month. Set up cost for production during a month is $250. Units made during a month may be used to meet demand for that month or any future month. Assume that production during each month must be a multiple of 100. Assume initial inventory level is 0 units, use dynamic programming to determine an optimal production schedule.
I let ft(i) be the min cost of meeting demand for month t, t+1,...,3 if i units are remain at the beginning of month t.
c(x)= cost of producing x units during a period, so c(x)=0 for x=0, or c(x)=250+x for x is multiple of 100 or x=1,2,4,5,10,20,25,50,100.
d(t)= number of units demand, so d(1)=200, d(2)=300, d(3)=300.
so the recursion is: ft(i)= min{ 1.5( i + x -d(t) ) + c(x) + ft+1( i + x - d(t) ) }
So I need to find f3(i), f2(i) and f1(i).
so far this is all I've got, something is missing in my recursion and c(x), but I'm not sure what it is. Please help. Thanks in advance.
month 1: 200 units
month 2: 300 units
month 3: 300 units
For each unit produce during month 1 and 2, a $10 variable cost is incurred; for each unit produced during month 3, a $12 variable cost is incurred. Inventory cost is $1.5 for each unit in stock at the end of the month. Set up cost for production during a month is $250. Units made during a month may be used to meet demand for that month or any future month. Assume that production during each month must be a multiple of 100. Assume initial inventory level is 0 units, use dynamic programming to determine an optimal production schedule.
I let ft(i) be the min cost of meeting demand for month t, t+1,...,3 if i units are remain at the beginning of month t.
c(x)= cost of producing x units during a period, so c(x)=0 for x=0, or c(x)=250+x for x is multiple of 100 or x=1,2,4,5,10,20,25,50,100.
d(t)= number of units demand, so d(1)=200, d(2)=300, d(3)=300.
so the recursion is: ft(i)= min{ 1.5( i + x -d(t) ) + c(x) + ft+1( i + x - d(t) ) }
So I need to find f3(i), f2(i) and f1(i).
so far this is all I've got, something is missing in my recursion and c(x), but I'm not sure what it is. Please help. Thanks in advance.