Wagner-Whitin algorithm F(T) = Cost of replenishment F(1) = Simply the Ordering
ID: 373468 • Letter: W
Question
Wagner-Whitin algorithm
F(T) = Cost of replenishment
F(1) = Simply the Ordering cost = $50
F(2) =
Minimum of the 2 options : Produce in period 1 for both period 1 & 2 (20+60) OR Produce in period 1 for 1 (20) and in period 2 for 2 (60)
Option 1 = c12 = $50 + $1 * 60 = $110 (ordering cost + storage cost)
Option 2 = c22 = $50 + $50 = $100 (ordering cost twice)
So our table now looks like this :
Lets calculate F(3) now.
We have three options:
Option 1 = Produce in period 1 for first three periods (20 + 60 + 10)
c13= $50 + $60 + $20 = $130 (Ordering cost + Holding cost for 60 units for one month + Holding cost for 10 units for two months)
Option 2 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2 & 3 (60 + 10)
c23 = $50 + $50 + $10 = $110 (Ordering cost twice + Holding cost for 10 units for one month)
Option 3 = Produce separately in all periods
c33 = $50 + $50 + $50 = $150 (Ordering cost thrice)
Lets calculate F(4) now.
We have four options:
Option 1 = Produce in period 1 for first four periods (20 + 60 + 10 + 80)
c14= $50 + $60 + $20 + $240 = $370 (Ordering cost + Holding cost for 60 units for one month + Holding cost for 10 units for two months + Holding cost for 80 units for three months)
Option 2 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2,3 & 4 (60 +10 + 80)
c24 = $50 + $50 + $10 + $160 = $270 (Ordering cost twice + Holding cost for 10 units for one month + Holding cost for 80 units for two months)
Option 3 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2 (60) and produce in period 3 for periods 3 & 4 (10 + 80)
c34 = $50 + $50 + $50 + $80 = $230 (Ordering cost thrice + Holding cost for 80 units for one month)
Option 4 = Produce separately in all periods
c44 = $50 + $50 + $50 + $50 = $200 (Ordering cost 4 times)
So now our table looks like,
Lets calculate F(5) now.
We have five options:
Option 1 = Produce in period 1 for first five periods (20 + 60 + 10 + 80 + 45)
c15= $50 + $60 + $20 + $240 + $180 = $550 (Ordering cost + Holding cost for 60 units for one month + Holding cost for 10 units for two months + Holding cost for 80 units for three months + Holding cost for 45 units for four months)
Option 2 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2,3,4 & 5 (60 +10 + 80 + 45)
c25 = $50 + $50 + $10 + $160 + $135 = $405 (Ordering cost twice + Holding cost for 10 units for one month + Holding cost for 80 units for two months + Holding cost for 45 units for three months)
Option 3 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2 (60) and produce in period 3 for periods 3,4 & 5 (10 + 80 + 45)
c35 = $50 + $50 + $50 + $80 + $90 = $320 (Ordering cost thrice + Holding cost for 80 units for one month + Holding cost for 45 units for two months)
Option 4 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2 (60) and produce in period 3 for period 3(10) and produce in period 4 for periods 4 & 5 (80 +45)
c45 = $50 + $50 + $50 + $50 + $45 = $245 (Ordering cost 4 times + Holding cost for 45 units for one month )
Option 5 = Produce separately in all periods
c55 = $50 + $50 + $50 + $50 + $50 = $250 (Ordering cost 5 times)
Lets calculate F(6) now.
We have six options:
Option 1 = Produce in period 1 for first six periods (20 + 60 + 10 + 80 + 45 + 2)
c16= $50 + $60 + $20 + $240 + $180 + $10 = $550 (Ordering cost + Holding cost for 60 units for one month + Holding cost for 10 units for two months + Holding cost for 80 units for three months + Holding cost for 45 units for four months + Holding cost for 2 units for five months)
Option 2 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2,3,4,5 & 6 (60 +10 + 80 + 45 + 2)
c26 = $50 + $50 + $10 + $160 + $135 + $8= $413 (Ordering cost twice + Holding cost for 10 units for one month + Holding cost for 80 units for two months + Holding cost for 45 units for three months + Holding cost for 2 units for four months)
Option 3 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2 (60) and produce in period 3 for periods 3,4,5 & 6 (10 + 80 + 45 + 2)
c36 = $50 + $50 + $50 + $80 + $90 + $6 = $326 (Ordering cost thrice + Holding cost for 80 units for one month + Holding cost for 45 units for two months + Holding cost for 2 units for three months)
Option 4 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2 (60) and produce in period 3 for period 3(10) and produce in period 4 for periods 4,5 & 6 (80 + 45 + 2)
c46 = $50 + $50 + $50 + $50 + $45 + $4 = $249 (Ordering cost 4 times + Holding cost for 45 units for one month + Holding cost for 2 units for two months)
Option 5 = Produce in period 1 for period 1 (20) and produce in period 2 for period 2 (60) and produce in period 3 for period 3(10) and produce in period 4 for period 4 (80) and produce in period 5 for periods 5 & 6 (45 + 2)
c56 = $50 + $50 + $50 + $50 + $50 + $2 = $252 (Ordering cost 5 times + Holding cost for 2 units for one month)
Option 6 = Produce separately in all periods
c66 = $50 + $50 + $50 + $50 + $50 + $50 = $300 (Ordering cost 6 times)
So now our table looks like,
As we see from the table, the lowest values in each column are highlighted.
This signifies that we produce three times:
Order 1 in Period 1 for demand of Period one>
Order 2 in Period 2 for demand of Period 2 & 3 (60+10) = 70
Order 3 in Period 4 for demand of Period 4,5 & 6 (80+45+2) = 127
Net Req. 20 60 10 80 45 2 Period 1 2 3 4 5 6 1 2 3 4 5 6Explanation / Answer
16. (1 point) Use the Wagner-Whitin algorithm to compute an "optial" 6 month production schedule based on the following lot-sizing data. The ordering cost (A) is $50 and the unit holding cost h is S1 t 1 23 5 6 D 20 60 10 80 45 2
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