2. 1 Wagner – Whitin Algorithm Prof. Yuan-Shyi Peter Chiu Feb. 2011 Material Management Class Note #1-B

3. 2 § M6: Wagner – Whitin Algorithm (page 4) Example ~ A general model for Production Planning Terms: Periods: 1,2,3,….N i : demand rate in period i h : holding cost / item / period K : setup cost c : unit cost : cost of producing enough items for period i thru. j at beginning of period i ◇

4. 3 (B) Formula...[Eq.6.1] …...[Eq.6.2] Lowest cost from period i to N that will satisfies demand § M6: Wagner – Whitin Algorithm (page 5) ◇

5. 4 Demand 1Q 2Q 3Q 4Q 3000 2000 3000 2500 P 1 P 2 P 3 P 4 λ 1 λ 2 λ 3 λ 4 X 2 X 3 X 4 [Eg.] § M6: Wagner – Whitin Algorithm (page 6) ◇

6. 5 [Eg] solution: § M6: Wagner – Whitin Algorithm (page 7) ◇

7. 6 [Eg] solution: § M6: Wagner – Whitin Algorithm (page 8) ◇

8. 7 C 1 =Min

9. 8 [Answer] To produce enough items from 1st period to 2nd period, then To produce enough items from 3rd period to 4th period. In other words, production plan is: “ to produce 5000 items at the beginning of the first period, then to produce 5500 items at the beginning of the 3 rd period ”. [Eg] solution: § M6: Wagner – Whitin Algorithm (page 10) ◇ ~ The End ~

10. 9 ~ The End ~