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1. Definitions      (p581)
   1. Aggregate Production Planning - intermediate-term planning that determines resources limited to staffing levels, production rates, and inventory policies. Time horizon is 6 to 12 months.
   2. Aggregate Production Planning Strategies
      1. Inventory  (Level Production)
      2. Hiring and Layoffs  (Chase Demand)
      3. Overtime and Undertime  (Idletime)
      4. Subcontracting
      5. Part-time Workers
      6. Back Ordering
      7. Influencing Demand - promotions, discounts (see p586)
      8. Counterseasonal Product Mix - lawn mowers and snow blowers
   3. Objective of Aggregate Production Planning  - choose a combination of the above strategies to minimize total cost.
   4. Aggregate Production Planning is developed for product lines, not individual products. A plan is specified in terms of a pseudo-product.
      1. Example, firm produces four different models of PCs, aggregate plan is specified in terms of a generic PC.
2. *Charting (Heuristic) Method    (p587)
   1. Example 13.1 - Candy Company, Pure strategy - Inventory (Level Production), p588.

      Input data
      Hiring cost =	$100	per worker
      Layoff (firing) cost =	$500	per worker
      Regular time production cost =	$2.00	per pound
      Inventory carrying cost =	$0.50	per pound per quarter
      Backordering cost =	$1.00	per pound per quarter (not included in text)
      Production per employee =	1000	pounds per quarter
      Beginning work force =	100	workers

       

      a. Determine the aggregate plan using the pure strategy of inventory (level production).
      The pure strategy of inventory uses inventory to absorb fluctuations while producing at a constant rate.
      Determine the Quarterly Production Rate.
      Quarterly (Regular time) Production Rate = (Annual Requirement) / 4                                = 400,000/4 = 100,000
      Quarter	Demand	Regular Time	Inventory	Backorders	Workers Needed	Workers Hired	Workers Fired
      Spring	80,000	100,000	20,000	0	100	0	0
      Summer	50,000	100,000	70,000	0	100	0	0
      Fall	120,000	100,000	50,000	0	100	0	0
      Winter	150,000	100,000	0	0	100	0	0
      Total	400,000	400,000	140,000	0		0	0
      Cost		$800,000	$70,000	$0		$0	$0
      Total Cost =		$870,000

   2. Pure strategy - Hiring and Layoffs (Chase Demand), p588.

      b. Determine the aggregate plan using the pure strategy of Hiring and Layoffs (chase demand).
      Quarter	Demand	Regular Time	Inventory	Backorders	Workers Needed	Workers Hired	Workers Fired
      Spring	80,000	80,000	0	0	80	0	20
      Summer	50,000	50,000	0	0	50	0	30
      Fall	120,000	120,000	0	0	120	70	0
      Winter	150,000	150,000	0	0	150	30	0
      Total	400,000	400,000	0	0		100	50
      Cost		$800,000	$0	$0		$10,000	$25,000
      Total Cost =		$835,000

   3. Time consuming to investigate several mixed strategies, even with PC worksheets. See Exhibit 13.2c, p592.
   4. No guarantee of optimal solution.

   Do assigned HW - Problem 13-4.

3. *Transportation Linear Programming Method             (p595)
   1. Considers overtime, subcontracting, inventory, and backorders.
   2. Does give optimal solution.
   3. Example 13.4 - Burruss Company with backordering
      1. Input data
         r - regular-time cost = $20/unit
         o - overtime cost = $25/unit
         s - subcontracting cost = $28/unit
         h - inventory holding cost = $3/unit-period
         b - backorder cost = $10/unit-period  (not included in text)
         R_j - max reg-time production in period j = 1000, 1200, 1300, 1300
         O_j - max overtime production in period j = 100, 150, 200, 200
         S_j - max subcontract production in period j = 500, 500, 500, 500
         D_j - demand for period j = 900, 1500, 1600, 3000
         I_o - initial inventory = 300
      2. Unit transportation costs: denoted by a_{i j}

         	Destinations   Period
         i= Origins	j=1	2	3	4
         1 Initial inventory	0.0	h	2h	3h
         2 Reg-time 1 3 Overtime 1 4 Subcontract 1	r o s	r+h o+h s+h	r+2h o+2h s+2h	r+3h o+3h s+3h
         5 Reg-time 2 6 Overtime 2 7 Subcontract 2	r+b o+b s+b	r o s	r+h o+h s+h	r+2h o+2h s+2h
         8 Reg-time 3 9 Overtime 3 10 Subcontract 3	r+2b o+2b s+2b	r+b o+b s+b	r o s	r+h o+h s+h
         11 Reg-time 4 12 Overtime 4 13 Subcontract 4	r+3b o+3b s+3b	r+2b o+2b s+2b	r+b o+b s+b	r o s

      3. Define decision variables
             X_{i j} - number of units transported from origin (production method) i to destination (period) j.
      4. Objective function - minimize total cost
             Z = S a_{i j} X_{i j}
      5. Constraints
            Origin 1  S X_1j £  I₀
             Origin 2  S X_2j £  R₁     Origin 8 S X_8j     £ R₃
             Origin 3 S X_3j £  O₁     Origin 9 S X_9j     £ O₃
             Origin 4 S X_4j £  S₁      Origin 10 S X_10j £ S₃
         
             Origin 5 S X_5j £ R₂     Origin 11 S X_11j £ R₄
             Origin 6 S X_6j £ O₂     Origin 12 S X_12j £ O₄
             Origin 7 S X_7j £ S₂      Origin 13 S X_13j £ S₄
         
            Dest 1    S X_i1   =   D₁ 
            Dest 2    S X_i2   =   D₂
            Dest 3    S X_i3   =   D₃
            Dest 4    S X_i4   =   D₄
      6. Solution: Aggregate plan

         	Period 1	Period 2	Period 3	Period 4
         Reg-time Overtime Subcontract	S X2j = 1000 S X3j =  100 S X4j =     0	S X5j = 1200 S X6j =   150 S X7j =   250	S X8j   = 1300 S X9j   =   200 S X10 j = 500	S X11 j = 1300 S X12 j =   200 S X13 j =   500

      7. To see Excel Solver solution, click worksheet, R513ex04.xls.

   Do assigned HW - Problem 13-14.
     (This page was last edit on August 16, 2006 .)