Aggregate Planning in a Supply Chain
Case:Abhay Kant 043001 Anirudh Singh 043010 Sonakshi Gulati
043053 Sumeet Anand 043056 Carole Pauquet fy1101
Aggregate PlanningAggregate Planning is a process by which a
company determines ideal levels of capacity, production,
subcontracting, inventory, stock outs, and even pricing over a
specified time horizon. The goal is to satisfy demand while
maximizing profit.
Case: Red Tomato Tools Demand for the gardening tools is highly
seasonal. Handle demand and maximize profits?? Options: Hire worker
in peak season Subcontraction of some work Build up inventory in
slow period Backlogging No limit on subcontracting, inventories,
stockouts, backlog All stockouts are backlogged from the following
month. Inventory costs are incurred on the ending inventory in a
month. Inventory level at the end of June is at least 500
units.
Constraints:
Table 8-1 MonthJanuary February March April May June
Demand Forecast at Red Tomato Tools Demand Forecast1600 3000
3200 3800 2200 2200
Red Tomato Tools-Initialization Unit price=$40/unit Inventory at
the beginning of January=1000 units Workforce at the beginning of
January=80 employees Total of 20 workdays/month are available
Regular work hours=8hrs/day/employee Overtime work hours can not
exceed 10hrs/month/employee Required labor hours= 4hrs/unit
Table 8-2Material Cost Inventory holding cost Marginal cost of
stockout/backlog Hiring and training costs Layoff cost Labor hours
required Regular time cost Overtime cost Cost of subcontracting
Cost for Red Tomato$ 10/unit $ 2/unit/month $ 5/unit/month $
300/worker $ 500/worker 4/unit $ 4/hour $ 6/hour $ 30/unit
Aggregate Planning (Define Decision Variables)Wt = Workforce
size for month t, t = 1, ..., 6 Ht = Number of employees hired at
the beginning of month t, t = 1, ..., 6 Lt = Number of employees
laid off at the beginning of month t, t = 1, ..., 6 Pt = Production
in month t, t = 1, ..., 6 It = Inventory at the end of month t, t =
1, ..., 6 St = Number of units stocked out (backlogged) at the end
of month t, t = 1, ..., 6 Ct = Number of units subcontracted for
month t, t = 1, ..., 6 Ot = Number of overtime hours worked in
month t, t = 1, ..., 6
? Min cost = Max profit Min cost and max profit are equivalent
if All demand has to be met in some way The unit price is fixed,
i.e., total revenue is fixed.
Then, min cost and max profit gives the same optimal plan.
Aggregate Planning (Define Objective Function)6 6 t 6 t 6
Min TC !6
640W 2It! 1 t
t! 1
6Ot! 1 6 t
300 H t 500 Lt t! t !1 1 Cost of Hiring 6 t Cost of Layoff
Regular Time Labor Cost 6
Overtime Labor Cost
5St! 1
10 Pt! 1
30 Ct! 1
t
Inventory Holding Cost
Stockout Cost
Production Cost
Subcontraction Cost
Workforce Balance Equations Workforce size for each month is
based on hiring and layoffsW t ! W t 1 H t Lt, or W t W t 1 H t Lt
! 0 for t ! 1,...,6, where W 0 ! 80.Ht Wt-1 Period t Wt
Lt
Inventory Balance EquationsPt It-1 Period t Ct It
St-1
Dt
St
I t 1 P t C t ! D t S t 1 I t S t , I t 1 P t C t D t S t 1 I t
S t ! 0, for t ! 1,...,6,where I 0 ! 1,000, S 0 ! 0,and I 6 u
500.
Production Capacity Constraints Production for each month cannot
exceed regular+overtime working capacity
P t e 40W t Ot 4 , 40W t Ot 4 P t u 0, for t ! 1,...,6.
Overtime Capacity Constraints Over time for each month
Ot e 10W t, 10W t Ot u 0, for t ! 1,...,6.
Average Flow Time Little s Law: Average Flow time=Average
Inventory/Throughput
T 1 1 T 1 1 1 Average Inventory ! ( I t 1 I t ) ! ( I 0 I T ) I
t T t !1 2 T 2 t !1
Average Flow Time for Red Tomato=895/2,667=0.34 months ?? What
happens to Average Flow Time if uncertainty in demand
increases?
Scenarios
Increased demand fluctuation Increase in holding cost (from $2
to $6) Overtime cost drops to $4.1 per hour
Table 8-3
Aggregate Plan for Red Tomato
Total No.Hire No. Laid Workforc Overtime, Inventory Stockout,
Subcontract Production, Pt Period,t d, Ht Off, Lt e Size, Wt Ot ,
It St , Ct
0 1 2 3 4 5 6
0 0 0 0 0 0 0
0 15 0 0 0 0 0
80 65 65 65 65 65 65
0 0 0 0 0 0 0
1000 1983 1567 950 0 117 500
0 0 0 0 267 0 0
0 0 0 0 0 0 0 2583 2583 2583 2583 2583 2583
Table 8-4 Demand Forecast with Higher Seasonal
FluctuationMonthJanuary February March April May June
Demand Forecast1000 3000 3800 4800 2000 1400
Table 8-5
Aggregate Plan for Red Tomato
Total No.Hired No. Laid Workforc Overtime, Inventory, Stockout,
Subcontract Production, Period,t Pt , Ht Off, Lt e Size, Wt Ot It
St , Ct
0 1 2 3 4 5 6
0 0 0 0 0 0 0
0 15 0 0 0 0 0
80 65 65 65 65 65 65
0 0 0 0 0 0 0
1000 2583 2167 950 0 0 500
0 0 0 0 1267 683 0
0 0 0 0 0 0 0 2583 2583 2583 2583 2583 2583
AnalysisOptimal aggregate plan is shown in Table 8-5. Monthly
production remains the same but both inventories and stock outs
(backlogs) go up compared to the aggregate plan in Table 8-3 for
the demand profile in Table 8-1. The cost of meeting the new demans
profile in Table 8-4 is higher at $432,858 (compared to $422,275
for the previous deamd profile in Table 8-1). The seasonal
inventory during the planning horizon is given by: Seasonal
Inventory:- 6450/6= 1075 The average flow time for this aggregate
plan over the planning horizon (using equation 8.6) is given by:
Average Flow Tim:- 1075/2667= 0.40 Months
Thank You
