aggregate and workforce planning (huvudplanering) · aggregate and workforce planning...
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Aggregate and Workforce Planning (Huvudplanering)
Production and Inventory Control (MPS)MIO030
The main reference for this material is the book Factory Physics by W. Hopp and M.L Spearman, McGraw-Hill, 2001.
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What is the Role of Aggregate Planning?
• Role of Aggregate Planning– Long-term planning function– Strategic preparation for tactical actions
• Aggregate Planning Issues– Production Smoothing: inventory build-ahead– Product Mix Planning: best use of resources– Staffing: hiring, firing, training– Procurement: supplier contracts for materials, components– Sub-Contracting: capacity vendoring– Marketing: promotional activities
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Aggregate Planning is Long Term
PersonnelPlan
FORECASTING
CAPACITY/FACILITYPLANNING
WORKFORCE PLANNING
MarketingParameters
Product/ProcessParameters
LaborPolicies
CapacityPlan
AGGREGATEPLANNING
AggregatePlan Strategy
WorkSchedule
WIP/QUOTASETTING
DEMANDMANAGEMENT
SEQUENCING & SCHEDULING
CustomerDemands
MasterProductionSchedule
SHOP FLOORCONTROL
WIPPosition Tactics
REAL-TIMESIMULATION
PRODUCTIONTRACKING
WorkForecast
Control
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Basic Aggregate Planning Situation
• Problem: plan production of single product over planning horizon.
• Motivation for Study:– mechanics and value of Linear Programming (LP) as a tool– intuition of production smoothing
• Inputs:– demand forecast (over planning horizon)– capacity constraints– unit profit– inventory carrying cost rate
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A Simple Aggregate Planning Model (I)
Notation:
. period of end at theinventory . period during soldquantity
. period during producedquantity period. onefor inventory ofunit one hold cost to
cost) holding including(not profit unit . periodin capacity . periodin demand
.,.......,1 periods,timetheofindex an
tItS
tXhr
tctd
ttt
t
t
t
t
t
=======
==
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Formulation
ttISXttSXIIttcXttdS
hIrS
ttt
tttt
tt
tt
tttt
,.....10,,,.....1,,.....1,.....1
subject to
max
1
1
=≥=−+==≤=≤
−
−
=∑
demandcapacityinventory balancenon-negativity
sales revenue - holding cost
summed over planning horizon
A Simple Aggregate Planning Model (II)
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Product Mix Planning (I)
• Problem: determine most profitable mix over planning horizon
• Motivation for Study:– linking marketing/promotion to logistics.– Bottleneck identification.
• Inputs:– demand forecast by product (family?); may be ranges– unit hour data– capacity constraints– unit profit by product– holding cost
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Product Mix Planning (II)
maximize profit
subject to:
production ≤ capacity, at all workstationsin all periods
sales ≤ demand, for all productsin all periods
Note: we will need some technical constraintsto ensure that variables represent reality.
Verbal Formulation
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Product Mix Planning (III)
. of endat product ofinventory . periodin soldproduct ofamount
periodin produced product ofamount . period onefor ofunit one hold cost to
product ofunit one fromprofit net
. periodin on workstatiofcapacity
.product ofunit one produce totion on worksta required time periodin product of allowed sales minimum
. periodin product for demand maximum
1 period, ofindex an ,1 on, workstatiofindex an
,.....,1 product, ofindex an
tiItiS
tiXtih
ir
tjc
ijatid
tid
t,......,ttn,.....jj
mii
it
it
it
i
i
jt
ij
it
it
==
===
=
=
==
====
==
Notation
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Product Mix Planning (IV)
tiISX
tiSXII
tjcXa
tidSd
IhSr
ititit
tiittiit
jtmi itij
ititit
itiitimi
tt
, allfor 0,,
, allfor ,
, allfor
, allfor subject to
max
1
1
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≥
−+=
≤
≤≤
−
−
=
==
∑
∑∑
(demand)
(capacity)
(inventory balance)
(non-negativity)
(sales revenue - holding cost)
Mathematical Formulation
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A Product Mix Example (I)
Assumptions:
Data:
• two products, P and Q• constant weekly demand, cost, capacity, etc.• Objective: maximize weekly profit
Product P Q Selling price $90 $100Raw Material Cost $45 $40Max Weekly Sales 100 50Minutes per unit on Workcenter A 15 10Minutes per unit on Workcenter B 15 35Minutes per unit on Workcenter C 15 5Minutes per unit on Workcenter D 25 14
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A Product Mix Example (II)
Formulation:
24001425240051524003515
24001015 :subject to
50006045max
≤+≤+≤+≤+
−+
QP
QP
QP
QP
QP
XXXXXX
XX
XX
Solution:
09.36
79.75 $557.94 Objective Optimal
*
*
=
=
=
Q
P
X
X
Net Weekly Profit : Round solution down (still feasible) to:
36
75*
*
=
=
Q
P
X
X
To get $45 ×75 + $60 ×36 - $5,000 = $535.
A Linear Programming (LP) Approach:
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Extensions to the Basic Product Mix Model (I)
Other Resource Constraints:
Utilization Matching: Let q represent fraction of rated capacity we are willing to run on resource j.
∑=
≤m
ijtitij tjqcXa
1, allfor
Notation:
Constraint for Shared Resource j: ∑=
≤m
ijtitij kXb
1
tiX
tjk
ijb
it
jt
ij
periodin produced product ofamount
periodin available resource of units ofnumber
product ofunit per required resource of units
=
=
=
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Backorders:
Overtime:
• Substitute • Allow to become positive or negative• Penalize differently in objective if desired
−+ −= ititit IIIitI
−+itit II ,
• Define Ojt as hours of OT used on resource j in period t and βj the cost of one overtime hour in workstation j
• Add Ojt to cjt in capacity constraint.
• Penalize Ojt in objective if desired
Extensions to the Basic Product Mix Model (II)
∑=
+≤m
1ijtjtitij tj, all forOcXa
{ }−+== −−∑∑ itiitiiti
m1i
t1t IIhSrmax π
{ }∑∑∑ =−+
== −−− n1j jtjitiitiiti
m1i
t1t OIIhSrmax βπ
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Workforce Planning
• Problem: determine most profitable production and hiring/firing policy over planning horizon.
• Motivation for Study:– hiring/firing vs. overtime vs. Inventory Build tradeoff– iterative nature of optimization modeling.
• Inputs:– demand forecast (assume single product for simplicity)– unit hour data– labor content data– capacity constraints – hiring/ firing costs– overtime costs– holding costs– unit profit
16hour-man oneby workforcedecrease cost tohour-man oneby workforceincrease cost to
hour-man/dollarsin overtime ofcost hour-man / dollarsin meregular ti ofcost . period onefor unit one hold cost to
.unit one fromprofit net
. periodin center work ofcapacity unit. one produce torequired hoursman ofnumber
tion on worksta hoursunit periodin allowed sales minimum
. periodin demand maximum
1 period, ofindex an ,1 ion, workstatofindex an
=′==′===
==
=
==
====
eell
thr
tjcb
jatd
td
t,......,ttn,.....jj
jt
j
t
t
A Workforce Planning Model (I)
Notation
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hoursin t periodin overtimeOhours.-man
in t to1 tperiod from cein workfor (fires) decreaseFhours.-man
in t to1t period from cein workfor (hires) increaseHmeregular ti of hours-manin t period workforceW
t of endat inventory It periodin soldamount S
t periodin producedamount X
t
t
t
t
t
t
t
=
−=
−=
=
=
=
=
Notation (cont.)
A Workforce Planning Model (II)
Note, this model only considers a single product. Generalizations to m products are straightforward!
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{ }
tFHWOISXtOWbX
tFHWW
tSXII
tcXatdSd
FeeHOllWIhSr
ttttttt
ttt
tttt
tttt
jttj
ttt
ttttttt
t
allfor 0,,,,,, allfor
allfor
allfor ,
allfor allfor
subject to
max
1
1
1
≥+≤
−+=
−+=
≤≤≤
′−−′−−−
−
−
=∑
A Workforce Planning Model (III)
Formulation
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Problem Description• 12 month planning horizon• 168 hours per month• 15 workers currently in system• regular time labor at $35 per hour• overtime labor at $52.50 per hour• $2,500 to hire and train new worker
$2,500/168=$14.88 ≈ $15/hour• $1,500 to lay off worker
$1,500/168=$8.93 ≈ $9/hour• 12 hours labor per unit• demand assumed met (St=dt, so St variables are unnecessary)
A Workforce Planning Example (I)
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• Solution:– LP optimal Solution: layoff 9.5 workers– Add constraint: Ft=0
• results in 48 hours/worker/week of overtime– Add constraint: Ot ≤ 0.2Wt
• Reasonable solution?
A Workforce Planning Example (II)