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Inventory Management V Finite Planning Horizon Lect ure 9 ESD.260 Fa ll 2003
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Inventory Management V Finite Planning Horizon
Lecture 9 ESD260 Fall 2003 Caplice
Assumptions Basic FPH Model
MIT Center for Transportation amp Logistics - ESD260 2 copy Chris Caplice MIT
bullDemand1048708 Constant vs Variable Known vs Random Continuous vs DiscretebullLead timebull1048708 Instantaneousbull1048708 Constant or Variablebull (deterministicstochastic)bullDependence of itemsbull1048708 Independentbull1048708 Correlatedbull1048708 IndenturedbullReview Timebull1048708 Continuous vs PeriodicbullNumber of Echelonsbull1048708 One vs ManybullCapacity Resourcesbull1048708 Unlimited vs Limited
bullDiscountsbull1048708 Nonebull1048708 All Units or IncrementalbullExcess Demandbull1048708 Nonebull1048708 All orders are backorderedbull1048708 Lost ordersbull1048708 SubstitutionbullPerishabilitybull1048708 Nonebull1048708 Uniform with timebullPlanning Horizonbull1048708 Single Periodbull1048708 Finite Periodbull1048708 InfinitebullNumber of Itemsbull1048708 Onebull1048708 Many
Example
Dem
and
Month
When should I order and for how muchCosts
D = 2000 items per year
Co = $50000 per order
Cp = $5000 per item
Ch = 24 per item per year
Chp = ( Ch Cp ) N
= $1 per month per item
N = number of periods per year
More Assumptions
bull Demand is required and consumed on first day of the period
bull Holding costs are not charged on items used in that period
bull Holding costs are charged for inventory ordered in advance of need
MIT Center for Transportation amp Logistics ndash ESD260 3 copy Chris Caplice MIT
Five Basic Approaches
1 The One-Time Buy2 Lot For Lot3 Simple EOQ4 The Silver Meal Algorithm5 Optimal Procedures Wagner-Whitin (Dynamic Programming) Mixed Integer Programming
MIT Center for Transportation amp Logistics - ESD260 4 copy Chris Caplice MIT
Approach One-Time Buy
On
Hand
Inventory
Month
MIT Center for Transportation amp Logistics - ESD260 5 copy Chris Caplice MIT
2000
Approach One-Time Buy
MIT Center for Transportation amp Logistics - ESD260 6 copy Chris Caplice MIT
MonthsDemand
OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 2000 $1800 $500 23002 150 0 $1650 $0 16503 100 0 $1550 $0 15504 50 0 $1500 $0 $15005 50 0 $1450 $0 $14506 100 0 $1300 $0 $13007 150 0 $1200 $0 $12008 200 0 $1000 $0 $10009 200 0 $800 $0 $80010 250 0 $550 $0 $55011 300 0 $250 $0 $25012 250 0 $0 $0 $0Totals 2000 2000 $13100 $500 $13600
Approach Lot for Lot
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 7 copy Chris Caplice MIT
200 150 100 50 50 100150200200250 300 250
Month
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Assumptions Basic FPH Model
MIT Center for Transportation amp Logistics - ESD260 2 copy Chris Caplice MIT
bullDemand1048708 Constant vs Variable Known vs Random Continuous vs DiscretebullLead timebull1048708 Instantaneousbull1048708 Constant or Variablebull (deterministicstochastic)bullDependence of itemsbull1048708 Independentbull1048708 Correlatedbull1048708 IndenturedbullReview Timebull1048708 Continuous vs PeriodicbullNumber of Echelonsbull1048708 One vs ManybullCapacity Resourcesbull1048708 Unlimited vs Limited
bullDiscountsbull1048708 Nonebull1048708 All Units or IncrementalbullExcess Demandbull1048708 Nonebull1048708 All orders are backorderedbull1048708 Lost ordersbull1048708 SubstitutionbullPerishabilitybull1048708 Nonebull1048708 Uniform with timebullPlanning Horizonbull1048708 Single Periodbull1048708 Finite Periodbull1048708 InfinitebullNumber of Itemsbull1048708 Onebull1048708 Many
Example
Dem
and
Month
When should I order and for how muchCosts
D = 2000 items per year
Co = $50000 per order
Cp = $5000 per item
Ch = 24 per item per year
Chp = ( Ch Cp ) N
= $1 per month per item
N = number of periods per year
More Assumptions
bull Demand is required and consumed on first day of the period
bull Holding costs are not charged on items used in that period
bull Holding costs are charged for inventory ordered in advance of need
MIT Center for Transportation amp Logistics ndash ESD260 3 copy Chris Caplice MIT
Five Basic Approaches
1 The One-Time Buy2 Lot For Lot3 Simple EOQ4 The Silver Meal Algorithm5 Optimal Procedures Wagner-Whitin (Dynamic Programming) Mixed Integer Programming
MIT Center for Transportation amp Logistics - ESD260 4 copy Chris Caplice MIT
Approach One-Time Buy
On
Hand
Inventory
Month
MIT Center for Transportation amp Logistics - ESD260 5 copy Chris Caplice MIT
2000
Approach One-Time Buy
MIT Center for Transportation amp Logistics - ESD260 6 copy Chris Caplice MIT
MonthsDemand
OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 2000 $1800 $500 23002 150 0 $1650 $0 16503 100 0 $1550 $0 15504 50 0 $1500 $0 $15005 50 0 $1450 $0 $14506 100 0 $1300 $0 $13007 150 0 $1200 $0 $12008 200 0 $1000 $0 $10009 200 0 $800 $0 $80010 250 0 $550 $0 $55011 300 0 $250 $0 $25012 250 0 $0 $0 $0Totals 2000 2000 $13100 $500 $13600
Approach Lot for Lot
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 7 copy Chris Caplice MIT
200 150 100 50 50 100150200200250 300 250
Month
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Example
Dem
and
Month
When should I order and for how muchCosts
D = 2000 items per year
Co = $50000 per order
Cp = $5000 per item
Ch = 24 per item per year
Chp = ( Ch Cp ) N
= $1 per month per item
N = number of periods per year
More Assumptions
bull Demand is required and consumed on first day of the period
bull Holding costs are not charged on items used in that period
bull Holding costs are charged for inventory ordered in advance of need
MIT Center for Transportation amp Logistics ndash ESD260 3 copy Chris Caplice MIT
Five Basic Approaches
1 The One-Time Buy2 Lot For Lot3 Simple EOQ4 The Silver Meal Algorithm5 Optimal Procedures Wagner-Whitin (Dynamic Programming) Mixed Integer Programming
MIT Center for Transportation amp Logistics - ESD260 4 copy Chris Caplice MIT
Approach One-Time Buy
On
Hand
Inventory
Month
MIT Center for Transportation amp Logistics - ESD260 5 copy Chris Caplice MIT
2000
Approach One-Time Buy
MIT Center for Transportation amp Logistics - ESD260 6 copy Chris Caplice MIT
MonthsDemand
OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 2000 $1800 $500 23002 150 0 $1650 $0 16503 100 0 $1550 $0 15504 50 0 $1500 $0 $15005 50 0 $1450 $0 $14506 100 0 $1300 $0 $13007 150 0 $1200 $0 $12008 200 0 $1000 $0 $10009 200 0 $800 $0 $80010 250 0 $550 $0 $55011 300 0 $250 $0 $25012 250 0 $0 $0 $0Totals 2000 2000 $13100 $500 $13600
Approach Lot for Lot
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 7 copy Chris Caplice MIT
200 150 100 50 50 100150200200250 300 250
Month
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Five Basic Approaches
1 The One-Time Buy2 Lot For Lot3 Simple EOQ4 The Silver Meal Algorithm5 Optimal Procedures Wagner-Whitin (Dynamic Programming) Mixed Integer Programming
MIT Center for Transportation amp Logistics - ESD260 4 copy Chris Caplice MIT
Approach One-Time Buy
On
Hand
Inventory
Month
MIT Center for Transportation amp Logistics - ESD260 5 copy Chris Caplice MIT
2000
Approach One-Time Buy
MIT Center for Transportation amp Logistics - ESD260 6 copy Chris Caplice MIT
MonthsDemand
OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 2000 $1800 $500 23002 150 0 $1650 $0 16503 100 0 $1550 $0 15504 50 0 $1500 $0 $15005 50 0 $1450 $0 $14506 100 0 $1300 $0 $13007 150 0 $1200 $0 $12008 200 0 $1000 $0 $10009 200 0 $800 $0 $80010 250 0 $550 $0 $55011 300 0 $250 $0 $25012 250 0 $0 $0 $0Totals 2000 2000 $13100 $500 $13600
Approach Lot for Lot
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 7 copy Chris Caplice MIT
200 150 100 50 50 100150200200250 300 250
Month
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach One-Time Buy
On
Hand
Inventory
Month
MIT Center for Transportation amp Logistics - ESD260 5 copy Chris Caplice MIT
2000
Approach One-Time Buy
MIT Center for Transportation amp Logistics - ESD260 6 copy Chris Caplice MIT
MonthsDemand
OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 2000 $1800 $500 23002 150 0 $1650 $0 16503 100 0 $1550 $0 15504 50 0 $1500 $0 $15005 50 0 $1450 $0 $14506 100 0 $1300 $0 $13007 150 0 $1200 $0 $12008 200 0 $1000 $0 $10009 200 0 $800 $0 $80010 250 0 $550 $0 $55011 300 0 $250 $0 $25012 250 0 $0 $0 $0Totals 2000 2000 $13100 $500 $13600
Approach Lot for Lot
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 7 copy Chris Caplice MIT
200 150 100 50 50 100150200200250 300 250
Month
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach One-Time Buy
MIT Center for Transportation amp Logistics - ESD260 6 copy Chris Caplice MIT
MonthsDemand
OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 2000 $1800 $500 23002 150 0 $1650 $0 16503 100 0 $1550 $0 15504 50 0 $1500 $0 $15005 50 0 $1450 $0 $14506 100 0 $1300 $0 $13007 150 0 $1200 $0 $12008 200 0 $1000 $0 $10009 200 0 $800 $0 $80010 250 0 $550 $0 $55011 300 0 $250 $0 $25012 250 0 $0 $0 $0Totals 2000 2000 $13100 $500 $13600
Approach Lot for Lot
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 7 copy Chris Caplice MIT
200 150 100 50 50 100150200200250 300 250
Month
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Lot for Lot
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 7 copy Chris Caplice MIT
200 150 100 50 50 100150200200250 300 250
Month
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Lot for Lot
MIT Center for Transportation amp Logistics - ESD260 8 copy Chris Caplice MIT
Month Demand
OrderingQuantity
HoldingCost
OrderingCost
PeriodCosts
1 200 200 $0 $500 $5002 150 150 $0 $500 $5003 100 100 $0 $500 $5004 50 50 $0 $500 $500 5 50 50 $0 $500 $5006 100 100 $0 $500 $5007 250 150 $0 $500 $5008 200 200 $0 $500 $5009 200 200 $0 $500 $50010 250 250 $0 $500 $50011 300 300 $0 $500 $50012 250 250 $0 $500 $500Yotals 2000 2000 $0 $6000 $6000
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach EOQ
On
Hand
Inventory
Month
400 400 400 400 400
MIT Center for Transportation amp Logistics - ESD260 9 copy Chris Caplice MIT
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach EOQ
MIT Center for Transportation amp Logistics - ESD260 10 copy Chris Caplice MIT
Month Demand OrderQuantity
Holding Cost
Ordering Cost
Period Costs
1 200 400 $200 $500 $7002 150 0 $50 $0 $503 100 400 $350 $500 $8504 50 0 $300 $0 $3005 50 0 $250 $0 $2506 100 0 $150 $0 $1507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 400 $150 $500 $65011 300 400 $250 $500 $75012 250 0 $0 $0 $0Totals 2000 2000 $1900 $2500 $4400
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Silver-Meal Algorithm
On
Hand
Inventory
MIT Center for Transportation amp Logistics - ESD260 11 copy Chris Caplice MIT
550 400250 550 250
Month
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Silver-Meal Algorithm
MIT Center for Transportation amp Logistics - ESD260 12 copy Chris Caplice MIT
Mon Dmd LotQty
Order Cost
Holding Cost LotCost
Mean Cost
1st Buy
1 200 200 $500 $0 $500 $5002 150 350 $500 $150 $650 $3253 100 450 $500 $150+$200 $850 $283
4 50 500 $500 $150+$200+$150 $1000 $250
5 50 550 $500 $150+$200+$150+$200
$1200 $240
6 100 650 $500 $150+$200+$150+$200+$500
$1700 $283
2nd Buy
6 100 100 $500 0 $500 $5007 150 250 $500 150 $650 $3258 200 450 $500 $150+$400 $1050 $350
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Silver-Meal Algorithm
Mon
Dmd Lot Qty
Order Cost
Holding Cost
Lot Cost
MeanCost
3rd Buy
8 200 200
$500 $0 $500 $500
9 200 400
$500 $200 $700 $350
10 250 650
$500 $200+$500
$1200 $400
4th Buy
10 250 250
$500 $0 $500 $500
11 300 550
$500 $300 $800 $400
12 250 800
$500 $300+$500
$1300 $433
5th Buy
12 250 250
$500 $0 $500 $500MIT Center for Transportation amp Logistics - ESD260 13 copy Chris Caplice MIT
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Silver-Meal Algorithm
Months Demand OrderQuantity
Holding Cost Ordering
CostPeriodCosts
1 200 550 $350 $500 $8502 150 0 $200 $0 $2003 100 0 $100 $0 $1004 50 0 $50 $0 $505 50 0 $0 $0 $06 100 250 $150 $500 $6507 150 0 $0 $0 $08 200 400 $200 $500 $7009 200 0 $0 $0 $010 250 550 $300 $500 $80011 300 0 $0 $012 250 250 $0 $500 $500Totals 2000 2000 $1350 $2500 $3850
MIT Center for Transportation amp Logistics - ESD260 14 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 15 copy Chris Caplice MIT
On
Hand
Inventory
550550 450450
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 16 copy Chris Caplice MIT
Decision VariablesQi = Quantity purchased in period iZi = Buy variable = 1 if Qigt0 =0 owBi = Beginning inventory for period IEi = Ending inventory for period
DataDi = Demand per period i = 1nCo = Ordering CostChp = Cost to Hold $unitperiodM = a very large numberhellip
MILP ModelObjective Functionbull Minimize total relevant costsSubject Tobull Beginning inventory for period 1 = 0bull Beginning and ending inventories must matchbull Conservation of inventory within each periodbull Nonnegativity for Q B Ebull Binary for Z
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Objective Function
Beginning amp EndingInventory Constraints
Conservation ofInventory Constraints
Ensures buys occuronly if Qgt0
Non-Negativity ampBinary Constraints
MIT Center for Transportation amp Logistics - ESD260 17 copy Chris Caplice MIT
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Approach Optimization (MILP)
MIT Center for Transportation amp Logistics - ESD260 18 copy Chris Caplice MIT
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
Comparison of Approaches
MIT Center for Transportation amp Logistics - ESD260 19 copy Chris Caplice MIT
Month Demand
OTB L4L EOQ SM OPT
1 200 2000 200 400 550 5502 150 150
3 100 100 400
4 50 50
5 50 50
6 100 100 250 450
7 150 150
8 200 200 400 400
9 200 200 450
10 250 250 400 550
11 300 300 400 550
12 250 250 250
Totals Cost $13600 $6000
$4400
$3850
$3750
