Logistics and Supply Chain Management
Content
Logistics and Supply Chain Management
Logistics
The process of planning, implementing, and controlling the efficient, cost-effective flow and storage of goods, services, and related information, from point of origin to point of consumption, for the purpose of conforming to customer requirements. Components of an Integrated Logistics System
± Physical Supply: links suppliers to operations process ± Internal Operations: manages in-process material flow ± Physical Distribution: links operations process to customers
Transportation and storage of inventory
Coal mining Raw Material Finished Goods Limestone mining Finished Goods Iron ore mining Raw Material Raw Material Raw Material Auto body stamping Finished Goods Raw Material Steel making Chassis building Finished Goods Finished Goods Finished Goods Raw Material Raw Material
Auto assembly
Finished Goods
Dealers
Customers
Supply Chain Management
A philosophy that describes how organizations should manage their supply chains to achieve strategic advantage The objective is to synchronize requirements of the final customer with the flow of materials and information along the supply chain. The goal is to eliminate variability and reach a balance between high customer service and low cost
SCM: the need to reduce variability or the impact of variability on the supply chain
Supply network variability
± late deliveries: weather,equipment breakdown ± quality problems
Manufacturing process variability
± machine reliability and equipment failure ± changeovers / setups / part expediting ± design and quality problems Carrying safety Customer network variability inventories are the ± cancellations and irregular orders most common ± equipment failure approach to dealing with variability ± scheduling
Information Technology in SCM
Seen as the key to variability reduction Links the success of independent suppliers, manufacturers, and customers Risks and rewards are shared among supply chain partners Many technologies are accepted among supply chain managers
± ± ± ± Electronic data interchange (EDI) Artificial intelligence / Expert systems Bar code and radio frequency systems Internet applications
Environmental Sensitivity
NOW: Supply chains create tremendous amounts of waste material to protect goods in shipment and storage. FUTURE: Distribution will use reverse logistics, the recycling or proper disposal of cardboard, packing material, strapping, shrink wrap, pallets, etc...
Two major problems in supply chain management
1. 2. How to synchronize to eliminate expensive decoupling inventory How to reduce transportation costs.
A study by A.T. Kearney & Company provides the average distribution cost (as a percentage of sales) across 270 companies. Functional Activity Administration Transportation : Inbound Outbound Receiving and shipping Packaging Warehousing Inventory carrying cost: Interest Taxes, insurance, obsolescence Order processing Total % of sales 2.4 2.1 4.3
6.4 1.7 2.6 3.7 2.2 3.8 1.2 21.8%
1.6
Supply
ai Sy c ro izatio a
i ear rogrammi g
T e Tra sportatio
ro lem: a general ormulation o a class o problems
related to the supply and distribution o goods and services across a net ork. Generally, the transportation problem is concerned ith the most cost e ective (or cost minimizing) ay to supply several demand locations (nodes) rom more than one supply location (nodes)
Example
Special tra sportatio co cer s: Route (or arcs) that have a ma ximum capacity Routes that cannot be traversed
The Transshipment Problem: a more generalized vers ion of the
transportation problem in which intermediate, transship ment, nodes are added to the network. Transshipment nodes are often used to model warehouses, material transfer locations, or junctions for mixed mode delivery of goods and services .
Example
Special transshipment concerns: Backwards or sidewards movement in the network Capacity limitations of the transshipment nodes
Quaker Oats has begun manufacturing, in two of its plants, a new granola product made of three parts oats, two parts raisins and one part almonds. Two oat vendors and two almond vendors have been identified, but only one reliable vendor of raisins could be found. The supply of raw materials and the shipped costs are provided Vendor Oat 1 Oat 2 Raisin Almond 1 Almond 2 Supply in tons 25,000 30,000 50,000 9,000 10,000 Cost to Plant 1 $100 $105 $550 $1,050 $1,200 Cost to Plant 2 $110 $95 $525 $1,150 $1,100
Quaker ships to three distribution facilities. The shipping cost of completed (6-ton) pallets of product and the demand at each distribution facility are provided Hannaford Plant 1 Plant 2 Demand $100 $95 2,500 Quaker $65 $70 5,000 WalMart $90 $90 10,000 Plant Capacity 9,500 8,500
Form latio
Minimize Z= 100 1Q1+110 1Q2+105 2Q1+95 2Q2+550 Q1+525 Q2+1050 1Q1+1150 1Q2+1200 2Q1+1100 2Q2+100Q 1H+65Q1 +90Q1W+95Q2H+70Q2 +90Q2W 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 1Q1+1 1Q2<=25000 1 2Q1+1 2Q2<=30000 1 Q1+1 Q2<=50000 1 1Q1+1 1Q2<=9000 1 2Q1+1 2Q2<=10000 1Q1H+1Q2H>=2500 1Q1 +1Q2 >=5000 1Q1W+1Q2W>=10000 1 1Q1+1 2Q1 3Q1H 3Q1 1 1Q2+1 2Q2 3Q2H 3Q2 1 Q1 2Q1H 2Q1 2Q1W=0 1 Q2 2Q2H 2Q2 2Q2W=0 1 1Q1+1 2Q1 1Q1H 1Q1 1 1Q2+1 2Q2 1Q2H 1Q2 Q1H+Q1 +Q1W<=9500 Q2H+Q2 +Q2W<=8500
ject
3Q1W=0 3Q2W=0
1Q1W=0 1Q2W=0
Combined Re port for Granola
Decision Solution Variable Value O O O O R R A A A A D W D W , , , , , , , , , , , . . . . . . . . . . , , , , . . . . . . , , , , , , . . . . . . Slack Surplus , , , . , , , . . . . , , , , . . , , . . . - . . . . . . , , . . , , , , , , , , , , , . . . . Shadow Price - . Allowable Min. R S , , , . . . . . . . . . . . . Allowable Max. R S , M M M M , , , , , , , , M , . . . . . . . . . Unit Cost Total Profit c(j) Contribution . . . , , , , , , , , , , , , , . . . . . . . . . . . Reduced Basis Cost Status basic at bound basic basic basic basic basic at bound at bound basic at bound basic basic basic at bound basic Allowable Allowable Min. c(j) Max. c(j) -M . . -M . -M , . , . , . -M . -, . . -, . . . M . , . M M , . M . . . M . . M M .
Objective Function (Min.) Const C C C C C C C C C C C C C C C C
Left and Right and Side Direction Side , , , , , , , , . . . . . . . . , , , , , . . . , , , . . . . .
. . . . . . . . .
Bullwhip Effect
The magnification of variability in orders in the supply-chain.
Retailer¶s Orders
Wholesaler¶s Orders
Manufacturer¶s Orders
Time
Time
Time
A lot of retailers each with little variability in their orders«.
«can lead to greater variability for a fewer number of wholesalers, and«
«can lead to even greater variability for a single manufacturer.
The i ent lem: d als with a ma ag rial d isio to assig r sour s (or ag ts) to sp ifi ustom rs (or tasks). Normally, th assig m t probl m is stru tur d to assig o a d o ly o ag t to o a d o ly o task. Exampl of a assig m t probl m
Ag 1 t 50 60 90 40 2 80 100 2 Task 1
Speci l
i nment c ncerns:
ultipl assig m ts Th umb r of ag ts ot qual to th umb r of tasks
3
30 50 60
3
T e arat o il Company operates t o refi eries, t o distri utio ce ters a on ompa y refineries, istri ution centers and t ree ta k aggo s ippi g poi ts to service its customers i t e sout east. efi e tank aggon ipping points in efined crude is s ipped from a refi ery to a distri utio ce ter a d fi ally to a ta k aggo s ippi g poi t for fi al sale to oil distri utors. la t capacities a d s ippi g costs (i $ per gallo ) from eac refi ery to eac distri utio ce ter ( ) are give elo : efi ery iami efi ery Spri gfield efi ery olum ia .004 .003 aco .006 .008 apacity 125,000 gals 95,000 gals
stimated customer dema d a d per unit s ipping costs (in $ per gallon) from eac to eac tank aggon s ipping point (T SP) are as follo s: istri ution enter Colum ia acon ont ly Demand: rade I il rade II il arleston T SP .0016 .0024 20,000 gals 40,000 gals Dur am T SP .0021 .0035 25,000 gals 35,000 gals Carver T SP .0031 .0022 45,000 gals 20,000 gals
rade I and II oil consume t e same amount of capacity to refine, o ever; only t e iami refinery is capa le of refining rade I oil.
Network
C1 M1 C2 D1 M2 M1 D2 Ch1 Ch2
Ca1 S2 M2 Ca2
Formulation
Minimize . M C1+ . M C2+ . MM 1+ . M M 2+ . C 2+ . M 2+ . 16C1CH1+ . 21C1D1+ . 1C1CA 1+ . 16C2CH2+ . 21C2D 2+ . 1C2CA 2+ . 24M M 1D1+ . 22M 1CA 1+ . 24M 2CH2+ . 1CH1+ . M 2D2+ . 22M 2CA 2 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 MC1+M C2+M M 1+MM 2< 125, SC2+SM 2< 5, -M C1+C1CH1+C1D 1+ C1CA 1= -M C2-SC2+C2CH2+ C2D2+C2CA 2= -MM 1+M 1CH1+M 1D1+M 1CA 1= -MM 2-SM 2+M 2CH2+M 2D2+M 2CA 2= C1CH1+M 1CH1=20000 C2CH2+M 2CH2=40000 C1D1+M 1D1= 25000 C2D2+M 2D2= 35000 C1CA 1+M 1CA 1=45000 C2CA 2+M 2CA 2=20000
Subject To:
Solution.
Decision Solution ariable alue 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 MC1 MC2 MM1 MM2 SC2 SM2 C1CH1 C1D1 C1CA1 C2CH2 C2D2 C2CA2 M1CH1 M1D1 M1CA1 M2CH2 M2D2 M2CA2 Objective Constrnt 1 2 3 4 5 6 7 8 9 10 11 12 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 45,000.00 0 45,000.00 0 95,000.00 0 20,000.00 25,000.00 0 40,000.00 35,000.00 20,000.00 0 0 45,000.00 0 0 0 nit Cost Total rofit c(j) Contri 0.0040 0.0060 0.0040 0.0060 0.0030 0.0080 0.0016 0.0021 0.0031 0.0016 0.0021 0.0031 0.0024 0.0035 0.0022 0.0024 0.0035 0.0022 180.0000 0 180.0000 0 285.0000 0 32.0000 52.5000 0 64.0000 73.5000 62.0000 0 0 99.0000 0 0 0 educed asis Cost Status 0 0.0030 0 0.0021 0 0.0041 0 0 0.0009 0 0 0 0.0008 0.0014 0 0.0017 0.0023 0 basic at bound basic at bound basic at bound basic basic at bound basic basic basic at bound at bound basic at bound at bound basic Allo able Allo able Min. c(j) Max. c(j) 0.0031 0.0030 0.0032 0.0039 -M 0.0039 -M -M 0.0022 -M -M 0.0014 0.0016 0.0021 -M 0.0007 0.0012 0.0001 0.0048 M 0.0049 M 0.0051 M 0.0024 0.0035 M 0.0033 0.0044 0.0052 M M 0.0031 M M 0.0039
unction (Min.) =
1,028.0000 Slack Shado or Surplus rice 35,000.00 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0040 -0.0030 -0.0040 -0.0039 0.0056 0.0046 0.0061 0.0051 0.0062 0.0061 Allo able Allo able Min. HS Max. HS 90,000.00 95,000.00 -35,000.0 0 -35,000.0 0 0 0 0 0 0 0 M M 45,000.0000 95,000.0000 45,000.0000 20,000.0000 55,000.0000 40,000.0000 60,000.0000 35,000.0000 80,000.0000 20,000.0000
eft Hand ight Hand Side Direction Side 90,000.00 95,000.00 0 0 0 0 20,000.00 40,000.00 25,000.00 35,000.00 45,000.00 20,000.00 <= <= = = = = = = = = = = 125,000.0000 95,000.0000 0 0 0 0 20,000.0000 40,000.0000 25,000.0000 35,000.0000 45,000.0000 20,000.0000
1 2 3 4 5 1 2 3 4 5 7 9 6 8 7 9
1. 2. 3. 4. 5. 6. nvent ie n m lti- e i l nnin imit ti n n i in ntitie Chan e in eman M ltim e hi in et n eve e l i tic
6
8
A Multi-Period Transshipment Problem
Tra sp rtati n a d the Travelin Salesma Problem Th t a li g sal sma p obl m is a sp ial t o k fo mulatio s that qui s a h u isti solutio fo all but th small st p obl ms. Th obj t of th TSP is to fi d a t o k y l that mi imi s qui d to isit all od s o . th total dista The nearest nei hbor procedure (heuristic) 1. 2. 3. 4. Sta t ith a od lo atio of th tou th d pot od Fi d th los st to th last Go ba k to st p 2 u til all Co t th fi st a d last to b isit d at th b gi i g . od add d to th tou . od s ha b add d. od s to ompl t th tou .
Example Use the following symmetric distance matrix to design a tour that minimizes total distance traveled. From Node 1 2 3 4 5 6 To Node (in miles) 2 3 4 5.4 2.8 10.5 5.0 9.5 5.0 7.8 9.5 7.8 5.0 6.0 5.0 8.5 3.6 9.5
1 5.4 2.8 10.5 8.2 4.1
5 8.2 5.0 6.0 5.0 9.2
6 4.1 8.5 3.6 9.5 9.2 -
T e Clark and
1. 2.
rig t avings He ristic
3. 4.
Select any n e as the e t n e n e 1 Com te the savin s, Sij , for lin in nodes i and j: S ij = c1i + c1j - cij for i and j nodes 2,3,...,n here cij = the cost of travelin from node i to node j an the savin s from largest to smallest Start at the top of the list, form larger subtours by lin ing appropriate nodes i and j. Stop hen complete tour is formed. ample
4
1 10 miles 3
2
Logistics
The process of planning, implementing, and controlling the efficient, cost-effective flow and storage of goods, services, and related information, from point of origin to point of consumption, for the purpose of conforming to customer requirements. Components of an Integrated Logistics System
± Physical Supply: links suppliers to operations process ± Internal Operations: manages in-process material flow ± Physical Distribution: links operations process to customers
Transportation and storage of inventory
Coal mining Raw Material Finished Goods Limestone mining Finished Goods Iron ore mining Raw Material Raw Material Raw Material Auto body stamping Finished Goods Raw Material Steel making Chassis building Finished Goods Finished Goods Finished Goods Raw Material Raw Material
Auto assembly
Finished Goods
Dealers
Customers
Supply Chain Management
A philosophy that describes how organizations should manage their supply chains to achieve strategic advantage The objective is to synchronize requirements of the final customer with the flow of materials and information along the supply chain. The goal is to eliminate variability and reach a balance between high customer service and low cost
SCM: the need to reduce variability or the impact of variability on the supply chain
Supply network variability
± late deliveries: weather,equipment breakdown ± quality problems
Manufacturing process variability
± machine reliability and equipment failure ± changeovers / setups / part expediting ± design and quality problems Carrying safety Customer network variability inventories are the ± cancellations and irregular orders most common ± equipment failure approach to dealing with variability ± scheduling
Information Technology in SCM
Seen as the key to variability reduction Links the success of independent suppliers, manufacturers, and customers Risks and rewards are shared among supply chain partners Many technologies are accepted among supply chain managers
± ± ± ± Electronic data interchange (EDI) Artificial intelligence / Expert systems Bar code and radio frequency systems Internet applications
Environmental Sensitivity
NOW: Supply chains create tremendous amounts of waste material to protect goods in shipment and storage. FUTURE: Distribution will use reverse logistics, the recycling or proper disposal of cardboard, packing material, strapping, shrink wrap, pallets, etc...
Two major problems in supply chain management
1. 2. How to synchronize to eliminate expensive decoupling inventory How to reduce transportation costs.
A study by A.T. Kearney & Company provides the average distribution cost (as a percentage of sales) across 270 companies. Functional Activity Administration Transportation : Inbound Outbound Receiving and shipping Packaging Warehousing Inventory carrying cost: Interest Taxes, insurance, obsolescence Order processing Total % of sales 2.4 2.1 4.3
6.4 1.7 2.6 3.7 2.2 3.8 1.2 21.8%
1.6
Supply
ai Sy c ro izatio a
i ear rogrammi g
T e Tra sportatio
ro lem: a general ormulation o a class o problems
related to the supply and distribution o goods and services across a net ork. Generally, the transportation problem is concerned ith the most cost e ective (or cost minimizing) ay to supply several demand locations (nodes) rom more than one supply location (nodes)
Example
Special tra sportatio co cer s: Route (or arcs) that have a ma ximum capacity Routes that cannot be traversed
The Transshipment Problem: a more generalized vers ion of the
transportation problem in which intermediate, transship ment, nodes are added to the network. Transshipment nodes are often used to model warehouses, material transfer locations, or junctions for mixed mode delivery of goods and services .
Example
Special transshipment concerns: Backwards or sidewards movement in the network Capacity limitations of the transshipment nodes
Quaker Oats has begun manufacturing, in two of its plants, a new granola product made of three parts oats, two parts raisins and one part almonds. Two oat vendors and two almond vendors have been identified, but only one reliable vendor of raisins could be found. The supply of raw materials and the shipped costs are provided Vendor Oat 1 Oat 2 Raisin Almond 1 Almond 2 Supply in tons 25,000 30,000 50,000 9,000 10,000 Cost to Plant 1 $100 $105 $550 $1,050 $1,200 Cost to Plant 2 $110 $95 $525 $1,150 $1,100
Quaker ships to three distribution facilities. The shipping cost of completed (6-ton) pallets of product and the demand at each distribution facility are provided Hannaford Plant 1 Plant 2 Demand $100 $95 2,500 Quaker $65 $70 5,000 WalMart $90 $90 10,000 Plant Capacity 9,500 8,500
Form latio
Minimize Z= 100 1Q1+110 1Q2+105 2Q1+95 2Q2+550 Q1+525 Q2+1050 1Q1+1150 1Q2+1200 2Q1+1100 2Q2+100Q 1H+65Q1 +90Q1W+95Q2H+70Q2 +90Q2W 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 1Q1+1 1Q2<=25000 1 2Q1+1 2Q2<=30000 1 Q1+1 Q2<=50000 1 1Q1+1 1Q2<=9000 1 2Q1+1 2Q2<=10000 1Q1H+1Q2H>=2500 1Q1 +1Q2 >=5000 1Q1W+1Q2W>=10000 1 1Q1+1 2Q1 3Q1H 3Q1 1 1Q2+1 2Q2 3Q2H 3Q2 1 Q1 2Q1H 2Q1 2Q1W=0 1 Q2 2Q2H 2Q2 2Q2W=0 1 1Q1+1 2Q1 1Q1H 1Q1 1 1Q2+1 2Q2 1Q2H 1Q2 Q1H+Q1 +Q1W<=9500 Q2H+Q2 +Q2W<=8500
ject
3Q1W=0 3Q2W=0
1Q1W=0 1Q2W=0
Combined Re port for Granola
Decision Solution Variable Value O O O O R R A A A A D W D W , , , , , , , , , , , . . . . . . . . . . , , , , . . . . . . , , , , , , . . . . . . Slack Surplus , , , . , , , . . . . , , , , . . , , . . . - . . . . . . , , . . , , , , , , , , , , , . . . . Shadow Price - . Allowable Min. R S , , , . . . . . . . . . . . . Allowable Max. R S , M M M M , , , , , , , , M , . . . . . . . . . Unit Cost Total Profit c(j) Contribution . . . , , , , , , , , , , , , , . . . . . . . . . . . Reduced Basis Cost Status basic at bound basic basic basic basic basic at bound at bound basic at bound basic basic basic at bound basic Allowable Allowable Min. c(j) Max. c(j) -M . . -M . -M , . , . , . -M . -, . . -, . . . M . , . M M , . M . . . M . . M M .
Objective Function (Min.) Const C C C C C C C C C C C C C C C C
Left and Right and Side Direction Side , , , , , , , , . . . . . . . . , , , , , . . . , , , . . . . .
. . . . . . . . .
Bullwhip Effect
The magnification of variability in orders in the supply-chain.
Retailer¶s Orders
Wholesaler¶s Orders
Manufacturer¶s Orders
Time
Time
Time
A lot of retailers each with little variability in their orders«.
«can lead to greater variability for a fewer number of wholesalers, and«
«can lead to even greater variability for a single manufacturer.
The i ent lem: d als with a ma ag rial d isio to assig r sour s (or ag ts) to sp ifi ustom rs (or tasks). Normally, th assig m t probl m is stru tur d to assig o a d o ly o ag t to o a d o ly o task. Exampl of a assig m t probl m
Ag 1 t 50 60 90 40 2 80 100 2 Task 1
Speci l
i nment c ncerns:
ultipl assig m ts Th umb r of ag ts ot qual to th umb r of tasks
3
30 50 60
3
T e arat o il Company operates t o refi eries, t o distri utio ce ters a on ompa y refineries, istri ution centers and t ree ta k aggo s ippi g poi ts to service its customers i t e sout east. efi e tank aggon ipping points in efined crude is s ipped from a refi ery to a distri utio ce ter a d fi ally to a ta k aggo s ippi g poi t for fi al sale to oil distri utors. la t capacities a d s ippi g costs (i $ per gallo ) from eac refi ery to eac distri utio ce ter ( ) are give elo : efi ery iami efi ery Spri gfield efi ery olum ia .004 .003 aco .006 .008 apacity 125,000 gals 95,000 gals
stimated customer dema d a d per unit s ipping costs (in $ per gallon) from eac to eac tank aggon s ipping point (T SP) are as follo s: istri ution enter Colum ia acon ont ly Demand: rade I il rade II il arleston T SP .0016 .0024 20,000 gals 40,000 gals Dur am T SP .0021 .0035 25,000 gals 35,000 gals Carver T SP .0031 .0022 45,000 gals 20,000 gals
rade I and II oil consume t e same amount of capacity to refine, o ever; only t e iami refinery is capa le of refining rade I oil.
Network
C1 M1 C2 D1 M2 M1 D2 Ch1 Ch2
Ca1 S2 M2 Ca2
Formulation
Minimize . M C1+ . M C2+ . MM 1+ . M M 2+ . C 2+ . M 2+ . 16C1CH1+ . 21C1D1+ . 1C1CA 1+ . 16C2CH2+ . 21C2D 2+ . 1C2CA 2+ . 24M M 1D1+ . 22M 1CA 1+ . 24M 2CH2+ . 1CH1+ . M 2D2+ . 22M 2CA 2 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 MC1+M C2+M M 1+MM 2< 125, SC2+SM 2< 5, -M C1+C1CH1+C1D 1+ C1CA 1= -M C2-SC2+C2CH2+ C2D2+C2CA 2= -MM 1+M 1CH1+M 1D1+M 1CA 1= -MM 2-SM 2+M 2CH2+M 2D2+M 2CA 2= C1CH1+M 1CH1=20000 C2CH2+M 2CH2=40000 C1D1+M 1D1= 25000 C2D2+M 2D2= 35000 C1CA 1+M 1CA 1=45000 C2CA 2+M 2CA 2=20000
Subject To:
Solution.
Decision Solution ariable alue 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 MC1 MC2 MM1 MM2 SC2 SM2 C1CH1 C1D1 C1CA1 C2CH2 C2D2 C2CA2 M1CH1 M1D1 M1CA1 M2CH2 M2D2 M2CA2 Objective Constrnt 1 2 3 4 5 6 7 8 9 10 11 12 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 45,000.00 0 45,000.00 0 95,000.00 0 20,000.00 25,000.00 0 40,000.00 35,000.00 20,000.00 0 0 45,000.00 0 0 0 nit Cost Total rofit c(j) Contri 0.0040 0.0060 0.0040 0.0060 0.0030 0.0080 0.0016 0.0021 0.0031 0.0016 0.0021 0.0031 0.0024 0.0035 0.0022 0.0024 0.0035 0.0022 180.0000 0 180.0000 0 285.0000 0 32.0000 52.5000 0 64.0000 73.5000 62.0000 0 0 99.0000 0 0 0 educed asis Cost Status 0 0.0030 0 0.0021 0 0.0041 0 0 0.0009 0 0 0 0.0008 0.0014 0 0.0017 0.0023 0 basic at bound basic at bound basic at bound basic basic at bound basic basic basic at bound at bound basic at bound at bound basic Allo able Allo able Min. c(j) Max. c(j) 0.0031 0.0030 0.0032 0.0039 -M 0.0039 -M -M 0.0022 -M -M 0.0014 0.0016 0.0021 -M 0.0007 0.0012 0.0001 0.0048 M 0.0049 M 0.0051 M 0.0024 0.0035 M 0.0033 0.0044 0.0052 M M 0.0031 M M 0.0039
unction (Min.) =
1,028.0000 Slack Shado or Surplus rice 35,000.00 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.0040 -0.0030 -0.0040 -0.0039 0.0056 0.0046 0.0061 0.0051 0.0062 0.0061 Allo able Allo able Min. HS Max. HS 90,000.00 95,000.00 -35,000.0 0 -35,000.0 0 0 0 0 0 0 0 M M 45,000.0000 95,000.0000 45,000.0000 20,000.0000 55,000.0000 40,000.0000 60,000.0000 35,000.0000 80,000.0000 20,000.0000
eft Hand ight Hand Side Direction Side 90,000.00 95,000.00 0 0 0 0 20,000.00 40,000.00 25,000.00 35,000.00 45,000.00 20,000.00 <= <= = = = = = = = = = = 125,000.0000 95,000.0000 0 0 0 0 20,000.0000 40,000.0000 25,000.0000 35,000.0000 45,000.0000 20,000.0000
1 2 3 4 5 1 2 3 4 5 7 9 6 8 7 9
1. 2. 3. 4. 5. 6. nvent ie n m lti- e i l nnin imit ti n n i in ntitie Chan e in eman M ltim e hi in et n eve e l i tic
6
8
A Multi-Period Transshipment Problem
Tra sp rtati n a d the Travelin Salesma Problem Th t a li g sal sma p obl m is a sp ial t o k fo mulatio s that qui s a h u isti solutio fo all but th small st p obl ms. Th obj t of th TSP is to fi d a t o k y l that mi imi s qui d to isit all od s o . th total dista The nearest nei hbor procedure (heuristic) 1. 2. 3. 4. Sta t ith a od lo atio of th tou th d pot od Fi d th los st to th last Go ba k to st p 2 u til all Co t th fi st a d last to b isit d at th b gi i g . od add d to th tou . od s ha b add d. od s to ompl t th tou .
Example Use the following symmetric distance matrix to design a tour that minimizes total distance traveled. From Node 1 2 3 4 5 6 To Node (in miles) 2 3 4 5.4 2.8 10.5 5.0 9.5 5.0 7.8 9.5 7.8 5.0 6.0 5.0 8.5 3.6 9.5
1 5.4 2.8 10.5 8.2 4.1
5 8.2 5.0 6.0 5.0 9.2
6 4.1 8.5 3.6 9.5 9.2 -
T e Clark and
1. 2.
rig t avings He ristic
3. 4.
Select any n e as the e t n e n e 1 Com te the savin s, Sij , for lin in nodes i and j: S ij = c1i + c1j - cij for i and j nodes 2,3,...,n here cij = the cost of travelin from node i to node j an the savin s from largest to smallest Start at the top of the list, form larger subtours by lin ing appropriate nodes i and j. Stop hen complete tour is formed. ample
4
1 10 miles 3
2
