Scope of lecture 2 - NTNU · Scope of lecture 2 • Logistics network configuration and design –...
Transcript of Scope of lecture 2 - NTNU · Scope of lecture 2 • Logistics network configuration and design –...
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Lecture 2
Supply Chain Planning and Control
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Scope of lecture 2• Logistics network configuration and design
– Optimization models and decision support– What is needed to optimize the value chain
• Data collection• Data aggregation• Modelling transportation• Modelling cots• Capacities• Demand• Model and data validation• Solution techniques
– Case 1: Location of plants under economics of scale– Key features for network configuration (design)
• Supply chain integration (first thoughts on the topic)– Push, Pull and Push- Pull systems– Demand and supply driven value chains– Distribution strategies– Decentralized decision making– Central versus local facilities– The impact of internet
– Case 2: Supply chain optimization in Gilde (continued from lecture 1/exercise1)
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Learning objectives• Configuration and design
– To understand the use of some typical classes of optimization based decision support tools
– Know how to approach a supply chain network design problem with analytical tools
• Integration– Be familiar with some categories of supply chains and the differences in
their design focus and control mechanisms
– To understand how coordination of supply chains is dealt with by the OR and OM traditions
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Optimization based planning
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Decision Support Traditions• Data processing/manipulation
– MRP, DRP (little optimization)
• Mathematical programming– LP, MIP, Heuristics, Stochastic Programming
• Simulation– Discrete time simulation, system dynamics
• AI (Production Planning & Scheduling)– Expert systems (rule based), constraint optimization, knowledge based
rules, neighborhood search
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Software – Historical Development• MRP (Material Requirements Planning)
– Data processing and manipulation, push system• MRPII (Manufacturing Resource Planning)
– Management accounting, more focus on planning, purchase and market• DRP (Distribution resource planning)
– Extension of MRP, ideas also on distribution, dynamics and coordination• JIT (Just in time)
– Small series, demand driven, integration of logistics, pull system • ERP (Enterprise Resource Planning)
– Coordination of profit centers and functions• Supply Chain Management
– Collaborative Planning– Supply Chain Optimization
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Hierarchical Planning and Operations Research• Decisions are very complex, especially in a setting with many locations,
plants, warehouses, machines, products, customers, etc. (not to talk about uncertainties of the future...)
• Decision support tools are therefore used to provide decision-makers with necessary support
• Most of today's decision support tools are based on optimization and methods of Operations Research
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Supply Chain Management Packages
Strategic
Tactical
Operational
Commercial Software
MRP, DRP, ERP
Economics, purchases, inventories, planning, etc.
Planning
Finite Capacity SchedulingOptimization tools
Transaction database
Supply chain flow Production planningInventories
SC CoordinationSC Management
Aggregated Production and Inventory Planning
SC Design SC ManagementCooperation and Competition
Vehicle Routing
Transportation Planning
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Analytical Applications• Applications with planning capabilities
– Procurement and Content Cataloging Applications– Advanced Planning and Scheduling– Transportation Planning and Control Systems– Demand Planning and Revenue Management– Customer Relationship Management and Sales Force Automation
• Applications with more operational capabilities– Inventory Management Systems– Manufacturing Execution System– Transportation Execution– Warehouse Management System
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Vendors of IT-Solutions• ERP systems
– SAP– Oracle– Peoplesoft– J. D. Edwards– Baan
• Analytical Applications– i2 Technologies– Manugistics– ERP players (to a certain degree)
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Strategic Decision Support
• Balances purchase, production-and distribution cost
• Distribution centers, warehouses, plants
– Optimal number– Location– Size
• Resource allocation
• Determine best distribution channels
– Strategic Vehicle Routing– Partners, Vehicles, Routes,
Functions
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Decision Classifications - Tactical Planning
• Effective allocation of manufacturing and distribution resources over a period of several months
1. Work- force size
2. Inventory policies
3. Definition of the distribution channels
4. Selection of transportation and trans- shipment alternatives
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Warehouses, example of tactical planning• Multiperiod inventory models
• Synchronizing inventory towards
– Production plan– Actual production– Supply Chain– Deliveries
• Demand mapping
• Inventory optimization– Adaptive inventory
management vs security buffer
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Decision Classifications- Operational Planning
• Includes day- to- day operational decisions
1. The assignment of customer orders to individual machines
2. Dispatching, expediting and processing orders
3. Vehicle scheduling
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Routing, example of operational planning
• Optimal routes
• Improves efficiency of personal and material
• Time windows• Dynamic planning• Continuously updating drivers• Example
– SINTEF Anvendt MatematikkGreen trip, Spider
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Decision support software
• What do you need to get it working?
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Data for Network Design and supply chain planning1. A listing of all products2. Location of customers, stocking points and sources3. Demand for each product by customer location4. Transportation rates5. Warehousing costs6. Shipment sizes by product7. Order patterns by frequency, size, season, content8. Order processing costs9. Customer service goals
©Copyright 2002 D. Simchi-Levi
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Mapping Allows You to Visualize Your Supply Chain
©Copyright 2002 D. Simchi-Levi
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Displaying the Solutions Allows you To Compare Scenarios
©Copyright 2002 D. Simchi-Levi
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Aggregating Customers
• Customers located in close proximity are aggregated using a grid network or clustering techniques. All customers within a single cell or a single cluster are replaced by a single customer located at the centroid of the cell or cluster.
We refer to a cell or a cluster as a customer zone.
• Why?
– The cost of obtaining and processing data
– The form in which data is available
– The size of the resulting location model
– The accuracy of forecast demand
©Copyright 2002 D. Simchi-Levi
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Comparing Output
Total Cost:$5,796,000Total Customers: 18,000
Total Cost:$5,793,000Total Customers: 800
Cost Difference < 0.05% ©Copyright 2002 D. Simchi-Levi
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Product Grouping
• Companies may have hundreds to thousands of individual items in their production line
1. Variations in product models and style
2. Same products are packaged in many sizes
• Collecting all data and analyzing it is impractical for so many product groups
• Aggregate the products by similar logistics characteristics– Weight– Volume– Holding Cost
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Sample Aggregation Test:Product Aggregation
Total Cost:$104,564,000Total Products: 46
Total Cost:$104,599,000Total Products: 4
Cost Difference: 0.03% ©Copyright 2002 D. Simchi-Levi
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Transport Rate Estimation
• Huge number of rates representing all combinations of product flow
• An important characteristic of a class of rates for truck, rail, UPS and other trucking companies is that the rates are quite linear with the distance.
©Copyright 2002 D. Simchi-Levi
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Transport Rate Estimation
©Copyright 2002 D. Simchi-Levi
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Solution Techniques
• Mathematical optimization techniques:
1. Exact algorithms: find optimal solutions
2. Heuristics: find “good” solutions, not necessarily optimal
• Simulation models: provide a mechanism to evaluate specified design alternatives created by the designer.
©Copyright 2002 D. Simchi-Levi
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• Optimization model– Suggests solutions
• Simulation model– Checks the effect of decisions
by calculating the results
Decision-Support and Simulation
Ruteplanlegger(optimeringsverktøy)
- deterministiske kjøretider- ingen usikkerhet
Simuleringsverktøy
Analyse avusikkerhet
Effekt av ruteplan ogusikkerhetRuteplan
usikre parametre
• Combined simulation and optimization– Model adjusts decisions according to the information becoming
available– Example: Deviation management implemented in the model
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Example from Simchi-Levi.
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Heuristics andthe Need for Exact Algorithms
• Single product
• Two plants p1 and p2– Plant P1 has an annual capacity of 200,000 units.
– Plant p2 has an annual capacity of 60,000 units.
• The two plants have the same production costs.
• There are two warehouses w1 and w2 with identical warehouse handling costs.
• There are three markets areas c1,c2 and c3 with demands of 50,000, 100,000 and 50,000, respectively.
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Heuristics andthe Need for Exact Algorithms
Table 1Distribution costs per unit
FacilityWarehouse
P1 P2 C1 C2 C3
W1W2
05
42
32
41
52
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Why Optimization Matters?
D = 50,000
D = 100,000
D = 50,000Cap = 60,000
Cap = 200,000
$4
$5
$2
$3
$4
$5
$2
$1
$2
Production costs are the same, warehousing costs are the same
$0
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Traditional Approach #1:Assign each market to closet WH. Then assign each plant based on cost.
D = 50,000
D = 100,000
D = 50,000Cap = 60,000
Cap = 200,000
$5 x 140,000
$2 x 60,000
$2 x 50,000
$1 x 100,000
$2 x 50,000
Total Costs = $1,120,000
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Traditional Approach #2:Assign each market based on total landed cost
D = 50,000
D = 100,000
D = 50,000Cap = 60,000
Cap = 200,000
$4
$5
$2
$3
$4
$5
$2
$1
$2
$0
P1 to WH1 $3P1 to WH2 $7P2 to WH1 $7P2 to WH 2 $4
P1 to WH1 $4P1 to WH2 $6P2 to WH1 $8P2 to WH 2 $3
P1 to WH1 $5P1 to WH2 $7P2 to WH1 $9P2 to WH 2 $4
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Traditional Approach #2:Assign each market based on total landed cost
D = 50,000
D = 100,000
D = 50,000Cap = 60,000
Cap = 200,000
$4
$5
$2
$3
$4
$5
$2
$1
$2
$0
P1 to WH1 $3P1 to WH2 $7P2 to WH1 $7P2 to WH 2 $4
P1 to WH1 $4P1 to WH2 $6P2 to WH1 $8P2 to WH 2 $3
P1 to WH1 $5P1 to WH2 $7P2 to WH1 $9P2 to WH 2 $4
Market #1 is served by WH1, Markets 2 and 3are served by WH2
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Traditional Approach #2:Assign each market based on total landed cost
D = 50,000
D = 100,000
D = 50,000Cap = 60,000
Cap = 200,000
$5 x 90,000
$2 x 60,000
$3 x 50,000
$1 x 100,000
$2 x 50,000
$0 x 50,000
P1 to WH1 $3P1 to WH2 $7P2 to WH1 $7P2 to WH 2 $4
P1 to WH1 $4P1 to WH2 $6P2 to WH1 $8P2 to WH 2 $3
P1 to WH1 $5P1 to WH2 $7P2 to WH1 $9P2 to WH 2 $4
Total Cost = $920,000
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The Optimization Model
The problem described earlier can be framed as the following linear programming problem.Let
• x(p1,w1), x(p1,w2), x(p2,w1) and x(p2,w2) be the flows from the plants to the warehouses.
• x(w1,c1), x(w1,c2), x(w1,c3) be the flows from the warehouse w1 to customer zones c1, c2 and c3.
• x(w2,c1), x(w2,c2), x(w2,c3) be the flows from warehouse w2 to customer zones c1, c2 and c3
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The problem we want to solve is: min 0x(p1,w1) + 5x(p1,w2) + 4x(p2,w1)+ 2x(p2,w2) + 3x(w1,c1) + 4x(w1,c2)+ 5x(w1,c3) + 2x(w2,c1) + 2x(w2,c3)
subject to the following constraints:x(p2,w1) + x(p2,w2) ≤ 60000
x(p1,w1) + x(p2,w1) = x(w1,c1) + x(w1,c2) + x(w1,c3)x(p1,w2) + x(p2,w2) = x(w2,c1) + x(w2,c2) + x(w2,c3)
x(w1,c1) + x(w2,c1) = 50000x(w1,c2) + x(w2,c2) = 100000x(w1,c3) + x(w2,c3) = 50000
all flows greater than or equal to zero.
The Optimization Model
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The Optimal Strategy
Table 2Distribution strategy
FacilityWarehouse
P1 P2 C1 C2 C3
W1W2
1400000
060000
500000
4000060000
500000
The total cost for the optimal strategy is 740,000.
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Facility Location under Economics of Scale – A strategic case from Gilde
Case
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• Slaughterhouse location analysis
• The company has approximately 25 slaughterhouses for cattle
• What would be the optimal number and locations if they were free to replace them today (using the animal populations they are currently serving)?
– Location– Size
• Requirements– All demand (from farmers) should be met– No animal should stay more than 8 hours in the car on its way to the
slaughterhouse
Background
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Slaughterhouse Cost I• Nonlinearities in objective• Economics of Scale in slaughterhouses• Numbers are from a German best practice study
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Slaughterhouse Cost II
• Includes– Fixed costs
• Capital cost, Personal, Insurance
– Variable costs• Energy, Personal, Water, Cleaning, Repairs, Classification, Material, Waste
management,
• Broken down to yearly numbers and further down to cost per kilo
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Total Slaughterhouse Costs (without transportation)
kr
tons
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Transportation Time and Cost Estimates• Time
– Time between slaughterhouse and region
– Time on roundtrip within region– Terminal time– Max limit for transportation is 8
hours
• Cost– Linear in travel distance and kilos
• Both time and cost depend on the size of the car used
– Two car types
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5 4
Start - stop
X-km
y-km6
9,5 animal per stopstoppcapasity per car is 45,7 animalThis leads to 4,8 stop
distance between stops is 23,6 km
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Facility Location Modelmin
,
1 (S2) ,
,
( , ) ( )
0 ( , )1 ( , )
ij ij b b jbi M j M j M b B
b jb ijb B i M
jbb B
ij ij M
ij ij i
ij
ij
C x Q P
Q g x j M
j M
x A i M
x T A i j MxM
T i j FT i j F
λ
λ
λ
∈ ∈ ∈ ∈
∈ ∈
∈
∈
+ ⋅ ⋅
= ∈
= ∈
= ∈
≤ ∈
= ∉
= ∈
∑∑ ∑∑
∑ ∑
∑
∑
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Original Locations
• originally 435 candidate locations• uncapacitated
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Simple Candidate Reduction Heuristic• 435 possible locations. Too much!• Identify candidates by solving min transportation cost problems with at
most– 5 slaughterhouses– 10 slaughterhouses– 15 slaughterhouse– 20 slaughterhouses
• The union of optimal solutions is the candidate set
• Solve Mixed Integer Program with 20-40 possible locations
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SLAKTERI-LOKASJONER
Storfe case 3/3a/3b/3c - Kandidatsett - sc8
Candidate set
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Typical Result (in this case on artificial data)
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Results
• Best solution found has 11 slaughterhouses– Current solution have 25
• Reduces costs with 30%
• Optimality gap :(UB-LB)/UB =27%
• Solution time about 12 hours!
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How should the model be used?
• The models indicates a potential for saving in today’s situation
• It does not indicate what should be the future structure
• It indicates that the number of slaughterhouses is more important to the overall cost than the exact location is
• There are many almost equally good solutions with the same number of slaughterhouses, but where the geographical distribution is different.
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Management accounting and supply chain
coordination
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The old cost oriented theories of managment accounting have a focus on :
– Intra company cost management– Cost based pricing in a intra- company perspective, not a supply chain perspective– Management by intra- company budgets based on forecasts for product demand– Product profitability within the company– Activity based costing and management within the company– Discussing centralized or decentralized decisions within the company– Incentive systems, contracts and compensation systems within the company– Financial accounting of the company’s performance– Balanced scorecard to evaluate the company’s behavior
• While much of the theory is still valid, the focus is now shifted to the inter-company relationships of the supply chain
• The management accounting literature is not updated to reflect this!• We will study some of the effects
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Supply
Sources:plantsvendorsports
RegionalWarehouses:stocking points
Field Warehouses:stockingpoints
Customers,demandcenterssinks
Production/purchase costs
Inventory &warehousing costs
Transportation costs
Inventory &warehousing costs
Transportation costs
©Copyright 2002 D. Simchi-Levi
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Functional or innovative value chains? (Fisher, M.L. 1997)
The supply chain has two types of functions and costs- Physical (production, transportation, storage)- Market mediation (supply exceeds/falls short of demand): lost sales, dissatisfied
customers
• Functional products:– Satisfy basic needs– Wide range of retail outlets– Stable predictable demand– Long life cycles– Cost and efficiency oriented
• Innovative– New designs– Unpredictable market– Short lifecycles– Focus on market mediation costs
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Fisher, M.L., 1997.
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Fisher, M.L., 1997.
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Fisher, M.L., 1997.
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Stock-out rate and profitExample 1Stock-out rate: 25%Margin 40%
Overhead from stock-outs: 40%*25%=10%
This is more than the normal profit rate of most companiesHigh margins and high stock-out means responsiveness should be in
Example 2• Stock-out 0,1%• Margin 10%
• Stock-out cost is negligible. Responsiveness less important
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How do you get a responsive system
• To get a responsive system, one needs to reduce uncertainty
• Lead-time is critical in responsive systems• Short lead-times is a way of dealing with demand uncertainty!
• Improving data-quality reduces uncertainty
• Hedging against uncertainty using buffers or excess capacity
• Mass customization: configuring products by the time of order– Needs flexible production systems!
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Shifts in focus in Supply chain management Kopczak & Johnson, 2003
• Shift no 1: From Cross functional integration to Cross-enterprise
Old: How do we get various functional areas of our company to work together to supply a product to our immediate customers?
New: How do we coordinate activities across companies as well as across internal functions to supply a product to the market
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Shifts in focus in Supply chain management Kopczak & Johnson, 2003• Shift no 2: From Physical efficiency to market mediation
Old: How do we minimize the costs our company incurs in production and distribution of our products?
New: How do we minimize the costs of matching supply and demand while continuing to reduce the costs of production and distribution?
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Price as a demand planning tool
Fisher, M.L., 1997.
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Shifts in focus in Supply chain management Kopczak & Johnson, 2003• Shift no 4: From single company product design to collaborative,
concurrent product, process and supply chain design
Old: How should our company design products to minimize product cost (material, production and distribution)?
New: How should collaborators design the product, process and supply chain to minimize cost?
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Shifts in focus in Supply chain management Kopczak & Johnson, 2003• Shift no 3: From supply focus to demand focus
Old: How can we improve the way we supply product in order to match supply and demand better, given the demand pattern?
New: How can we get earlier demand information or affect the demand pattern to match supply and demand?
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Shifts in focus in Supply chain management Kopczak & Johnson, 2003• Shift no 5: From cost reduction to breakthrough business model
Old: How can reduce our company’s production and distribution costs?
New: What new supply chain and marketing approach would lead to a breakthrough in customer value?
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Shifts in focus in Supply chain management Kopczak & Johnson, 2003• Shift no 6: From mass-market supply to tailored offerings
Old: How should we organize our company’s operations to serve the mass market efficiently while offering customized products?
New: How should we organize the supply chain to serve each customer or segment uniquely and provide a tailored customer experience?
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Information as a basis for tailored offerings Kopczak & Johnson, 2003
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Centralization versus decentralization
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Central versus local facilities• Safety stock: risk pooling in centralized systems
• Overhead: Economics of scale suggests few sites
• Lead time: more warehouses normally leads to shorter lead times
• Transportation costs: usually increases with fewer warehouses
• Service. Depends on how servie is defined. Hipping time increaes with fewer warehouses, while the proability that the coofs ae in stock increases even with lower total inventory levels.
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Management accounting:Does it favor Centralized or decentralized decisions?
• Why decentralize (Kaplan & Atkinson, advanced management accounting)
– Environment: Contingency theory suggests that the complexity of a firms environment will suggest the complexity of the internal structure
– Information specialization: avoiding the difficulties of sharing information– Timeliness of response: need no central approvement. – Conservation of central management time– Computational complexity– Training for local managers– Motivation for local managers
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Management accounting:Organization of decentralized units
• Cost centers– Applicable whenever it is possible to define and measure the relationship between inputs and
outputs.– In general managers are not held responsible for variations in activity level– Efficiency is measured by the amount of inputs used to produce the demanded output– Quality and timeliness standards must be defined– Decisions about price, quality , product mix and quantity are made elsewhere
• Revenue centers exists in order to organize marketing activities– Responsible for physical volume, marketing and sales, and normally buys from a manufacturing
division– Prices may be given centrally – What about costs?
• Some notion should be given.• What happens if only revenues are used to measure performance?• MC=MR
– Activity based costing can be used to turn revenue centers into profit centers
• Discretionary expense centers– Appropriate for units were no strong relation exists between resources expended (inputs) and
results achieved (outputs)• General and administrative departments, R&D, marketing• Determining the budget nee the judgment of informed professionals
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• Profit centers– Cost centers, revenue centers and discretionary expense centers have limited
decentralization of decisions– A significant increase in responsibility is given when managers control both
production and sales– Decisions include, quantities, volume, price, marketing, product mix, resource
allocation, etc– They are in the position to optimize performance of their local centers by making
tradeoffs between price, volume, quality and cost.– If investments are not made locally, profit may be a good performance measure. It is
a short run indicator on how well mangers are creating value from existing resources• Investment centers
– When the manager in addition has responsibility for working capital and physical assets, the performance measure should include the level of physical and financial assets as well. Return on investment and economic value added are typical measures.
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Problems with decentralization• Ideally the performance measure should be consistent with the overall company
goal• It is clear that there could exist goal congruence between divisions• Also because of uncertainty, private information, lack of observability one
divisions decisions can affect another divisions performance such that simple prices or cost based measures does not give a correct view on performance
• Over consumption of perquisites– A local manager may decide to improve his local environment by increasing his
expenditures. This will reduce his performance measure, but the manager may prefer the benefits for the working environment, rather than a small increase in compensation that could be earned by foregoing the expenditures.
– Another example on this is empire building: maximizing he size of the organization.
• What happens in a supply chain setting with several companies?
• How should you measure performance of one link in the chain, and how should the reward or compensation system be designed?
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Suppy chain integration (first thoughts on the
topic)
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A new Supply Chain Paradigm• A shift from a Push System...
– Production decisions are based on forecast• …to a Push-Pull System
– Parts inventory is replenished based on forecasts– Assembly is based on accurate customer demand
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From Make-to-Stock Model….
ConfigurationAssemblySuppliers
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Push-Pull Supply Chains
Push-Pull Boundary
PUSH STRATEGY PULL STRATEGY
Low Uncertainty High Uncertainty
The Supply Chain Time Line
CustomersSuppliers
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….to Assemble-to-Order Model
ConfigurationAssemblySuppliers
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Business models in the Book Industry
• From Push Systems...– Barnes and Noble
• ...To Pull Systems– Amazon.com, 1996-1999
• And, finally to Push-Pull Systems– Amazon.com, 1999-present
• 7 warehouses, 3M sq. ft.,
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Business models in the Grocery Industry
• From Push Systems...– Supermarket supply chain
• ...To Pull Systems– Peapod, 1989-1999
• Stock outs 8% to 10%
• And, finally to Push-Pull Systems– Peapod, 1999-present
• Dedicated warehouses• Stock outs less than 2%
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Matching Supply Chain Strategies with Products
Pull Push
Pull
Push
IComputer
II
IV III
Demand uncertainty
(C.V.)
Delivery costUnit price
L H
H
L
Economies of Scale
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Locating the Push-Pull Boundary
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Organizational Skills Needed
RawMaterial Customers
PullPush
Low Uncertainty
Long Lead Times
Cost Minimization
Resource Allocation
High Uncertainty
Short Cycle Times
Service Level
Responsiveness
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Distribution Strategies
StrategyAttribute
DirectShipment
CrossDocking
Inventory atWarehouses
RiskPooling
TakeAdvantage
TransportationCosts
ReducedInbound Costs
ReducedInbound Costs
HoldingCosts
No WarehouseCosts
No HoldingCosts
DemandVariability
DelayedAllocation
DelayedAllocation
Distribution strategies
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Case 2Continuation from exercise 1 and
lecture 1
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SCM in Gilde• Weekly planning
– Facilities are fixed
• Purpose– Balancing the supply and the demand of the supply chain using
• Available production resources and marketing• Suppliers own the value chain (farmers)• Supermarket chains are the main customers• Both pull and push oriented!
– Demand planning• Price and marketing
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The Supply Chain
I
C
C
P
P
D
D
S - Slaughtering
D - Distribution centreP - Processing
Supply chain for Beef, veal, lamb and pork meat
I - Inventory
S
S
I I
C - Cutting
PC
PPPC
PP Set of processing prescriptionsPC Set of cutting prescriptions
PP
Customers
CustomersInput
Input
Other companies Within region flowOutside region flow
I
I
Region North
Region West
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I
C
C
P
P
D
D
S
S
I I
PC
PPPC
PP
Customers
CustomersInput
Input
Other companies Within region flowOutside region flow
I
I
Xij - mengde slaktet i region i av dyr j
Xij
Xij
Yijk
Yijk
Zijk
Zijk
Sji
Sji
Yijk - mengde delt til produkt k av dyr j i region i
Zijk - mengde av produkt j benyttet i produksjon av produkt k i region i
Sji - mengde av produkt j solgt i region i
Tjih - mengde av produkt j transportert fra region i til region f
Tjih Tjih Tjih Tjih
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I
C
C
P
P
D
D
S
S
I I
PC
PPPC
PP
Customers
CustomersInput
Input
Other companies Within region flowOutside region flow
I
I
Ki- slaktekapasitet i region i
Xij≤ Ki Yijk≤ Li Zijk≤ PiSji
Sji
Li - delekapasitert i region i
Pi - produksjonskapasitet i region i
Mi - transportkapasitet mellom region i og region f
Tjih≤ Mi Tjih≤ Mi Tjih≤ MiTjih≤ Mi
Xij≤ Ki Yijk≤ Li Zijk≤ Pi
•Balanse-mengde inn i node =mengde ut av nodeLager (tidsapspektet)- Lager inn +produsert - sendt = lager utMålfunksjon
vare solgt *pris vare solgt - råvarer kjøpt *prisråvarer kjøpt
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Modelling the market (short term)
• income from sales• production costs• transportation costs
c
sales income at time t inscenario s for a product
stcδ8.0−stδ
stδ8.0 stδ2.1
p+c
p
pα
stpδ8.0
salesst
• inventory costs• cost of inputs• penalty costs
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Supply Chain Integration - Dealing with Conflicting Goals• Lot Size vs. Inventory• Inventory vs. Transportation• Lead Time vs. Transportation• Product Variety vs. Inventory• Cost vs. Customer Service
• Can ecommerce help with this?