Timing in the order up-to model

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Topic 11 Supply Chain and Coordination

• Stochastic EOQ models
• The reorder point the order up to model
• 3. Simulation of inventory models
• 4. Supply chain coordination with LP
• 6. Aggregate planning
• 7. The aggregate planning formulation with LP

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Criteria often used as cost surrogates
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Continuous Review of Inventory (ROP or Q System)
Place an order for Q units whenever inventory
withdrawal brings inventory position to R
The reorder point (R) is normally calculated by
adding some level of safety stock (B) to the
expected demand over leadtime
L
L
L
Inventory
R
Time
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Numerical Example of a Q system
Demand over leadtime N(36,15) and CSL 90
1-CSL
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Periodic Review of Inventory (PRS or P System)
Review an items inventory position every P time
periods. At that time, place and order to
replenish to T units
The up-to order level(T) is normally calculated
by adding some level of safety stock (B) to the
expected demand over the protection interval (L
P)
T
L
L
Inventory
P
Time
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Numerical Example of a P System
D N(40,15) per week L 3 weeks CSL 80 What
P is required to approximate the cost tradeoffs
of a 400 unit EOQ? What is the desired level
of T?
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Numerical Example

• D N(15,6) units per week A 50 per order
• h 12 per unit per year L 2 weeks CSL 80
• Assume Continuous review System
• A. What is the EOQ?
• B. What is the desired B?
• C. What is the desired R ?

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Numerical Example (cont.)

• D N(15,6) units per week A 50 per order
• h 12 per unit per year L 2 weeks CSL 80
• Assume Periodic Review
• A. What value of P provides approximate EOQ
  tradeoffs?
• B. What is the desired
• B and T?

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Advantages of P and Q Systems

• Continuous (Q) systems
• Carry less safety stock
• Order size is constant
• Individualize replenishment intervals
• Suited to quantity discounts and capacity
  limitations
• Periodic (P) systems
• Less need to take additional physical inventory
• Fixed replenishment intervals
• Can coordinate replenishment of multiple items

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A Reorder Point (ROP) Inventory Model
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• GEN
• LIMITS,10,,,10
• EQUIVALENCE, INVPOS, XX1
• EQUIVALENCE, ONHAND, XX2
• EQUIVALENCE, BACKORD, XX3
• EQUIVALENCE, LOST, XX4
• EQUIVALENCE, ORDERS, XX6
• EQUIVALENCE, ROPOINT, XX8
• EQUIVALENCE,QUANT,XX9
• INITIALIZE,0.0,10000,YES
• INTLC,INVPOS,6,ONHAND,6,ROPOINT,4,QUANT,12
  
• TIMST,,INVPOS,"INVENTORY POSITION",0,0.0,1.0
• TIMST,,ONHAND,"INVENTORY ON HAND",0,0.0,1.0
• TIMST,,BACKORD,"BACKORDERS",0,0.0,1.0
• TIMST,,LOST,"DEMAND LOST",0,0.0,1.0
• TIMST,,ORDERS,"ORDERS PLACED",0,0.0,1.0
• NET
• FIN

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An Order-Up-To Inventory Model
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• GEN,"UPTO MODEL",,,,YES,YES
• LIMITS,10,,,10
• EQUIVALENCE, INVPOS, XX1
• EQUIVALENCE, ONHAND, XX2
• EQUIVALENCE, BACKORD, XX3
• EQUIVALENCE, LOST, XX4
• EQUIVALENCE, UPTO, XX5
• EQUIVALENCE, PERIOD, XX7
• EQUIVALENCE, QUANT, ATRIB1
• INITIALIZE,0.0,10000,YES
• INTLC,INVPOS,6,ONHAND,6,UPTO,12,PERIOD,6
  
• TIMST,,INVPOS,"INVENTORY POSITION",0,0.0,1.0
• TIMST,,ONHAND,"INVENTORY ON HAND",0,0.0,1.0
• TIMST,,BACKORD,"BACKORDERS",0,0.0,1.0
• TIMST,,LOST,"DEMAND LOST",0,0.0,1.0
• NET
• FIN

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What is the bullwhip effect?

• Demand variability increases as you move up the
  supply chain from customers towards supply

Customer
Retailer
Distributor
Factory
Tier 1 Supplier
Equipment
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Bullwhip effect in autos to machine tools
Autos

• Machine tools

change in demand
GDP solid line
SourceAnderson, Fine and Parker (1996)
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Bullwhip effect in the US PC supply chain
Annual percentage changes in demand (in s) at
three levels of the semiconductor supply chain
personal computers, semiconductors and
semiconductor manufacturing equipment.
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Consequences of the bullwhip effect

• Inefficient production or excessive inventory.
• Low utilization of the distribution channel.
• Necessity to have capacity far exceeding average
  demand.
• High transportation costs.
• Poor customer service due to stockouts.

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Causes of the bullwhip effect

• Order synchronization
• Multiple retailers who tend to order around the
  same time period
• Manufacturers responding to an MRP system that
  place raw material orders at the beginning of the
  month
• Order batching
• In order to save on shipping or ordering costs,
  firms order a full pallet or full truck load
• Trade promotions and forward buying
• Supplier offers a discount on product ordered in
  a specific time period
• Supplier offers a quantity discount
• A retailer orders a large quantity intending to
  take advantage of a discount and sells excess
  product to a second retailer (this strategy is
  called diversion)
• Reactive and over-reactive ordering
• A retailer who is not sure that demand is stable
  over time may act aggressively when faced with
  periods of lower or higher than expected demand
  
• Shortage gaming
• A retailer who wants to insure product from an
  under-capacitated supplier may over order
  expecting to only receive a portion of the
  ordered quantity

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Strategies to combat the bullwhip effect

• Information sharing
• Collaborative Planning, Forecasting and
  Replenishment (CPFR)
• Smooth the flow of products
• Coordinate with retailers to spread deliveries
  evenly.
• Reduce minimum batch sizes.
• Smaller and more frequent replenishments (EDI).
• Eliminate pathological incentives
• Every day low price
• Restrict returns and order cancellations
• Order allocation based on past sales in case of
  shortages
• Vendor Managed Inventory (VMI) delegation of
  stocking decisions

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Example
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Example
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EXAMPLE
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A Multi-Period Transshipment Problem
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2
6
3
Monday
7
4
9
5
1
8
2
6
3
Tuesday
7
4
9
5
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Aggregate Production Planning (APP)
Aggregate Production Planning (APP)
Demand Planning and Forecasting
A macro approach to operational planning that
focuses on overall capacity. APP links
higher-level facility planning to lower level
scheduling decisions within a medium-term
planning horizon (2 to 18 months).
Master Production Scheduling (MPS)
Material Requirements Planning (MRP)
Capacity Planning (CRP)
Material and Capacity Plans
Shop Floor Control
Purchasing
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APP (cont)

• Role of Aggregate Planning
• Long-term planning function
• Strategic preparation for tactical actions
• Aggregate Planning Issues
• Staffing -hiring, firing, training
• Procurement - supplier contracts for materials,
  components
• Sub-Contracting - capacity vendoring
• Marketing - promotional activities

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Basic Aggregate Planning (cont.)
Cotton Shirts
Mens
Womens
Boys
Girls
Style B
Style C
Style A
Week1
Week2
Week3
Week4
Week5
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Pure APP Planning Strategies
Demand
Production
Units
Time
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Pure APP Planning Strategies
Demand Production
Units
Time
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A Basic Linear Programming Formulation

• The heart of the APPLP formulation is the
  production constraint
• (Beginning Inventory) Production (Ending
  Inventory) Demand
• Or I1 P - I2 D
• Chained over multiple periods by inventory flow
• I1 P1 - I2 D1
• I2 P2 - I3 D2
• I3 P3 - I4 D3
• etc

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A More Complete Production Constraint
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Work Force Capacity Constraints

• The APPLP can incorporate short-term capacity
  adjustments
• For example, a work force can be increased or
  diminished
• (Workers in p1) (Workers in p0) (p0 hires)
  (p0 layoffs)
• or Wi Hi Fi W0
• and chained over multiple periods by work force
  level
• W1 - H1 L1 W0
• W2 - W1 - H2 L2 0
• W3 - W2 - H3 L3 0

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