Supply chain management II: Interaction in the chain

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Supply chain management IIInteraction in the
chain

• Inventory management

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Why do firms keep stock?

• Buffer stock
• Pipeline stock
• Safety stock
• Cycle stock
• Seasonal stock
• Speculation stock
• But remember Inventory is bad!

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Inventory is bad because

• Cost
• Opportunity cost of capital interest cost
• Maintenance holding cost
• Inventory looses value obsolescence
• Inventory hides problems

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Goals of inventory management

• Keep inventory costs low
• Keep cost of the supply chain low
• Make sure that customer orders are fulfilled
  service degree.

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What is service degree

• Percentage of demand that can be supplied from
  stock
• Percentage of orders that can be supplied from
  stock
• Percentage of customers whose orders can be
  supplied from stock
• Probability of going out of stock per month
• Average time between stock outs

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Inventory models

• Deterministic demand demand is known, and hence
  a service degree of 100 is easy. Goal minimize
  cost.
• Probabilistic demand High revenu requires high
  service degrees which require high inventory and
  therefore high cost The task is to find the
  right balance between cost an revenue.

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Models

• Minimize cost for a given service degree
• Maximize servicegraad for a given cost
• Optimize a function of service degreeand cost
• Solution methods analytic optimization or
  simulation

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Analytical methods

• The EOQ model which has an exact, provably
  optimal solution
• Optimizing safety stock with a uniformally
  distributed demand when service degree is
  measured in terms of the costs of non delivery.
  (so that inventory costs and holding costs can be
  added to obtain total cost.)

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Economic Order Quantity

• Procurement price P
• Replenishment cost B
• Interest rate R
• Holding cost D
• Yearly demand volume V
• Order quantity Q

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EOQ model

• When to order and how much to order?
• Assumption 1 demand is constant and known
• Assumption 2 ordering is always possible and in
  any quantity
• Assumption 3 Back log is not permitted
• Costs 1 Holding costs
• Cost 2 Replenishment costs
• Cost 3 Procurement costs
• Goal Minimize total costs

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What will be the graph of an optimal inventory
policy?
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Replenishment costs B V/Q
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Holding costsQ/2 P R
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Totale costs

• P V B V/Q Q/2 P R
• The EOQ is robust!

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Optimizing

• Taking derivate (in Q)
• -BV/Q2 PR/2
• Zero values
• Q /-sqrt(2VB/PR)
• Is 2VB/PR a minimum ?

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Homework questions (for Friday)

• What are the replenishment costs when ordering
  the optimal quantity?
• What are the holding costs when ordering the
  optimal quantity?
• Explain the relationship between the two.

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Model with uncertainty in demand holding cost
versus service degree

• Cost per day for holding 1 item in inventory 1
• Service degree in euros cost per item demand
  not fulfilled 2.
• Demand D per day 0 lt D lt 1.
• How much to order each day?
• Is there a constant optimal replenishment
  quantity???

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Expected costs at inventory level V with uniform
demand between 0 and 1
min
max
1
0
V
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Expected costs at inventory level V with uniform
demand between 0 and 1
V V/2 1 (1-V) 1/2(1-V) 2

• P(demandltinventory)
• expected excess
• Holding costs
• P(demandgtinventory)
• expected shortage
• (non fulfillment costs)

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V V/2 1 (1-V) 1/2(1-V) 2 V2/2 (1-V)
(1-V) V2/2 (1-2VV2) 1-2V
3/2V2. Derivative 3V-2.
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Optimization

• Optimal strategy
• Minimize total cost
• Zero values of derivative.
• V2/3
• Is this a minimum?

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Consequences

• So what is the optimal replenishment quantity?
• Indeed, it depends on how much is left from the
  previous day..order the quantity that is
  required to start the day with 2/3 inventory.

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Determination of the inventory

• Average demand equals 0.5
• Inventory equals 2/3 gt1/2)
• Therefore ½ of inventory is kept to deal with
  expected demand, and 1/6 is kept to protect
  against uncertainty safety stock!

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Home work question

• What is de optimal replenishment strategy if
  costs for non fulfillment are a with a gt 1 (a2
  in the previous calculations, so the question is
  to generalize.)

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5 practical replenishment systems

• Order the same quantity every day, e.g. the EOQ
  that results when assuming that average demand is
  deterministic demand. Remember that the EOQ is
  robust
• Notice that this disregards the current inventory
  position!

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5 (2)

• 2.(s,Q) order point-order quantity
• Replenish inventory if level below s, order
  quantity Q
• Q can be determined using EOQ, taking expected
  demand as deterministic demand.

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5. (3)

• 3. (s,S) order point-order up to level
• Consider the stock position, order up to level S
  if level is below s.
• It is customary to choose s and S such that
• S-sEOQ
• (again EOQ based)

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5. (4)
4. (R,S) periodic review-order up to
level Consider stock periodically and order up
to level S. Often R and S are chosen such that
the expected replenishment quantity equals the
EOQ (when taking average demand as deterministic
demand)
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5. (5)
5. (R,s,S) . Consider stock periodically and
order up to level S if level is below s. It is
customary to choose R, s, and S such that the
expected quantity (S-s?) equals the EOQ (when
taking average demand as deterministic demand)
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The Costs of inventory systems

• (s,Q) and (s,S) systems require continuous data.
• Periodic review systems require only periodic
  data, and can therefore be cheaper.
• But.periodic review systems will entail higher
  costs... Remember Walmart!!

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A,B,C Classification

• Divide stock keeping units (SKUs) in categories
  A,B en C.
• Category A are items that represent 80 of value,
  B and C the rest, where B takes 80 of the rest.
• For category A SKUs more expensive inventory
  management technology is worth the investment,
  for B and C not.