Planning and Managing Inventories in a Supply Chain

1
Planning and Managing Inventories in a Supply
Chain

• Optimal Matching of Supply and Demand

2
Outline

• The role of inventory in the supply chain
• Why hold inventory?

3
Outline

• The role of inventory in the supply chain
• Why hold inventory?
• Economies of scale
• Batch size and cycle time
• Quantity discounts
• Short term discounts / Trade promotions
• Stochastic variability of supply and demand
• Evaluating service level given safety inventory
• Evaluating safety inventory given desired service
  level
• Levers to improve performance

4
Role of Inventory in the Supply Chain

• Overstocking Amount available exceeds demand
• Liquidation, Obsolescence, Holding
• Understocking Demand exceeds amount available
• Lost margin and future sales
• Goal Matching supply and demand

5
Role of Inventory in the Supply Chain
Cost
Availability
Responsiveness
Efficiency
6
Cycle Inventory Cost Terminology
7
Cycle Inventory Cost Product
The annual cost of products purchased for cycle
inventory is straightforward to calculate
Cost RC
Annual Demand
Cost per unit
8
Cycle Inventory Cost Ordering
There are nR/Q orders per year, and each has
fixed cost S
Cost (R/Q)S
Cost per order
Total demand
Lot size

• S includes such costs as
• Shipping
• Per-order fees (handling)
• Labor for per-order duties, such as
• Inventory checking
• Filling out order
• Receiving order

9
Cycle Inventory Cost Holding
Since the lot size is Q, the average inventory
size is Q/2. The inventory holding cost for a
year is
Cost hC(Q/2)
Holding cost fraction
Avg inventory size
Product unit cost

• h includes such costs as
• Opportunity/capital cost (see WACC, p. 170)
• Obsolescence/spoilage
• Handling/maintenance
• Occupancy/space

10
Cycle Inventory Cost Total Cost
The total cost of cycle inventory is the sum of
Product, Ordering, and Holding costs

• Product cost fixed in this formulation, but
  might change due to volume discount schemes
• As lot size goes up, ordering cost goes ?

11
Cycle Inventory Cost Total Cost
The total cost of cycle inventory is the sum of
Product, Ordering, and Holding costs

• Product cost fixed in this formulation, but
  might change due to volume discount schemes
• As lot size goes up, ordering cost goes DOWN
• As lot size goes up, holding cost goes ?

12
Cycle Inventory Cost Total Cost
The total cost of cycle inventory is the sum of
Product, Ordering, and Holding costs

• Product cost fixed in this formulation, but
  might change due to volume discount schemes
• As lot size goes up, ordering cost goes DOWN
• As lot size goes up, holding cost goes UP
• Wheres the optimal balance?

13
Cycle Inventory Cost Economic Order Quantity
(Optimal policy)
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Example

• Demand, R 12,000 computers per year
• Unit cost, C 500
• Holding cost, h 0.2
• Fixed cost, S 4,000/order
• Q 980 computers
• Cycle inventory Q/2 490
• Flow time Q/(2R) 0.49 month
• Reorder interval, T 0.98 month

15
Key Points from Batching

• In deciding the optimal lot size the trade off is
  between setup (order) cost and holding cost.
• If demand increases by a factor of 4, it is
  optimal to increase batch size by a factor of 2
  and produce (order) twice as often. Cycle
  inventory (in days of demand) should decrease as
  demand increases.
• If lot size is to be reduced, one has to reduce
  fixed order cost. To reduce lot size by a factor
  of 2, order cost has to be reduced by a factor of
  4.

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Strategies for reducing fixed costs

• Wal-Mart 3 day replenishment cycle
• Seven Eleven Japan Multiple daily replenishment
• PG Mixed truck loads
• Efforts required in
• Transportation (Cross docking)
• Information
• Receiving
• Aggregate across products, supply points, or
  delivery points.

17
Lot Sizing with Multiple Products

• Demand per year
• RL 12,000 RM 1,200 RH 120
• Common transportation cost, S 4,000
• Product specific order cost
• sL 1,000 sM 1,000 sH 1,000
• Holding cost, h 0.2
• Unit cost
• CL 500 CM 500 CH 500

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Delivery Options

• No Aggregation Each product ordered separately
• Complete Aggregation All products delivered on
  each truck
• Tailored Aggregation Selected subsets of
  products on each truck

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No Aggregation Order each product independently
Total order inventory cost 155,140
20
Complete Aggregation Order all products jointly
Annual order cost 9.757,000 68,250 Annual
total cost 136,528
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Tailored Aggregation Ordering Selected Subsets

• Step 1 Identify most frequently ordered product
• Step 2 Identify frequency of other products as a
  multiple
• Step 3 Recalculate ordering frequency of most
  frequently ordered product
• Step 4 Identify ordering frequency of all
  products

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Tailored Aggregation Steps 1 2

• Step 1 We already determined (No Aggregation)
  that the three products would require individual
  frequencies of nL11.0/y, nM3.5/y, nH1.1/y
• Assuming orders for the less-frequent products
  can piggy-back on the same common transportation
  cost, determine optimal frequencies using
  product-specific ordering costs

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Tailored Aggregation Step 2 (contd)

• How many L orders should include M as well?
• One out of every 11.0/7.7 1.42 orders
• Round up 1 in 2 (every other order)
• How many L orders should include H as well?
• One out of every 11.0/2.4 4.6 orders
• Round up every 5th order

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Tailored Aggregation Step 3

• But now that other orders are included with the
  11 L orders per year, the costs are different
  than with L alone, so the EOQ must be
  recalculated
• Total annual inventory cost (hCR)is
• 0.250012,000 0.25001,200 0.2500120
  1,332,000
• Total ordering cost is common each
  product-specific
• 4000 1000(/1) 1000/2 1000/5 5,700
• nL sqrt(1,332,000/(25,700)) 10.8
• QL 12,000/10.8 1,111

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Tailored Aggregation Step 4

• Based on the policy for L, we can now compute the
  ordering policies for M and H
• nM nL/2 10.8/2 5.4 orders/year
• QM RM/nM 1,200/5.4 222 units/order
• nH nL/5 10.8/5 2.16 orders/year
• QH RH/nH 120/2.16 56 units/order

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Tailored Aggregation Order selected subsets
Annual order cost 61,560 Total annual cost
131,004
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Impact of product specific order cost
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Lessons From Aggregation

• Aggregation allows firm to lower lot size without
  increasing cost
• Complete aggregation is effective if product
  specific fixed cost is a small fraction of joint
  fixed cost
• Tailored aggregation is effective if product
  specific fixed cost is large fraction of joint
  fixed cost

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Quantity Discounts

• Lot size based
• All units
• Marginal unit
• Volume based
• How should buyer react?
• What are appropriate discounting schemes?

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All-Unit Quantity Discounts
Cost/Unit
Total Material Cost
3
2.96
2.92
5,000
10,000
Order Quantity
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All-Unit Quantity Discounts

• Evaluate EOQ for price in range qi to qi1
• If qi ? EOQ lt qi1 , evaluate cost of ordering
  EOQ
• If EOQ lt qi, evaluate cost of ordering qi
• If EOQ ? qi1 , evaluate cost of ordering qi1
• Evaluate minimum cost over all price ranges

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All-Unit Quantity Discounts

• Example Prices 3.00, 2.96, 2.92 for orders of
  at least 0,5000,10000, h 0.2, R 100,000/y,
  S200/order
• At C 3, EOQ 8164, so Q5000, n20
• Total cost 3100,000 20200 25000.23
  297,460
• At C 2.96, EOQ 8220, so Q8220, n 12.16
• Total cost 2.96100,000 12.16200
  41100.22.96 296,833
• At C 2.92, EOQ 8276, so Q10000, n 10
• Total cost 2.92100,000 10200
  100000.22.92 296,920
• Recommended ordering policy 12.16 lots of 8220
  per year, or 10 lots of 10,000 if it is more
  convenient.

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Marginal Unit Quantity Discounts
Cost/Unit
Total Material Cost
3
2.96
2.92
5,000
10,000
Order Quantity
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Marginal-Unit Quantity Discounts

• Terms qiith breakpoint Ci ith price Vi
  cost of buying qi units.
• Evaluate EOQ for price in range qi to qi1 with
  special formula
• If qi ? EOQ lt qi1 , evaluate cost of ordering
  EOQ
• If EOQ lt qi, or EOQ ? qi1 evaluate cost of
  ordering qi or qi1
• Evaluate minimum total cost over all price ranges
• Total cost nS (lot price)h/2 n(lot price)
• Lot price is exclusive of ordering cost Vi
  (Q-qi)Ci

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Marginal-Unit Quantity Discounts Example

• q(0,5000,10000), C(3,2.96,2.92), V (0, 15000,
  29800)
• For (q0, C3.00, V0), Q8164, so evaluate Q
  5000, n20
• Lot price 3.00 5000 15000
• Total cost 20200 150000.2/2 2015000
  305,500
• For (q5000, C2.96, V15000), Q11624, so
  evaluate Q 10000, n10
• Lot price 3.00 5000 2.965000 29800
• Total cost 10200 298000.2/2 1029800
  302,980
• For (q10000, C2.92, V29800), Q16552, so
  evaluate Q16552, n6
• Lot price 3.00 5000 2.965000 2.926552
  48932
• Total cost 6200 489320.2/2 648932
  303,378
• Final recommendation order n10 lots of Q10,000
  each

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Manufacturer/Retailer Coordination

• R 120,000 bottles/year
• SR 100, hR 0.2, CR 3
• SS 250, hS 0.2, CS 2
• Suppliers optimal lot size 12,247 bottles, but
  
• Retailers optimal lot size 6,324 bottles?
• Retailer cost 3,795 Supplier cost 6,009
• Total supply chain cost 9,804

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Manufacturer/Retailer Coordination

• What can the supplier do to decrease supply chain
  costs?
• Coordinated lot size 9,165 Retailer cost
  4,059 Supplier cost 5,106 Supply chain cost
  9,165.
• Effective pricing schemes
• All unit quantity discount
• 3 for lots below 9,165
• 2.9978 for lots of 9,165 or more
• Pass some fixed cost to retailer (enough that he
  raises order size from 6,324 to 9,165)

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Short Term Discounting
Lower price ? higher lot size. If a one-time
discount is offered, why not just evaluate the
EOQ at the discounted price to determine the size
of the single discounted lot?
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Short Term Discounting
Lower price ? higher lot size. If a one-time
discount is offered, why not just evaluate the
EOQ at the discounted price to determine the size
of the single discounted lot? Because the EOQ
assumes unchanging prices, demands, etc. for the
foreseeable future I.e. the above policy would
determine lot-size on the assumption that the
discounted price will always be available.
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Short Term Discounting

• Q Normal order quantity
• C Normal unit cost
• d Short term discount
• R Annual demand
• h Fractional Holding Cost
• Qd Short term order quantity

Forward buy Qd - Q
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Short Term Discounts Forward buying

• Normal cost, C 3 per bottle
• Discount per bottle, d 0.15
• Annual demand, R 120,000
• Holding cost, h 0.2
• Normal order size, Q 6,324 bottles
• Qd 38,326
• Forward buy 31,912 bottles!

42
Promotion Pass Through to Consumers

• Demand curve at retailer 300,000 - 60,000p ?
• Retailer profit (300,000-60,000p)(p-C)
• -60,000p2 (300,00060,000C)p 300,000C
• Derivative of profit -120,000p
  300,00060,000C?optimal p(5C)/2
• Normal supplier price, C 3.00
• Optimal retail price 4.00
• Customer demand 60,000
• Promotion discount 0.15
• Optimal retail price 3.925
• Customer demand 64,500
• Retailer only passes through half the promotion
  discount and demand increases by only 7.5

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Levers to Reduce Lot Sizes Without Hurting Costs

• Cycle Inventory Reduction
• Reduce transfer and production lot sizes
• Aggregate fixed cost across multiple products,
  supply points, or delivery points
• Are quantity discounts consistent with
  manufacturing and logistics operations?
• Volume discounts on rolling horizon
• Two-part tariff
• Are trade promotions essential?
• Base on sell-thru rather than sell-in