ISEN 315
Spring 2011
Dr. Gary Gaukler
Inventory Control
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Deterministic inventory control
Stochastic inventory control
MRP / Lot sizing / JIT
Supply chain management
Reasons for Holding Inventories
Relevant Costs
• Holding Costs - Costs proportional to the
quantity of inventory held.
Relevant Costs (continued)
• Ordering Cost (or Production Cost).
Can include both fixed and variable components.
slope = c
K
Relevant Costs (continued)
• Penalty or Shortage Costs. All costs that
accrue when insufficient stock is available to
meet demand.
Simple EOQ Model
• Assumptions:
1. Demand is fixed at l units per unit time.
2. Shortages are not allowed.
3. Orders are received instantaneously.
4. Order quantity is fixed at Q per cycle.
5. Cost structure:
a) Fixed and marginal order costs (K + cx)
b) Holding cost at h per unit held per unit time.
Inventory Levels for the EOQ Model
Cost Equation for the EOQ Model
The Average Annual Cost Function G(Q)
The Average Annual Cost Function G(Q)
Properties of the EOQ Solution
2K l
Q
h
Example
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Desk production rate = 200 per month
Each desk needs 40 screws
Screws cost $0.03
Fixed delivery charges are $100 per order
25% interest rate for holding cost
• What is the optimal order size?
Example
EOQ Cost Function
Quantity Discount Models
• All Units Discounts: the discount is
applied to ALL of the units in the order.
• Incremental Discounts: the discount is
applied only to the number of units
above the breakpoint.
All-Units Discount Order Cost Function
Incremental Discount Order Cost Function
All-unit Discount
• Compute EOQs for all discounts
• Find realizable EOQ values
• Compare cost of realizable EOQ with cost
at breakpoints
All-Units Discount Average Annual Cost
All-unit Discount Optimality
Incremental Discount
• Cost structure:
Incremental Discount
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Establish C(Q) curve
Determine “cost per unit” C(Q)/Q
Substitute C(Q)/Q into G(Q)
Compute G(Q) for each range
Pick feasible solution with lowest cost
Average Annual Cost Function
for Incremental Discount Schedule
Incremental Discount Example
• Demand 600 bags / year
• Setup cost for ordering: $8
• Unit cost
– Up to 500: $0.30
– Up to 1000: first 500 at $0.30, remaining at $0.29
– Over 1000: first 500 at $0.30, next 500 at $0.29,
remaining at $0.28
• Holding cost: 20%
Incremental Discount Example
Incremental Discount Example
Incremental Discount Example
Properties of the Optimal Solutions
• For all units discounts, the optimal will occur at
the bottom of one of the cost curves or at a
breakpoint. One compares the cost at the largest
realizable EOQ and all of the breakpoints
succeeding it.
• For incremental discounts, the optimal will
always occur at a realizable EOQ value.
Compare costs at all realizable EOQ’s.