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The Economic Production Quantity EPQ Model

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TP: production cycle (time facility is producing per order cycle) ... Qmax = TP(P - D) = Q(1 - D/P) Average inventory = Qmax/2. Number of orders per unit time = D/Q ... – PowerPoint PPT presentation

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Title: The Economic Production Quantity EPQ Model


1
The Economic Production Quantity (EPQ) Model
2
  • Similar assumptions to the EOQ model, except
    that production/delivery is not instantaneous
  • Units are produced and delivered one unit at a
    time
  • Production capacity is finite with a finite
    production rate P

3
Notation
  • P production rate (number of units/time period)
  • TP production cycle (time facility is producing
    per order cycle)
  • TD withdrawal cycle (time facility is idle per
    order cycle)
  • T total inventory cycle (time between setups)
  • Qmax maximum inventory level (units)

4
Inventory versus Time
5
  • TP Q/P
  • TD Qmax/D
  • Qmax TP(P - D) Q(1 - D/P)
  • Average inventory Qmax/2
  • Number of orders per unit time D/Q

6
Costs
  • Total holding cost hQmax/2hQ(1-D/P)/2
  • Total ordering/setup cost AD/Q
  • Total production/purchasing cost cD
  • Total cost AD/Q hQ(1 - D/P)/2 cD
  • Unit cost A/Q hQ(1 - D/P)/2D c

7
The Economic Production Quantity
8
  • The EPQ is equivalent to an EOQ model with
    holding cost hh(1-D/P).
  • Consequently, the optimal cost under the EPQ
    model is lower than the optimal cost under the
    EOQ model with holding cost h.

9
Production Facility Utilization
  • U D/P (capacity utilization)
  • We must not operate above capacity (i.e., always
    keep U ? 1)
  • What happens when D gt P?
  • What happens when D P?

10
EOQ vs. EPQ
  • Q(EPQ) ? Q(EOQ) when U ? 1
  • Q(EPQ) Q(EOQ) when U ? 0
  • Q(EPQ) ? infinity when U ? 1 (continuous
    production)
  • Y(Q(EPQ)) ? cD when U ? 1

11
Systems with Multiple Products
N number of products Di demand rate for
product i Pi production rate for product i hi
holding cost per unit per unit time for product
i Ai Ordering/setup cost for product i ci
production cost for product i
12
Objective
Minimize total cost while guaranteeing that no
stockouts occur for any product.
13
  • In order to ensure feasibility, we must have
  • Choosing can
    lead to stockouts

14
A Cyclic Policy
  • A strictly cyclic policy is used (in each cycle,
    there is exactly one setup per product)
  • Cycle time, T, is the time between two
    consecutive setups for any given product
  • During T, a quantity Qi of each product i is
    produced and consumed therefore, Qi DiT

15
Inventory versus Time
P1 P2 P3
Inventory
Time
16
Order Quantities and Order Interval
  • Cost for Product i

17
Order Quantities and Order Interval
  • Cost for Product i
  • Total Cost

18
Order Quantities and Order Interval
  • Cost for Product i
  • Total Cost
  • Since Qi/Di T,

19
Optimal Order Interval and Order Quantities
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