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The Economic Production Quantity (EPQ) Model

The Economic Production Quantity (EPQ) Model. 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. Notation.

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The Economic Production Quantity (EPQ) Model

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  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 Qmax Inventory Tp TD 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/2=hQ(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 h’=h(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 > 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))  cDwhen 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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