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Chapter 3 Economic Order Quantity

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The third bin holds a reserve that is only used in an emergency. ... We have assumed that the order size is independent of the lead time and the reorder level. ... – PowerPoint PPT presentation

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Title: Chapter 3 Economic Order Quantity


1
Chapter 3Economic Order Quantity
2
Defining the economic order quantity
3
Background to the model
  • The approach is to build a model of an idealized
    inventory system and calculate the fixed order
    quantity that minimizes total costs. This optimal
    order size is called the economic order quantity
    (EOQ).

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Assumption for a basic model
  • The demand is known exactly, is continuous and is
    constant over time.
  • All costs are known exactly and do not vary.
  • No shortages are allowed.
  • Lead time is zero so a delivery is made as soon
    as the order is placed.

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Other assumptions implicitly in the model
  • We can consider a single item in isolation, so we
    cannot save money by substituting other items or
    grouping several items into a single order.
  • Purchase price and reorder costs do not vary with
    the quantity ordered.
  • A single delivery is made for each order.
  • Replenishment is instantaneous, so that all of an
    order arrives in stock at the same time and can
    be used immediately.

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  • The most important assumption here is that demand
    is known exactly, is continuous and constant over
    time (Fig. 3.2)
  • The assumptions give an idealized pattern for a
    stock level. (Fig. 3.3)

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Variables used in the analysis
  • Four costs of inventory
  • Unit cost (UC)
  • Reorder cost (RC)
  • Holding cost (HC)
  • Shortage cost (SC)

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Three other variables
  • Order quantity (Q)
  • Cycle time (T)
  • Demand (D)

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Derivation of the economic order quantity
  • Three steps
  • Find the total cost of one stock cycle.
  • Divided this total cost by the cycle length to
    get a cost per unit time.
  • Minimize this cost per unit time.

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  • Amount entering stock in cycle
  • amount leaving stock in cycle
  • So
  • Q D x T
  • Total cost per cycle unit cost reorder cost
    holding cost (component)

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  • The optimal time between orders is
  • To Qo/D 500/6,000 0.083 years 1 month
  • The associate variable cost is
  • VCo HC Qo 6 500 3,000 a year
  • This gives a total cost of
  • TCo UC D VCo 30 60000 3000
    183,000 a year

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Summary
  • We have built a model of an idealized inventory
    system that relates order size to costs and
    demand. This shows that large, infrequent orders
    have a high holding cost component, so the total
    cost is high small, frequent orders have a high
    reorder cost component, so the total cost is also
    high. A compromise finds the optimal order size
    or economic order quantity that minimizes
    inventory costs.

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Adjusting the economic order quantity
  • Moving away from the EOQ
  • The EOQ suggests fractional value for things
    which come in discrete units (e.g. an order for
    2.7 lorries)
  • Suppliers are unwilling to split standard package
    sizes.
  • Deliveries are made by vehicles with fixed
    capacities.
  • It is simply more convenient to round order sizes
    to a convenient number.

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How much costs would rise if we do not use the EOQ
  • Example
  • D 6000 units a year
  • Unit cost, UC 30 a unit
  • Reorder cost, RC 125 an order
  • Holding cost, HC 7 a unit a year

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Order for discrete items
  • This suggests a procedure for checking whether it
    is better to round up or round down discrete
    order quantities
  • Calculate the EOQ, Qo.
  • Find the integers Q and Q-1 that surround Qo.
  • If Q(Q-1) is less than or equal to Qo2, order
    Q.
  • If Q(Q-1) is greater than Qo2, order Q-1.

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Uncertainty in demand and costs
  • Error in parameters
  • Few organizations know exactly what demand they
    have to meet in the future.
  • The variable cost is stable around the EOQ and
    small errors and approximations generally make
    little difference.

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Adjusting the order quantity
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or
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or
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Adding a finite lead time
  • Time for order preparation
  • Time to get the order to the right place in
    suppliers
  • Time at the supplier
  • Time to get materials delivered from suppliers
  • Time to process the delivery

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Reorder level
  • The amount of stock needed to cover the lead time
    is also constant at
  • Lead time demand per unit time
  • Reorder level lead time demand lead time
    demand per unit time
  • ROL LT D

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  • (b) Substituting value LT 2 and D 100,
  • gives
  • ROL LT D 2 100 200 units
  • As soon as the stock level declines to 200
    units, Carl should place an order for 250 units.

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Longer lead times
  • The cycle length is
  • T Q/D 250/100 2.5 weeks
  • What happens when the lead time is increased to 3
    weeks ?
  • ROL LT D 3 100 300

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  • Stock on hand stock on order LT D 300
    units
  • Reorder level lead time demand stock on order
  • n T lt LT lt (n1) T
  • Reorder level lead time demand stock on order
  • ROL LT D n Qo

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Some practical points
  • This chapter has shown when to place an order
    set by the reorder level.
  • How much to order set by the economic order
    quantity.
  • A two-bin system gives a simple procedure for
    controlling stock without computers or continuous
    monitoring of stock levels.

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Three-bin system
  • The two-bin system can be extended to a three-bin
    system which allows for some uncertainty.
  • The third bin holds a reserve that is only used
    in an emergency.
  • The normal stock is used from bin A.

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  • Our calculations assume that the lead time is
    known exactly and constant.
  • In practice, there can be quite wide variation,
    allowing for availability, supplier reliability,
    checks on deliveries, transport conditions,
    customs clearance, delays in administration, and
    so on.

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  • Some stock levels are not recorded continuously
    but are checked periodically, perhaps at the end
    of the week.
  • Then an unexpectedly large demand might reduce
    stocks well below the reorder level before they
    are checked.

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  • Another problem appears with large stocks, such
    as chemical tanks, coal tips or raw materials,
    where the stock level is only known
    approximately. Then the reorder level might be
    passed without anyone noticing.

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  • We have assumed that the order size is
    independent of the lead time and the reorder
    level.
  • In practice, people often prefer larger orders if
    there are longer lead times, and they raise the
    reorder level to add an element of safety.
  • The reorder level can be also influence the order
    size, with people typically placing smaller
    orders with higher reorder levels.
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