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Chapter 11. Order Point Inventory Control Methods

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					Chapter 11. Order Point Inventory Control Methods




      Homework problems: 1, 2, 3, 5.




                                                1
Order Point Inventory Control Methods

Order point methods are used to determine
appropriate order quantities and timing for
individual independent-demand product items
that are characterized by random customer
demand.
Performed well, these inventory management
functions can provide appropriate levels of
customer service without excess levels of
inventory and/or cost.
             1. Basic Concepts
Independent Demand
  When item’s demand is influenced by market conditions and is
  not related to (i.e., is “independent” of) production decision for
  any other item.
  Wholesale and retail merchandise (finished goods), service
  industry inventory, end-item and replacement-part inventories,
  spare-parts, MRO (maintenance, repair, and operating) supplies.
  Demand must be forecast

Dependent Demand
  When item’s demand derives from (i.e., “depend” on) the
  production decisions for its parents.
  All intermediate and purchased items in manufacturing.
  Demand must be derived.



                                                                3
Functions of the 4 Types of Inventory
 Cycle Stock/Inventory
   Created when we place orders LESS frequently.
   The longer the cycle, the bigger the Q (order quantity).
   Helps with customer service, ordering cost, setups,
   transportation rates, and material costs.
   Equal to Q/2, when demand rate is constant and uniform.


 Safety Stock/Inventory
   Created when we place an order sooner than when it is needed,
   or more than the expected demand during lead time. .
   Protects against three types of uncertainty: demand, lead time,
   and supply.
   Helps with customer service and missing parts.


                                                               4
          Functions of Inventory
Anticipation Stock/Inventory
   Created by overproducing during the slack season or
   overbuying before a price increase or capacity shortage.
   Helps absorb uneven rates of demand and supply.

Pipeline (transit) Stock/Inventory
   Created by the time spent to move and produce materials.
   Can be in any of three stages:
    Ø Inbound, within the plant, outbound
   Equal to d x L, where,
    Ø d: avg. demand per period
    Ø L: the # of periods in the lead time to move between two
      points.


                                                                 5
      Functions of Inventory Example
   Management has decided to establish three distribution centers
   (DCs) in different region of the country to save on transportation
   costs. For one of the products, the average weekly demand at
   each DC will be 50 units. The product is valued at $650 per unit.
   Average shipment sizes into each DC will be 350 units per trip.
   The average lead time will be two weeks. Each DC will carry one
   week’s supply as safety stock, since the demand during the lead
   time sometimes exceed its average of 100 units (50x2).
   Anticipation inventory should be negligible.

a) How many dollars of cycle inventory will be held at each DC, on
   the average?
b) How many dollars of safety stock will be held at each DC?
c) How many dollars of pipeline inventory will be in transit for each
   DC, on the average?
d) How much inventory, on the average, will be held at each DC?
e) Which type of inventory is your first candidate for reduction?


                                                                        6
    Functions of Inventory Example
l Solution:
a) Cycle Inventory = (350/2)($650)=$113,750.
b) Safety stock = (1)(50)($650)=$32,500.
c) Pipeline inventory = (2)(50)($650)= $65,000
d) Inventory at DC = cycle + safety + pipeline =
   $211,250
e) Cycle inventory




                                                   7
               Inventory Reduction
Type           Primary Lever                    Secondary

Cycle          Reduce Q                 Reduce ordering and setup
                                        costs.

Safety         Place orders closer      Improve forecasting.
               to the time when         Reduce lead time.
               they must be received    Reduce uncertainty.
Anticipation   Vary production rate     Level out demand rates.
               to follow demand rate
Pipeline       Cut production-          Forward inventory positioning.
               distribution lead time   Selection of suppliers and
                                        carriers.
                                        Reduce Q.

                                                                    8
   Where are the Inventories?

Inventories are held in: manufacturing
(36%), retail trade (25%), wholesales
trade (23%), farm (8%), other (8%).
Inventory Total:
  3.6 monthly sales in 1970s
  3.1 monthly sales in 1980s
  2.7 monthly sales in 1990s (> $1 trillion)



                                               9
  2. Management Issues – Two Fundamental
        Inventory Questions/Decisions


          1.   How Much?
          2.   When?




See. Figure 11.2 for models
                                           10
 Inventory System Performance
Inventory Measures
  Start with physical count in units, volume, or weight.
  Average aggregate inventory value (total value of
  all items held in inventory)
  Weeks of Supply. Divide average aggregate
  inventory value by weekly sales (at cost, i.e., cost of
  goods sold) of finished goods.
  Inventory Turnover (turns). Divide annual sales
  (at cost, i.e., cost of goods sold) by average
  aggregate inventory value.
  Fill Rate. The % of units immediately available
  when requested by customers, measuring customer
  service level.
                                                      11
 Inventory System Performance Example
l A recent accounting statement showed average
  aggregate inventories (RM+WIP+FG) to be $6,821,000.
  This year’s cost of goods sold is $19.2 million. The
  company operates 52 weeks per year. How many
  weeks of supply are being held? What is the inventory
  turnover?

Solution:

Weeks of supply= ($6,821,000)/($19,200,000)/52=18.5 weeks.
Inventory turnover= ($19,200,000)/($6,821,000)= 2.8 turns.

                                                         12
Inventory Costs =

Ordering costs: physical counting, paperwork, fax/phone,
            receipt verification, etc. e.g., $95/order vs.
            $7/order

+Holding/carrying costs: cost of capital (5~35%), taxes,
            insurance, obsolescence, warehousing, etc.
            Typically annual holding costs = 20~40%.

+Stockout/shortage costs: back order, lost sales, lost
            goodwill. Customer service level ↔
            inventory investment

+ Cost of items
                                                         13
 Five Assumptions of EOQ
Demand is known and constant
Whole lots ordering
Only two relevant costs
Item independence
Certainty in lead time and supply



                                    14
   Economic Order Quantity (EOQ)
A: annual demand
Q: order quantity
CP: ordering (preparation) cost per order
CH: carrying cost per unit per year

  Annual inventory carrying cost= (Q/2)·CH
  Annual ordering cost= (A/Q) ·CP
  Total annual cost (TAC) = (A/Q)·CP + (Q/2)·CH
  Finding the optimal order quantity that minimizes TAC using
     Calculus
     Observation (Fig 11.4)
  Economic time between order (TBO) in weeks = EOQ/(A/52)

                                                                15
              EOQ Sensitivity
What happens to cycle inventory if the demand rate
increases?
What happens to lot sizes if setup/ordering cost
decreases?
What happens to lot size if interest rates drop?
How critical are errors in estimating A, CP, CH ?
  Overestimate A by 300% → overestimate EOQ by 100%
  Total cost curve is relatively “flat” around the minimum cost
  ordering quantity, implying total cost performance is
  relatively insensitive to small changes in order quality around
  the optimal order quantity.
  EOQ is robust.
  When setup cost → 0, EOQ → small → small lot production
  in JIT.

                                                               16
     Reorder Timing Decisions
Under the (Q,R) rule, an order for a fixed quantity (Q)
is placed whenever the stock level reaches a reorder
point (R).
Reorder point = average demand during the average
replenishment lead time + safety stock.

                R= d + S
Reorder point is influenced by demand, lead time,
demand uncertainty, and lead time uncertainty.
When both demand and lead time are constant,
reorder point = expected demand during lead time,
and no safety stock is needed.


                                                     17
             Reorder Point Decisions:
  Discrete Distribution of Demand during Lead Time

Safety Stock can be determined using (1) stockout risk or
probability or (2) customer service level (fill rate).
   Stockout Risk: the probability of not meeting demand
         during ANY given replenishment order cycle.
         e.g., 5% stockout; See Figure 11.5.
   Fill Rate (Customer Service Level): the % of demand,
           measured in units, that can be supplied directly
           out of inventory. See Fig. 11.7
Normal Distribution provides a close approximation to a
given discrete distribution, facilitating and simplifying the
reorder point (and thus safety stock) calculations.
                                                           18
Reorder point and Stockout Probability
 Reorder point of 7
 units will provide
 5% chance of
                                  With a lead time
 stockout during a
                                  of one day, 95%
 one day lead time
                                  of cycles will
                                  experience
                                  demand for 7 or
                                  fewer units




                             Sum of demand
                             probability is 0.05 (5%)
                    Reorder Point Decisions:
    Continuous Distribution of Demand during Lead Time

Note. Service level is               The ROP based on a Normal
defined differently with             distribution of lead time demand
continuous demand.
           Reorder Point Decisions:
Continuous Distribution of Demand during Lead Time
              Reorder Point Decisions:
  Continuous Distribution of Demand during Lead Time

uProbability of Stocking Out Criterion
   uConstant demand and variable lead time
              R= d x LT + Z·d·σLT
   uVariable demand and constant lead time

              R= d x LT + Z· √LT · σd         (cf. equation 11.18)

   uVariable demand and variable lead time

                             √
              R= d x LT + Z· LT· σd2 + d 2 · σ2LT   (cf. equation 11.20)


  Where d= average daily or weekly demand,
          σd = standard deviation of demand per day or week,
         σLT = standard deviation of lead time per day or week
                                                                           22
Reorder Point Decisions: Continuous Demand Example

The injection molding department of a company uses 40 ponds of a
powder a day. Inventory is reordered when the amount on hand is
240 pounds. Lead time averages 5 days. It is normally distributed
and has a standard deviation of 2 days.
a). What is the probability of a stockout during lead time?
b). What reorder point would provide a 5% stockout?




                                                               23
             Reorder Point Decisions

Note that while discrete demand distributions (e.g.,
Figure 11.5) can be approximated by the continuous
Normal distribution for reorder point decisions (e.g.,
discussions in the section of Continuous Distribution on
page 433 and Customer Service Criterion on page 435),
the results won’t be optimal.

Thus, when demand is discrete, equation 11.8 should
be used. When demand is continuous, the formulas on
slide 21 should be used.




                                                      24
                   Principles
The difference between dependent and independent
demand must serve as the first basis for determining
appropriate inventory management procedures.
Organizational criteria must be clearly established
before we set safety stock levels and measure
performance.
Savings in inventory-related costs can be achieved by a
joint determination of the order point and order quantity
parameters.
The functions of inventory are useful principles to apply
in determining whether or not inventory reductions can
be made.

				
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