Inventory Management - 2

Transcription

1 Inventory Management - 2

2 Supporting Calculations-Basic EOQ No Safety Stock With Safety Stock Number of orders per year Length of order cycle Maximum inventory D Q 0 Q 0 D Q 0 D Q 0 Q 0 D Q + SS 0 Average inventory Total annual cost D Q 0 S Q 0 2 Q H D Q 0 Q 0 + SS 2 Q0 S SS H 2

3 When to Order: Reorder Point Assumptions: 1. Demand rate known and constant 2. Lead time known and constant R where D LT R = = = = D LT Annual demand, units/year Lead time, years Reorder point, units Note: D and LT may be expressed in terms of some time units other than years, but time units must be consistent! Note: LT value should be less than the length of the stock-cycle 3

4 Reorder Point Example Example: Demand = 10,000 yards/year Store open 311 days/year Lead time = L = 10 days Daily demand = d = 10,000 / 311 = yards/day R = d*l = (32.154)*(10) = yards 4

5 Reorder Point [ROP] when LT > Length of the Stock-Cycle ROP (Reorder Level) = Lead time demand Stock on order ROL = LT x D Stock on order 5

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7 Safety Stock and Service Level Safety stock is additional inventory set aside to reduce the probability of running out of stock Service level is the probability of not running out of stock on a given replenishment cycle. This is a complement to Safety Stock. D LT represents the average demand during the lead time, so setting R = D LT will result in a service level of 50% To increase the service level, we add the safety stock to the reorder point, so that R = D LT + SS (this means that we place our order sooner) 7

8 Re-order Point for the system with Safety Stock and Service Level The reorder point is set based on the demand during lead time (DDLT) and the desired customer service level Reorder point (ROP) = Expected demand during lead time (EDDLT) + Safety stock (SS) ROP = EDDLT + SS The amount of safety stock needed is based on the degree of uncertainty in the DDLT and the customer service level desired 8

9 DDLT Distributions If there is variability in the DDLT, the DDLT is expressed as a distribution discrete continuous In a discrete DDLT distribution, values (demands) can only be integers A continuous DDLT distribution is appropriate when the demand is very high 9

10 Setting Order Point for a Discrete DDLT Distribution Assume a probability distribution of actual DDLTs is given or can be developed from a frequency distribution Starting with the lowest DDLT, cumulate the probabilities. These are the service levels for DDLTs [See the example given in the next slide] Select the DDLT that will provide the desired customer level as the order point 10

11 Example: OP for Discrete DDLT Distribution One of Sharp Retailer s inventory items is now being analyzed to determine an appropriate level of safety stock. The manager wants an 80% service level during lead time. The item s historical DDLT is: DDLT (cases) Occurrences Total # of Occurrences 20 11

12 OP for Discrete DDLT Distribution (Contd.) Construct a Cumulative DDLT Distribution Probability Probability of DDLT (cases) of DDLT DDLT or Less To provide 80% service level, OP = 5 cases 12

13 OP for Discrete DDLT Distribution (Contd.) Safety Stock (SS) OP = EDDLT + SS SS = OP EDDLT Here the EDDLT =.4(3) +.3(4) +.2(5) +.1(6) = 4.0 Therefore SS = 5 4 = 1 13

14 Setting Order Point for a Continuous DDLT Distribution Assume that the lead time (LT) is constant Assume that the demand per day is normally distributed with the mean (d ) and the standard deviation (V d ) The DDLT distribution is developed by adding together the daily demand distributions across the lead time. The resulting DDLT distribution is a normal distribution.... more 14

15 Setting Order Point for a Continuous DDLT Distribution For the continuous DDLT distribution, we have the following parameters: EDDLT = LT(d) σ DDLT = LT( Vd) 2 15

16 Setting Order Point for a Continuous DDLT Distribution The customer service level is converted into a Z value using the normal distribution table The safety stock is computed by multiplying the Z value by V DDLT. The order point is set using OP = EDDLT + SS, or by substitution OP = LT(d) + z LT( 2 d 16

17 Example: OP - Continuous DDLT Distribution Auto Zone sells auto parts and supplies including a popular multi-grade motor oil. When the stock of this oil drops to 20 gallons, a replenishment order is placed. The store manager is concerned that sales are being lost due to stockouts while waiting for an order. It has been determined that lead time demand is normally distributed with a mean of 15 gallons and a standard deviation of 6 gallons. The manager would like to know the probability of a stockout during lead time. 17

18 Example: OP - Continuous DDLT Distribution EDDLT = 15 gallons σ DDLT = 6 gallons OP = EDDLT + Z(σ DDLT ) 20 = 15 + Z(6) 5 = Z(6) Z = 5/6 Z =

19 Example: OP - Continuous DDLT Distribution Standard Normal Distribution Area =.2967 Area =.2033 Area = z 19

20 Example: OP - Continuous DDLT Distribution The Standard Normal table shows an area of.2967 for the region between the z = 0 line and the z =.833 line. The shaded tail area is = The probability of a stockout during lead time is

21 Rules of Thumb in Setting OP Set safety stock level at a percentage of EDDLT OP = EDDLT + j(eddlt) where j is a factor between 0 and 3. Set safety stock level at square root of EDDLT OP = EDDLT + EDDLT 21

22 Fixed Period Model Answers how much to order Orders placed at fixed intervals Inventory brought up to target amount Amount ordered varies No continuous inventory count Possibility of stockout between intervals Useful when vendors visit routinely 22

23 Inventory Level in a Fixed Period System Various amounts (Q i ) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to target maximum Target maximum On-Hand Inventory Q 1 Q 2 Q 3 Q 4 p p p Time 23

24 Fixed-Order-Interval Model Orders are placed at fixed time intervals Order quantity for next interval? Suppliers might encourage fixed intervals May require only periodic checks of inventory levels 24

25 Fixed-Order-Interval Model Assumption: Lead time is less than the cycle length Order Quantity = Target Stock Level (TSL) Stock on Hand Where Target Stock Level = Demand * (T+LT) + Safety Stock Safety stock = Z * Standard deviation of (T+LT) = Z * V * (T+LT) NOTE: If the above assumption is not true, then Order Quantity = Target Stock Level Stock on Hand Stock on Order 25

26 Exercise: Fixed-Order-Interval Model Demand for an item has a mean of 200 units a week and standard deviation of 40 units. Stock is checked every four weeks and lead time is constant at two weeks. Describe a policy which will give a 95% service level. If the holding cost is $2 a unit a week, what is the cost of the safety stock with this policy? What would be the effect of a 98% service level? 26

27 Comparison of Reorder Point and Periodic Review Systems Reorder Point / Fixed Order Quantity Order quantity constant, time between orders varies Less safety stock required (shorter protection interval) Perpetual system required Emphasis on optimizing individual items Good for A items Periodic Review / Fixed Order Interval Time between orders constant, amount ordered varies Good for perishable items (order interval shelf life) Facilitates combining multiple items into same order Easy, inexpensive to operate 27

28 Current Trends in Inventory Management Inventory is a liability, not an asset. Average amount of inventory relative to annual sales is decreasing. Firms are focusing on reducing setup and order costs, resulting in smaller economic order quantities. Firms are working more closely with vendors to reduce product throughput times and, consequently, lead times. 28