Inventory Management S Periodic Review System stock level Q 1 Q Q 3 Q 1 Q Q 3 R review 1 review review 3 S - Target stock - ead time R - Review Period Q - Order quantity time 1
Periodic Review System At each review place order: current stock + order = target level Set target stock level: S = Demand in (Review period + ead time) +safety stock Periodic Review System - Advantages All stock reviewed periodically - obsolescent items spotted Orders placed at regular intervals smooth spread of admin effort. enables efficient planning Quantity discounts may be available
Periodic Review System - Disadvantages arger stocks - not EOQ. ess responsive to changes in demand Variable demand How long review period possible stock-outs Stochastic Demand (Variable Demand) Aims: Minimise stock holding cost Provide given service level Service level no. satisfied customers no. potential customers 95% service level - on 95% of occasions there will be no stock out 3
Increasing demand Stochastic Demand 95% Service evel safety stock 5% Demand not met average demand in lead time Probability Stochastic Demand Reorder evel System Reorder Quantity = EOQ Reorder level =Ave. Demand in lead time + safety stock R=µ + 1.64 σ(for 95% service level) In general:r = *µ µ + k* *σ - lead time (weeks) µ - ave demand /week σ - s.d. weekly demand k =1.64 for 95% service level k =.3 for 99% service level 4
Stochastic Demand Periodic Review System Target stock = ave demand in Review period + safety stock In general: S = (R+)*µ µ + k* (R+)*σ S - Target stock R - Review period - lead time (weeks) µ -ave demand /week σ - s.d. weekly demand k = 1.64 95% service level k =.3 99% service level Example: Design a Reorder level System for the following:- Weekly Consumption (D) 700 tonnes Cost (c) 75 / tonne ead time () weeks stock holding Cost (h) 15% / tonne p.a. Order cost (S) 3000 (assume 50 working weeks p.a) (H= h*c) DS 700 50 3000 EOQ = = = 430 H 015. 75 reorder level = D = 700 x = 1400 stock 1400 430 weeks 5
Example: Design a Reorder level System for stochastic demand given:- Weekly Consumption (D) Standard deviation Weekly Consumption (σ) Cost (c) ead time () stock holding Cost (h) Order cost (S) 3000 Require a 99% service level (assume 50 working weeks p.a) (H= h*c) 700 tonnes 100 tonnes 75 / tonne weeks 15% / tonne p.a. DS 700 50 3000 EOQ = = H 015. 75 = 430 reorder level = µ µ + k σ = 700 x +.3 x x 100 = 1400 +38 = 178 Example: Design a Reorder level System for stochastic demand stock 178 430 1400 38 weeks 6
Example: Design a Periodic Review System for stochastic demand with 4 week review period (using previous data) Target stock = Demand in lead time +safety stock (R+)µ µ + k (R+)σ =(4 +) x 700 +.3 (4+)x 100 = 400 + 568 = 4768 Design a Periodic Review System for stochastic demand with 4 week review period 4768 100 100 Q Q Q 3 1 Q 1 Q Q 3 review 1 review review 3 Review 1 order = 4768-100 = 3568 Review order = 4768-100 = 668 time 7
Pareto Analysis Some companies have 1000 s stock lines Which stock control system to use for each product? Use Pareto Analysis to identify lines needing careful control Rank lines by value of turnover Category A - high turnover, typically 10-0% lines account for 70-80% value: use RO system Category B Middle value turnover - use PR short reviews Category C low value turnover - use PR long reviews Pareto Analysis Item No. Annual Usage 1 1500 6450 3 5000 4 00 5 0000 6 84 7 800 8 300 9 10000 10 000 11 5000 1 350 13 9000 14 900 15 800 16 675 17 1470 18 800 19 150 0 500 Unit Cost 5.00 0.00 45.00 1.50 35.00 50.00 80.00 5.00 35.00 65.00 5.00 15.00 0.50 10.00 15.00 00.00 100.00 15.00 0.16 0.0 Value Of Usage 7500 19000 5000 500 700000 1000 64000 1500 350000 130000 15000 40650 4500 9000 1000 135000 147000 13000 00 500 8
9 Pareto Analysis Cum % tot Cum. Value Unit Annual Item No. Rank Value value Of Usage Cost Usage 6.79% 700000 700000 35.00 0000 5 1 4.34% 110650 40650 15.00 350 1 55.73% 145650 350000 35.00 10000 9 3 64.34% 168150 5000 45.00 5000 3 4 69.97% 18850 147000 100.00 1470 17 5 75.14% 196350 135000 00.00 675 16 6 80.11% 09350 130000 65.00 000 10 7 85.05% 50 19000 0.00 6450 8 89.83% 34750 15000 5.00 5000 11 9 94.54% 47050 13000 15.00 800 18 10 96.99% 53450 64000 80.00 800 7 11 98.10% 56350 9000 10.00 900 14 1 98.90% 58450 1000 50.00 84 6 13 99.36% 59650 1000 15.00 800 15 14 99.65% 603750 7500 5.00 1500 1 15 99.8% 60850 4500 0.50 9000 13 16 99.9% 610750 500 1.50 00 4 17 99.97% 6150 1500 5.00 300 8 18 99.99% 61750 500 0.0 500 0 19 100.00% 61950 00 0.16 150 19 0 500000 1000000 1500000 000000 500000 3000000 0 5 10 15 0 Pareto Analysis Category A Category B Category C