1. MGTSC 352 Lecture 19: Distribution Planning One last look at shortest paths Inventory Management What is it, why keep it, inventory policies

2. Inventory Management (pg. 132) Inventory = goods that have not yet been sold • raw material • work-in-process • finished goods • supplies

3. More Recent Data Active learning: (1 min. / pairs) What does the inventory / monthly shipments ratio mean?

4. Why Keep Inventory? • Seasonality (anticipated variation) • Provide flexibility (unanticipated variation) a.k.a.: • Economies of scale • Price speculation (not an ops reason) • Something to work on • NDR,JP

5. Inventory Policy Answers two general questions • When to order? (ROP = reorder point) • How much to order? (Q = reorder quantity)

6. Acquisition cost ($/unit purchased) Ordering costs($/order) clerical expenses delivery, inspection setup (prod.) Carrying costs = Holding costs($/unit/time unit) cost of capital insurance shrinkage, spoilage, obsolescence material handling (fork lifts, space) Shortage costs($/unit short) lost goodwill, discounts, penalties lost sales shut down of assembly line (prod.) Relevant Costs

7. A&E Noise (VCRs) (pg. 134) • Cost: $150 • Price: $175 • Ordering cost:$30/order • Holding cost:0.25150/365 = $0.1/unit-day • Inventory policy • Order 80 when inventory position ≤ 60 • Inventory position = inv. on hand + inv. in transit • Lead time:5 days

8. Inventory POSITION includes inventory in transit. Example 1 - the Distribution Game Example 2 - Today is 21 Aug. 1997, and there are 50 units in stock. The last two orders were placed on 9 Aug. and 18 Aug. Should Jane order today? I = 50 + 80 = 130 > 60, do not order today(Aug 18 order in transit) Order 80 when inventory pos. ≤ 60Lead time: 5 days

9. Maximum inventory Avg. inventory ROP Demand during leadtime Q Leadtime Minimum inventory Inventory Time

10. Finding Good Inventory Policies • Approach 1: Simulation • We will use historical sales (instead of generating random future sales) • We will assume demand = sales(an approximation) • Experiment with different values of Q and ROP • Approach 2: EOQ + LTD • An approximate model • Simpler to use • More abstract to Excel

11. Acquisition Costs (pg. 142) • Total units sold per year  (10.12 VCRs/day)(365 days/year) = 3695 VCRs/year • Total acquisition costs per year  ($150/VCR)(3695 VCRs/year) = $554,350/year • Total acquisition costs per year if order size were changed to 90  $554,350 / year Acquisition costs are not affected by inventory policy, as long as demand is satisfied and there are no volume discounts

12. Order Costs • Cost per order = $20 + ($20 / hour)(0.5 hours) = $30 / order • Number of orders per year  (3695 VCRs / year)/(80 VCRs / order) = 46.2 orders / year • Total order cost per year  (46.2 orders / year)($30 / order) = $1385.63 / year

13. Inventory Simulated inventory profile Time

14. Approximation 1: constant demand Inventory Time

15. Maximum inventory Avg. inventory ROP Q Leadtime Minimum inventory Inventory LTD = Demand during leadtime Time

16. Holding Costs (pg. 143) • Minimum inventory  ROP – LTD = 60 VCRs – (5 days)(10.12 VCRs/day) = 9.4 units • Maximum inventory  Min. inv. + Q = 9.4 + 80 = 89.4 VCRs • Average inventory  (min + max)/2 = (9.4 + 89.4)/2 = 49.4 VCRs • Total VCR-years of inventory per year  (49.4 VCRs)(1 year) = 49.4 VCR-years • Total holding cost per year  (49.4 VCR-years)($37.5 / VCR / year) = $1852.50 / year

17. Avg. inventory Inventory What is a “VCR-year” of inventory? 5 VCRs Total inventory for the year: 5 VCR-years 1 VCR-year of inventory 4 VCRs 1 VCR-year of inventory 3 VCRs 1 VCR-year of inventory 2 VCRs 1 VCR-year of inventory 1 VCR 1 VCR-year of inventory 1 year Time