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

Inventory Management (pg. 132) Inventory = goods that have not yet been sold –raw material –work-in-process –finished goods –supplies YearTotal inventory % of GDP Total inventory / monthly shipments 95$52 B6.7%1.4

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

Why Keep Inventory? 1.Seasonality (anticipated variation) 2.Provide flexibility (unanticipated variation) a.k.a.: 3.Economies of scale 4.Price speculation (not an ops reason) 5.Something to work on 6.NDR,JP

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

Relevant Costs 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.)

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

Order 80 when inventory pos. ≤ 60 Lead time: 5 days 1.Inventory POSITION includes inventory in transit. 2.Example 1 - the Distribution Game 3.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 = = 130 > 60, do not order today (Aug 18 order in transit)

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

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

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

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) = $ / year

Time Inventory Simulated inventory profile

Time Inventory Approximation 1: constant demand

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

Holding Costs (pg. 143) Minimum inventory  ROP – LTD = 60 VCRs – (5 days)(10.12 VCRs/day) = 9.4 units Maximum inventory  Min. inv. + Q = = 89.4 VCRs Average inventory  (min + max)/2 = ( )/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) = $ / year

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