Supply Chains: Inventory Basics

Transcription

1 Department of Industrial Engineering Supply Chains: Inventory Basics Jayant Rajgopal, Ph.D., P.E. Department of Industrial Engineering University of Pittsburgh Pittsburgh, PA 15261

2 Effective inventory control can yield huge rewards U.S. GDP (Q2 2016): ~$18.44 trillion Total value of business inventories (as of July 2016): $1.813 trillion (~10% of GDP) That is a LOT of money - even a 1% decrease in inventories is over 18 billion dollars saved! Jul. 2016, U.S. Business Inventories: $1,813 billion Retail $602b; 33.2% Manufacturing $620b; 34.2% Wholesale $591b; 32.6%

3 Optimizing inventory levels Completely eliminating inventory! There are reasons for maintaining inventories they exist for a purpose Identify these reasons Then minimize the levels that will serve the purpose Nice goal (perhaps ), but not to be taken literally!

4 Different types of inventory Raw Materials Components Maintenance, Repair and Operating (MRO) supplies Subassemblies and work-in-process Finished Goods Distribution Retail

5 Primary reasons why inventories exist Guarding against uncertainty in demand in supply SAFETY STOCK Economies of scale Smoothing variability CYCLE STOCK

6 Other reasons: To decouple stages in the production process or the supply chain B 2 B 3 Transportation/pipeline stocks As a hedge against anticipated price increases in the future Etc

7 Inventory Turnover Ratio is a measure of inventory efficiency Department of Industrial Engineering Turnover Ratio = (Cost of goods sold/yr.) (value of average inventory) Measure of how long inventory sits on the shelf or how quickly inventory moves out of the system E.g., for the 2015 fiscal year (approx. figures in $billion ) Company COGS Avg. Inventory Turnover Ratio Toyota ~201 ~18.3 ~11 Ford ~126 ~8.3 ~15.2 GM ~134 ~13.7 ~9.8 Nissan ~85 ~10.2 ~8.3 Honda ~101 ~11.7 ~8.6

8 Computing Average Inventory 400 I(t) Department of Industrial Engineering I = 400 = I(t) I(t) I = = = 300 I = = 200 I(t) = 350 In general, I = ( ) t 1 t 2

9 The A-B-C classification scheme is based on a simple idea: expend more attention on more important items Importance of an item is determined by two things: (1) its demand and (2) its value Captured via Annual Dollar Volume, D $, where D $ = (Annual Demand)*(Dollar Value /unit) If we arrange all the SKUs (stock keeping units) in descending order of their D $ values, then typically, about 80% of the TOTAL Dollar Volume, is accounted for by about the first 20% of the items on the list Pareto principle Rule important few vs. unimportant many

10 Item Dollar volume $ > $ > $ > $ > $ = $ 0.8* $ 0.2* $ Source: Ravindran and Warsing

11 A-B-C Classification of Inventory CLASS A Items: typically the first 5-10% of SKUs on the list, account for roughly 60-70% of D $ most important items requiring closest attention CLASS B Items: typically the next 10-25% of SKUs on the list, account for roughly 20-30% of D $ of secondary importance, requiring moderate attention CLASS C Items: typically the last 65-75% of SKUs on the list, Department of Industrial Engineering account for roughly 5-10% of D $ least important: use some simple method to control

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13 Before developing an inventory control strategy there are two critical tasks Characterize Demand Characterize Relevant Costs

14 Independent vs. Dependent Demand Independent demand is driven by market forces outside the direct control of the company Typically, finished goods Sometimes called distribution inventory Dependent demand is driven by the demand for other items produced by the company, and can be controlled by internal operating decisions Typically, components, raw materials, WIP, etc. Sometimes called manufacturing inventory NOTE: Dependent and Independent could be context-driven not absolute!!

15 Department of Industrial Engineering Stationary (or static) vs. Non-stationary (or dynamic) demand Stationary implies steady steady or stable or timeinvariant Non-stationary implies variable or varying over time

16 Deterministic vs. Probabilistic demand Deterministic: Known (at least with reasonable certainty ) Demand Probabilistic: Can at best be characterized by some probability distribution Demand

17 Characterizing the various costs Inventory Holding Cost Opportunity cost of the capital that is tied up as inventory Costs from having the item in stock cost of storage space taxes and insurance breakage / pilferage / spoilage etc. special costs (e.g., refrigeration)

18 Example Notation: Costs are specified as h $/unit/unit time, or i $/$/unit time (more typical) If the dollar value of the item is $c, then h=ic. E.g. 0.20(capital)+ 0.06(storage)+ 0.02(taxes/insurance) (damage) i =0.29 $/$/yr. So if c=$180, then h=0.29*180 = $52.20/unit/year and if we held an average of 400 items over the year then average annual inventory holding costs= 400*52.20 = $20,880

19 Other Relevant Costs Order Placement Cost: This is incurred whenever an order is placed. It has two components A setup cost $A per order which is independent of the size of the order Administrative costs for generating, submitting & tracking the order Costs of coordinating with carriers Physical costs for receiving the order and placing items into stock A variable order cost proportional to the order quantity Q (=cq) Total Order Cost = A+cQ

20 Other Relevant Costs (cont d) Shortage Cost (or stockout cost or penalty cost): Incurred whenever demand exceeds availability & includes such things as lost profit (in the lost sales case) backorder cost (if demand is backordered) loss of goodwill Specified as p $/unit short. Note: For simplicity, we will assume that if the item is backordered, p is independent of how long it takes to fill the backorder.

21 The replenishment lead-time (L) It is the interval of time between 1. when an order is released (to a vendor/supplier if it is a purchase, or to the shop-floor if it is a production order) and 2. when the order is received and available for use lead-time (L) We might distinguish the lead-time as Procurement lead time (if ordered from outside) Manufacturing lead time (if manufactured internally)

22 Other Characteristics to Consider STOCKOUTS: When demand exceeds availability. There are two basic possibilities Back ordering: Demand held over to be satisfied at a later date Lost sales: Customer goes elsewhere In practice, some combination of both possibilities could occur. SPECIAL SITUATIONS: Obsolescence, perishability etc.

23 There are three main decisions in inventory control systems The review Interval (I): How often to review inventory status? Nowadays we mostly use continuous review (I=0) The Reorder point (R): Based on the review, when should more items be re-ordered? The order Quantity (Q): How much to order when an order is placed? Cycle stocks are tied to Q Safety stocks are tied to R

24 The Newsvendor Model Assumptions: single period, single item with independent demand random demand D with known probability distribution function (pdf) given by f(x); let us denote its cumulative distribution function (cdf) by F(x)=Pr(D x) linear overage (excess) and underage (or shortage) costs examples include newspapers, Christmas trees, seasonal goods, items with limited shelf-life, etc.

25 The problem: How much to order (Q)? Order Q is placed before we know demand the D Note that Demand D is then realized No. of units short = Max(D-Q,0), No. of units over = Max(Q-D,0) D>Q shortage (or underage); lost profits and/or shortage; cost of c U per unit short D<Q excess (or overage); inventory costs, loss of investment (less any salvage value), etc.; cost of c O per unit in excess

26 Expected Cost G(Q,D) = c O E[units over] + cu E[units short] = c O + c U = c O c O + c U c U c O + c U

27 To find the Q that minimizes the above expression, we differentiate Y(Q,D) w.r.t. Q and equate to zero using Leibnitz s rule Let s apply this to c O + cu with a 1 (Q)=0, a 2 (Q)=Q, g(x,q)= (Q-x) f(x) for term 1 a 1 (Q)=Q, a 2 (Q)=, g(x,q)= (x-q) f(x) for term 2

28 G(Q,D) =c O + cu G(Q,D) = co + c O c U + c U = c O c U = co c U Equate to zero for the optimal Q: i.e.,. We may now solve this for Q *

29 Expected Cost Equating the derivative to zero we obtain 1 F(x) Q *