Introduction to Operations Management Inventory Management (Ch. 12) Hansoo Kim (金翰秀) Dept. of Management Information Systems, YUST

Schedule 5/31 – Inventory Management 6/7 – No Class 6/14 – APP & MRP 6/21 – Final Exam

X X X X X X X X X X X OM Overview Class Overview (Ch. 0) Operations, Productivity, and Strategy (Ch. 1, 2) X Project Management (Ch. 17) Strategic Capacity Planning (Ch. 5, 5S) Process Selection/ Facility Layout; LP (Ch. 6, 6S) X X X X X Mgmt of Quality/ Six Sigma Quality (Ch. 9, 10) Queueing/ Simulation (Ch. 18) Supply Chain Management (Ch 11) X Location Planning and Analysis (Ch. 8) X X JIT & Lean Mfg System (Ch. 15) Demand Mgmt Forecasting (Ch 3) X Aggregated Planning (Ch. 13) Inventory Management (Ch. 12) MRP & ERP (Ch 14) Term Project

Today’s Outline 재고란? (What is inventory?) 재고의 기능 (The function of inventory) 재고비용 항목 (Inventory Costs) 재고보관비 주문비 품절비 재고 모델 (Inventory Model) 정량발주모델 EOQ 모델 EPQ (or POQ) 모델 확률적 모델 정기발주모델

Question 1 ? 년간 수요, Annual Demand (D) = 1000 units/yr 주문 비용, Ordering Cost (S) = $10/order 재고 보관비 비율, Inventory Carrying rate (I) = 5% 년간 작업일 수, Working days in a year = 250 days/year 단위 가격, Unit Price (P) = $10/unit 배송 시간, Lead Time (L) = 5 days 몇 개를 주문해야 년간 재고비용이 최소화 되는가? (Order Quantity to minimize annual inventory cost?) 평균 년간 주문 회수는 얼마인가? (Average number of orders?) 평균 주문 주기는 얼마인가? (Average ordering period?) 再발주 시점은 언제인가? (Reporder point?)

Question 2 ? 대안 할인 수량 할인률 (%) 할인가격 (P) 1 0 to 999 No discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75 년간수요 = 5000 units/yr, 주문비=49$/order, 재고 보관비 비율 = 20%, 당신은 할인 혜택을 받으시겠습니까? (Will you take discount or not?) 몇 개를 주문해야 할까요? (How many quantity to be ordered?)

재고란? What is Inventory? Stock of materials Stored capacity 사용할 수 있으나, 지금 당장 사용하지는 않는 물자들

재고가 필요한 이유 (Why Inventory?) 예측하지 못한 수요에 대한 대응 Meet unexpected demand 계절적, 주기적 수요 변화에 대한 대응 Smooth seasonal or cyclical demand 생산 공정의 독립성 제고 및 분리 Decouple or separate various parts of the production process 가격할인의 잇점 (쌀때 왕창 사두자!) Take advantage of price discounts 대량할인의 잇점 Take advantage of quantity discounts 갑작스런 가격 상승에 대한 대비 Hedge against price increases

재고의 종류 (Types of Inventory) 원자재 (Raw Material) 가공되지 않은 구매된 자재 재공재고 (Work-In-Process) 원자재와 완재품 사이의 반제품 상태의 자재 소모품 (Maintenance/repair/operating supply) 유지 보수 혹은 운영을 위해 소모되는 물품 완제품 재고 (Finished Goods) 판매 가능한 최종 제품

자재의 흐름 (Material Flow) 비사용 Raw Material 가공중 WIP 판매가능 Finished Goods

재고의 문제점 (Problems caused by inventory) 재고 = 지금 당장 사용할 수 없는 자산 재고 관련 비용의 증가 구매비, Item cost (if purchased) 주문비, Ordering (or setup) cost 보관비, Holding (or carrying) cost 창고 임대비, 보험료, 세금 등… 품절 비용, Shortage Cost Temporary or permanent loss of sales when demand cannot be met 재고 통제의 어려움 생산공정의 문제를 숨김 Hides production problems

재공재고(WIP)가 많이 있는 경우 Scrap Work in process inventory level (hides problems) Unreliable Vendors Capacity Imbalances NO PROBLEM!!! Really? The analogy presented in this and the next four slides may help to illustrate the action of inventory in hiding problems.

재고 수준을 낮춘다면? 암초에 걸리기 시작… 문제가 드러남! Scrap Unreliable Vendors Capacity Imbalances WIP

재고의 분류 Inventory Classifications Process stage Demand Type Number & Value Other Raw Material WIP Finished Goods Independent Dependent A Items B Items C Items Maintenance Operating © 1984-1994 T/Maker Co.

ABC 분석 (ABC Analysis) 재고의 수량과 가치에 따라 세 종류로 나눔 Divides on-hand inventory into 3 classes A class, B class, C class 년간 $ x 부피 ($ volume)의 단위에 기초 Basis is usually annual $ volume $ volume = Annual demand x Unit cost ABC 분석에 따른 전략 Policies based on ABC analysis A Class 제품을 집중 관리함 It might be helpful here to discuss some of the differences in the ways we would manage items in the three different levels. What actions would we actually take in managing A versus in managing C?

ABC 분석에 의한 재고 분류 Class % $ Vol % Items A 80 15 B 15 30 C 5 55 Are we back to Pareto analysis?

ABC 분석에 의한 재고 분류 (예제) PART UNIT COST ANNUAL USAGE 1 $ 60 90 2 350 40 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE Example 10.1

ABC 분석에 의한 재고 분류 A B C PART UNIT COST ANNUAL USAGE 1 $ 60 90 2 350 40 1 $ 60 90 2 350 40 3 30 130 4 80 60 5 30 100 6 20 180 7 10 170 8 320 50 9 510 60 10 20 120 PART UNIT COST ANNUAL USAGE TOTAL % OF TOTAL % OF TOTAL PART VALUE VALUE QUANTITY % CUMMULATIVE 9 $30,600 35.9 6.0 6.0 8 16,000 18.7 5.0 11.0 2 14,000 16.4 4.0 15.0 1 5,400 6.3 9.0 24.0 4 4,800 5.6 6.0 30.0 3 3,900 4.6 10.0 40.0 6 3,600 4.2 18.0 58.0 5 3,000 3.5 13.0 71.0 10 2,400 2.8 12.0 83.0 7 1,700 2.0 17.0 100.0 $85,400 A B C Example 10.1

ABC 분석에 의한 재고 분류 C B A % of Value | | | | | | 0 20 40 60 80 100 100 – 80 – 60 – 40 – 20 – 0 – | | | | | | 0 20 40 60 80 100 % of Quantity % of Value A B C

Example 1

독립재고 대 종속재고 Independent vs. Dependent Demand 독립재고, Independent demand - demand for item is independent of demand for any other item (e.g. Finished goods) 종속재고, Dependent demand - demand for item is dependent upon the demand for some other item

독립재고 대 종속재고 Item Materials With Independent Demand Dependent Demand Source Company Customers Parent Items Material Type Finished Goods WIP & Raw Materials Method of Estimating Forecast & Booked Customer Orders Calculated Planning Method EOQ & ROP MRP We start this chapter by linking Dependent Demand Inventory back to Independent Demand Inventory. You might note to students that independent demand is created external to the company, dependent demand, internally. It makes no sense to independently forecast dependent demands.

재고관련 비용들… 재고 보관비 (Holding or Carrying Cost) 주문비 (Ordering Cost) 재고를 보관하는데 드는 비용 시간이 길 수록 비용이 증가한다 주문비 (Ordering Cost) 물건을 주문하고 수령하는데 드는 비용 준비비 (Setup Cost) 생산에 앞서 설비를 준비하는데 드는 비용 판매유실 비용 (Lost Sales Cost) 판매기회 상실에 따는 기회비용 및 잠재비용

재고 보관비 (Holding or Carrying Cost) 재고를 유지하고 보관하는데 드는 비용 일반적으로 재고 수량과 비례적 관계 Obsolescence (열화) Insurance (보험) Extra staffing (관리) Interest (이자) Pilferage (도난) Damage (손상) Warehousing (보관) Etc.

주문비 (Ordering Cost) 물건을 주문하고 수령하는데 드는 비용 일반적으로 제품의 수량과 관련이 없다 Supplies (공급관련 비용) Forms (양식) Order processing (주문처리) Clerical support (사무적 지원) Etc.

준비비 (Setup Cost) 생산에 앞서 설비를 준비하는데 드는 비용 Clean-up costs Re-tooling costs Adjustment costs Etc.

재고모델 (Inventory Models) Help answer the inventory planning questions! 정량발주 모델 Fixed order-quantity models 경제적 주문 수량 Economic order quantity (EOQ) 경제적 생산 수량 Production order quantity (POQ) 대량할인 Quantity discount 확률적 모델 Probabilistic models 정기발주 모델 Fixed order-period models This slide simply introduces some of the available models. Additional details are provided in subsequent slides.

EOQ 모델의 가정 고정적이고 이미 알고 있는 수요 Known and constant demand 고정적이고 이미 알고 있는 리드타임(배송시간) Known and constant lead time 순간적인 물자 입고 Instantaneous receipt of material 대량할인이 없다 No quantity discounts 주문비(혹은 준비비)와 보관비만 고려 Only order (setup) cost and holding cost 제품 품절은 없다 No stockouts

재고 주문 사이클 Figure 10.1

주문량과 재고수준과의 관계

EOQ 모델 얼마를 주문해야 하는가? Annual Cost Order quantity Total Cost Curve Holding Cost Curve Total Cost Curve Order (Setup) Cost Curve Optimal Order Quantity (Q*) Minimum total cost

Why Holding Costs Increase More units must be stored if more are ordered Purchase Order Description Qty. Microwave 1000 Order quantity Purchase Order Description Qty. Microwave 1 Order quantity

Why Order Costs Decrease Cost is spread over more units Example: You need 1000 microwave ovens Purchase Order Description Qty. Microwave 1 1 Order (Postage $ 0.33) 1000 Orders (Postage $330) Order quantity 1000

EOQ 구하는 법 주문비 (혹은 준비비)에 대한 식을 구한다 Develop an expression for setup or ordering costs 보관비에 대한 식을 구한다 Develop an expression for holding cost 준비비와 보관비가 동일하게 수식을 세운다 Set setup cost equal to holding cost 수식을 풀면, EOQ가 계산 된다 Solve the resulting equation for the best order quantity Students may find it helpful if you actually go through each of these steps - at least through writing the equation, and setting setup cost equal to holding cost.

계산 Holding Cost: Ordering Costs: s per order, so Calculation

예제) Demand, D = 1000 racks per year Price, P = $250 Ordering Cost, s = $500 (estimated from supplier’s pricing) Holding Cost, h = $35 per unit per year, or H = IP, I = annual interest rate for inventory carrying cost. Then, I = 1.4 %

EOQ모델의 비용 그래프 S/Q P

EOQ Model Equations = × Q* D S H N T d ROP L 2 Optimal Order Quantity Expected Number of Orders Expected Time Between Orders Working Days / Year = × Q* D S H N T d ROP L 2 D = Demand per year S = Setup (order) cost per order H = Holding (carrying) cost d = Demand per day L = Lead time in days For some students, it is most important at this point to explain in detail the meaning and significance of each equation. It might be helpful to actually work through a numerical example.

재발주점과 리드타임 The Reorder Point (ROP) Curve Q* ROP (Units) Slope = units/day = d Lead time = L Time (days) Inventory level (units)

예제 년간 수요 (D) = 1000 units/yr 주문비 (S) = $10/order 재고 보관비 비율 (I) = 5% 년간 작업일수 = 250 days/year 단위 가격 (P) = $10/unit 리드타임 (L) = 5 days EOQ?, 년간 총 비용? 평균 년간 발주 회수 (N)? 평균 발주 주기 (T)? 재발주점 (ROP)?

Robustness of EOQ (Eg. 6) What if D is changed to 1500 units/yr (50% under-estimate)? Total Cost (Q=200)? Total Cost (Q=244.9)? How much different?

Production Order Quantity (POQ)Model 언제 얼마나 생산해야 하는가에 대한 답을 준다 Answers how much to order and when to order 제품의 입고가 점진적이다 Allows partial receipt of material EOQ와는 다른 가정 경제적 제품생산량을 결정하는데 유용하다 Suited for production environment Material produced, used immediately Provides production lot size EOQ모델 보다 재고 보관비용이 적게 나타난다Lower holding cost than EOQ model

EOQ POQ (or EPQ) Model When To Order Time Inventory Level 생산과 소비가 동시에 이루어 진다 소비만 이루어 진다 Maximum inventory level

POQ Model Inventory Levels Time Inventory Level Production Portion of Cycle Max. Inventory Q·(1- d/p) Q* Supply Begins Supply Ends Inventory level with no demand Demand portion of cycle with no supply (P-D)*Q/P=Q(1-D/P) P P-D t=Q/P

Maximum inventory level POQ Model Equations 2*D*S = * Q = Optimal Order Quantity ( ) p d H* 1 - p ( ) - d p Maximum inventory level * = 1 Q D = Demand per year S = Setup cost H = Holding cost d = Demand per day p = Production per day D Here again, it may be helpful to actually go through a numerical example, but it will probably be necessary to explain in detail the meaning and significance of each equation = * S Setup Cost Q ( ) d Holding Cost = 0.5 * H * Q 1 - p

Solution to POQ Model Annual Cost Function: Solution (by taking derivative and setting equal to zero): setup holding production tends to EOQ as P otherwise larger than EOQ because replenishment takes longer

예제 D = 1000 units/yr S = $10/order H = $0.5/unit*year p = 8 units/day, Working Days=250days/yr P = 2000 units/yr POQ? Total Cost?

대량할인 모델 Quantity Discount Model 언제 얼마나 생산해야 하는가에 대한 답을 준다 Answers how much to order & when to order 대량구매시 할인이 있다. Allows quantity discounts Reduced price when item is purchased in larger quantities Other EOQ assumptions apply 가격할인과 재고보관 비용에 대한 절충 Trade-off is between lower price & increased holding cost

대량할인 Quantity Discount Schedule Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 No discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $4.75 D = 5000 units/yr, S=49$/order, I = 20%,

대량할인 문제 푸는 방법 각각의 할인에 대해서 EOQ를 사용하여 각각의 최적 주문량을 구한다. For each discount, calculate a value for optimal order size Q*, using EOQ formula 만약 최적 주문량이 할인을 허용하는 최초치 보다 더 작을 경우, 할인이 가능한 최소치로 변경시킨다. For any discount, if the order quantity is too low to qualify for the discount, adjust the order quantity upward to the lowest quantity that will qualify for the discount 비용을 구하는 공식을 사용히여, 각각의 주문량, Q*, 에 대하여 총 비용을 구한다. Using the preceding total cost equation compute a total cost for every Q* determined in steps 1 and 2. If you had to adjust Q* upward because it was below the allowable quantity range, be sure to use adjusted value for Q* 이 비용중, 최소의 총 비용을 갖는 주문량, Q*를 선택한다. Select the Q* that has the lowest total cost, as computed in step 3. It will be the quantity that will minimize the total inventory cost

Quantity Discount – How Much to Order

해답 – Price Discount Model Discount Number Discount Quantity Discount (%) Discount Price (P) 1 0 to 999 No discount $5.00 2 1,000 to 1,999 4 $4.80 3 2,000 and over 5 $3 D = 5000 units/yr, S=49$/order, I = 20%, adjusting

다른 예제.. Quantity Discount Example QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900 S = $2,500 H = $190 per computer D = 200 Q* = = = 72.5 PCs 2SD H 2(2500)(200) 190 TC = + + PD = $233,784 SD Q* HQ* 2 For Q = 72.5 TC = + + PD = $194,105 SD Q HQ 2 For Q = 90

재발주점 계산 예제 년간수요 , D = 10,000 units/year 년간 작업일수, Store open 311 days/year 일간수요, d = 10,000 / 311 = 32.154 units/day 리드타임, L = 10 days R = dL = (32.154)(10) = 321.54 units

확률적 모형 수요에 변동이 있을수 있다. Allow demand to vary 언제 얼마나 생산해야 하는가에 대한 답을 준다 Answer how much & when to order 수요에 변동이 있을수 있다. Allow demand to vary 수요는 정규분포를 따른다 (Follows normal distribution) Other EOQ assumptions apply 봉사수준과 안전재고를 고려한다 Consider service level & safety stock 봉사수준, Service level = 1 - Probability of stockout (품절확률) 더 높은 봉사수준을 위해서는 더 많은 안전재고가 필요하다 Higher service level means more safety stock 더 많은 안전재고는 더 높은 재발주점을 의미한다. More safety stock means higher ROP

Probabilistic Models When to Order? Reorder Point (ROP) Optimal Order Quantity X Safety Stock (SS) Time Inventory Level Lead Time SS ROP Service Level P(Stockout) Place order Receive order Frequency 32

안전재고 (Safety Stocks) Safety stock (안전재고) Stockout (품절) 제품의 품절을 줄이기 위해, 리드타임 동안의 수요에 대비한 추가적인 재고 buffer added to on hand inventory during lead time Stockout (품절) 재고 부족 (an inventory shortage) Service level (봉사 or 서비스 수준) 리드타임 동안의 재고가 부족하지 않을 확률 probability that the inventory available during lead time will meet demand

Variable Demand with a Reorder Point point, R Q LT Time Inventory level

Reorder Point with a Safety Stock point, R Q LT Time Inventory level Safety Stock Figure 10.6

Inventory Holding Cost 예제 10 Number of Units Probability 30 40 50 60 70 0.2 0.3 0.1 Demand for reorder period 재발주점 계산 ROP = d*L + SS, SS=Safety Stock (안전재고) d*L=50 units H=$5/년, 품절비용 (C)=$40/개, 년간 발주수=6 Safety Stock Inventory Holding Cost Stockout Cost Total Cost 20 10 20*$5=100 10*$5=50 10*0.1*$40*6=240 10*0.2*$40*6+20*0.1*$40*6=960 $100 $290 $960

고정발주시스템 Fixed Period Model 얼마나 주문할 것인가에 대해 답변 Answers how much to order 주문을 일정한 간격으로 한다 Orders placed at fixed intervals 적정재고 수준까지 주문 Inventory brought up to target amount 주문량을 그때 그때 달라요. Amount ordered varies 계속적으로 재고를 관찰하지 않아도 된다. No continuous inventory count 재고 부족현상이 나타날수 있다. Possibility of stockout between intervals 보통 공급자가 정기적으로 방문하는 경우 사용 Useful when vendors visit routinely Example: P&G representative calls every 2 weeks This represents a model in which orders are based upon time, not the quantity needed. The following slide provides a graphical representation.

Inventory Level in a Fixed Period System Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to target maximum p Q1 Q2 Q3 Q4 Target maximum Time On-Hand Inventory

Example 고정발주시스템에서 Back order = 3 units Product inventory = 0 unit Target Value = 50 unit 이전에 한 주문은 없다. (None of earlier order) 이번에 몇개를 주문해야 하는가? What is Quantity for order in this time period? Sol) Q = Taget – On-hand Inventory – Earlier orders not yet received + Back Order = 50 – 0 – 0 + 3 = 53 units

Announcement HW Review Examples Review Solved Problems

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