Introduction. Introduction. Introduction LEARNING OBJECTIVES LEARNING OBJECTIVES

Transcription

1 Valua%on and pricing (November 5, 2013) LEARNING OBJECTIVES Lecture 9 Control 1. Understand the importance of inventory control and ABC analysis. 2. Use the economic order quantity (EOQ) to determine how much to order. 3. Compute the reorder point (ROP) in determining when to order more inventory. 4. Handle inventory problems that allow quantity discounts or noninstantaneous receipt. Olivier J. de Jong, LL.M., MM, MBA, CFD, CFFA, AA Copyright 2015 Pearson Education, Inc. 6 2 LEARNING OBJECTIVES 5. Understand the use of safety stock. 6. Describe the use of material requirements planning in solving dependent-demand inventory problems. 7. Discuss just-in-time inventory concepts to reduce inventory levels and costs. 8. Discuss enterprise resource planning systems. Introduction is an expensive and important asset Any stored resource used to satisfy a current or future need Raw materials Work-in-process Finished goods Balance high and low inventory levels to minimize costs Copyright 2015 Pearson Education, Inc. 6 3 Copyright 2015 Pearson Education, Inc. 6 4 Introduction Lower inventory levels Can reduce costs May result in stockouts and dissatisfied customers All organizations have some type of inventory planning and control system Determine what goods/services are produced or purchased FIGURE 6.1 Planning and Control Introduction Feedback metrics to revise plans and forecasts Planning on what to stock and how to get it Controlling inventory levels Forecasting parts/product demand Copyright 2015 Pearson Education, Inc. 6 5 Copyright 2015 Pearson Education, Inc. 6 6

2 Importance of Control Five uses of inventory 1. The decoupling function 2. Storing resources 3. Irregular supply and demand 4. Quantity discounts 5. Avoiding stockouts and shortages Decouple manufacturing processes A buffer between stages Reduces delays and improves efficiency Importance of Control Storing resources Seasonal products stored to satisfy off-season demand Materials stored as raw materials, work-in-process, or finished goods Labor can be stored as a component of partially completed subassemblies Irregular supply and demand Not constant over time used to buffer the variability Copyright 2015 Pearson Education, Inc. 6 7 Copyright 2015 Pearson Education, Inc. 6 8 Importance of Control Quantity discounts Lower prices may be available for larger orders Higher storage and holding costs More cash invested Avoiding stockouts and shortages Stockouts may result in lost sales Dissatisfied customers may choose to buy from another supplier Loss of goodwill Decisions Two fundamental decisions 1. How much to order 2. When to order Major objective is to minimize total inventory costs 1. Cost of the items (purchase or material cost) 2. Cost of ordering 3. Cost of carrying, or holding, inventory 4. Cost of stockouts Copyright 2015 Pearson Education, Inc. 6 9 Copyright 2015 Pearson Education, Inc TABLE 6.1 Cost Factors ORDERING COST FACTORS Developing and sending purchase orders Processing and inspecting incoming inventory Bill paying inquiries Utilities, phone bills, and so on, for the purchasing department Salaries and wages for the purchasing department employees Supplies such as forms and paper for the purchasing department CARRYING COST FACTORS Cost of capital Taxes Insurance Spoilage Theft Obsolescence Salaries and wages for warehouse employees Utilities and building costs for the warehouse Supplies such as forms and paper for the warehouse Cost Factors Ordering costs are generally independent of order quantity Many involve personnel time The amount of work is the same no matter the size of the order Holding costs generally vary with the amount of inventory or order size Labor, space, and other costs increase with order size Cost of items purchased can vary with quantity discounts Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 12

3 Economic Order Quantity Economic order quantity (EOQ) model One of the oldest and most commonly known inventory control techniques Easy to use A number of important assumptions Objective is to minimize total cost of inventory Economic Order Quantity Assumptions: Demand is known and constant Lead time is known and constant Receipt of inventory is instantaneous Purchase cost per unit is constant The only variable costs are ordering cost and holding or carrying cost These are constant throughout the year Orders are placed so that stockouts or shortages are avoided completely Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Usage Over FIGURE 6.2 Level Minimum 0 Order Quantity = Q = Maximum Level Copyright 2015 Pearson Education, Inc Costs in the EOQ Situation Average inventory level = Q 2 Annual ordering cost is number of orders per year times cost of placing each order Annual carrying cost is the average inventory times carrying cost per unit per year INVENTORY LEVEL DAY BEGINNING ENDING AVERAGE April 1 (order received) April April April April Maximum level April 1 = 10 units Total of daily averages = = 25 Number of days = 5 Average inventory level = 25/5 = 5 units TABLE 6.2 Copyright 2015 Pearson Education, Inc Costs in the EOQ Situation Q = number of pieces to order EOQ = Q* = optimal number of pieces to order D = annual demand in units for the inventory item C o = ordering cost of each order C h = holding or carrying cost per unit per year Costs in the EOQ Situation Q = number of pieces to order EOQ = Q* = optimal number of pieces to order D = annual demand in units for the inventory item C o = ordering cost of each order C h = holding or carrying cost per unit per year Annual Number of ordering = orders placed cost per year Annual demand = Number of units in each order Ordering cost per order Ordering cost per order = D Q C o Annual holding = Average inventory cost = Carrying cost per unit per year Order quantity (Carrying cost per unit per year) 2 = Q 2 C h Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 18

4 Cost Minimum Total Cost Costs in the EOQ Situation FIGURE 6.3 Total Cost as a Function of Order Quantity Curve for Total Cost of Carrying and Ordering Optimal Order Quantity Carrying Cost Curve Ordering Cost Curve Order Quantity Copyright 2015 Pearson Education, Inc Finding the EOQ When the EOQ assumptions are met, total cost is minimized when Solving for Q Annual ordering cost = Annual holding cost D Q C o = Q 2 C h Q 2 C h = 2DC o Q 2 = 2DC o C h Q = 2DC o Thus EOQ = Q * = 2DC o C h C h Copyright 2015 Pearson Education, Inc Finding the EOQ Equation summary Annual ordering cost = D Q C o Annual holding cost = Q 2 C h Sumco Pump Company Sells pump housings to other companies Reduce inventory costs by finding optimal order quantity Annual demand = 1,000 units Ordering cost = $10 per order Average carrying cost per unit per year = $0.50 EOQ = Q * = 2DC o C h Q * = 2DC o = 2(1,000)(10) = 40,000 = 200 units C h 0.50 Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Sumco Pump Company Total cost TC = D Q C o + Q 2 C h Sumco Pump Company Cost Curve for Total Cost of Carrying and Ordering = 1, (10) (0.5) = $50 + $50 = $100 $100 $50 Carrying Cost Curve Ordering Cost Curve Number of orders per year = (D/Q) = 5 Average inventory (Q/2) = 100 Q = 200 Order Quantity Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 24

5 Purchase Cost of Items Total inventory cost can be written to include the cost of purchased items Annual purchase cost is constant at D x C no matter the order policy, where C is the purchase cost per unit D is the annual demand in units The average dollar level of inventory Average dollar level = (CQ) 2 Copyright 2015 Pearson Education, Inc Purchase Cost of Items Carrying cost often expressed as an annual percentage of the unit cost or price of the inventory New variable I = Annual inventory holding charge as a percentage of unit price or cost Cost of storing inventory for one year = C h = IC Thus Q * = 2DC o IC Copyright 2015 Pearson Education, Inc Sensitivity Analysis with the EOQ Model The EOQ model assumes all values are know and fixed over time Values are estimated or may change Sensitivity analysis determines the effects of these changes Because the EOQ is a square root, changes in the inputs result in relatively small changes in the order quantity Sensitivity Analysis with the EOQ Model Sumco Pump example EOQ = 2(1,000)(10) 0.50 Increase C o to $40 EOQ = 2(1,000)(40) 0.50 = 200 units = 400 units EOQ = Q * = 2DC o C h In general, the EOQ changes by the square root of the change to any of the inputs Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Reorder Point: Determining When To Order Next decision is when to order between placing an order and its receipt is called the lead time (L) or delivery time Generally expressed as a reorder point (ROP) Reorder Point Graphs FIGURE 6.4 Level Q ROP 0 Lead time = L ROP < Q Demand ROP = per day Lead time for a new order in days Level Q On Order = d L On hand Copyright 2015 Pearson Education, Inc Lead time = L ROP > Q Copyright 2015 Pearson Education, Inc. 6 30

6 Procomp s Computer Chips Procomp s Computer Chips Annual demand = 8,000 Daily demand = 40 units Delivery in three working days Annual demand = 8,000 Daily demand = 40 units Delivery in three working days Now 12 days ROP = d L = 40 units per day 3 days = 120 units An order for the EOQ (400) is placed when the inventory reaches 120 units The order arrives 3 days later just as the inventory is depleted ROP = d L = 40 units per day 12 days = 480 units position = + on hand 480 = on order New order placed when inventory = 80 and one order is in transit Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc EOQ Without Instantaneous Receipt When inventory accumulates over time, the instantaneous receipt assumption does not apply Daily demand rate must be taken into account Production run model Level Maximum Part of Cycle During Which Production is Taking Place There is No Production During This Part of the Cycle Annual Carrying Cost for Production Run Model Setup cost replaces ordering cost Model variables Q = number of pieces per order, or production run C s = setup cost C h = holding or carrying cost per unit per year p = daily production rate d = daily demand rate t = length of production run in days t FIGURE 6.5 Control and the Production Process Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Annual Carrying Cost for Production Run Model Maximum inventory level = (Total produced during the production run) (Total used during the production run) = (Daily production rate)(number of days production) (Daily demand)(number of days production) = (pt) (dt) Since Total produced = Q = pt and t = Q p Maximum inventory level = pt dt = p Q p d Q p = Q! 1 d $ # & " p % Annual Carrying Cost for Production Run Model Average inventory is one-half the maximum and Average inventory = Q! 2 1 d $ # & " p % Annual holding cost = Q! 2 1 d $ # &C h " p % Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 36

7 Annual Setup Cost for Production Run Model Setup cost replaces ordering cost becomes Annual setup cost = D Q C s Annual ordering cost = D Q C o Determining the Optimal Production Quantity Set setup costs equal to holding costs and solve for the optimal order quantity Annual holding cost = Annual setup cost Solving for Q, we get Q! 2 1 d $ # &C h = D " p % Q C s Q * = C h 2DC s! 1 d $ # & " p % Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Production Run Model Equation summary Annual holding cost = Q! 2 1 d $ # &C h " p % Annual setup cost = D Q C s Optimal production quantity Q * = 2DC s! 1 d $ # & " p % Copyright 2015 Pearson Education, Inc C h Brown Manufacturing Produces commercial refrigeration units in batches Annual demand = D = 10,000 units Setup cost = C s = $100 Carrying cost = C h = $0.50 per unit per year Daily production rate = p = 80 units daily Daily demand rate = d = 60 units daily 1. How many units should Brown produce in each batch? 2. How long should the production part of the cycle last? Copyright 2015 Pearson Education, Inc Brown Manufacturing Q * = C h 2DC s! 1 d $ # & " p % Q * = 2 10, ! $ # & " 80% = 2,000, ( 1 4 ) = 4,000 units 2. = 16,000,000 Production cycle = Q p = 4,000 = 50 days 80 Quantity Discount Models Quantity discounts are commonly available Basic EOQ model is adjusted by adding in the purchase or materials cost Total cost = Material cost + Ordering cost + Holding cost where Total cost = DC + D Q C o + Q 2 C h D = annual demand in units C o = ordering cost of each order C = cost per unit C h = holding or carrying cost per unit per year Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 42

8 Quantity Holding cost per Discount unit based on Models cost, so Quantity discounts are C h commonly = IC available Basic where EOQ model is adjusted by adding in the purchase I = holding or materials cost as a percentage cost of the unit cost (C) Total cost = Material cost + Ordering cost + Holding cost Quantity Discount Models Discount schedule and EOQs might not align Buying at the lowest unit cost may not result in lowest total cost TABLE 6.3 Quantity Discount Schedule where Total cost = DC + D Q C o + Q 2 C h D = annual demand in units C o = ordering cost of each order C = cost per unit C h = holding or carrying cost per unit per year DISCOUNT NUMBER DISCOUNT QUANTITY DISCOUNT (%) DISCOUNT COST ($) 1 0 to ,000 to 1, ,000 and over Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Quantity Discount Models FIGURE 6.6 Total Cost Curve for the Quantity Discount Model Total Cost $ TC Curve for Discount 1 TC Curve for Discount 3 Quantity Discount Models Steps in the process 1. For each discount price (C), compute EOQ = 2DC o IC 2. If EOQ < Minimum for discount, adjust the quantity to Q = Minimum for discount TC Curve for Discount 2 3. For each EOQ or adjusted Q, compute Total cost = DC + D Q C o + Q 2 C h EOQ for Discount 2 0 1,000 2,000 Order Quantity Copyright 2015 Pearson Education, Inc Choose the lowest-cost quantity Copyright 2015 Pearson Education, Inc Brass Department Store Toy race cars Quantity discounts available Step 1 Compute EOQs for each discount EOQ 1 = EOQ 2 = EOQ 3 = (2)(5,000)(49) (0.2)(5.00) (2)(5,000)(49) (0.2)(4.80) (2)(5,000)(49) (0.2)(4.75) = 700 cars per order = 714 cars per order = 718 cars per order Brass Department Store Step 2 Adjust quantities below the allowable discount range The EOQ for discount 1 is allowable The EOQs for discounts 2 and 3 are outside the allowable range, adjust to the possible quantity closest to the EOQ Q 1 = 700 Q 2 = 1,000 Q 3 = 2,000 Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 48

9 Brass Department Store Step 3 Compute total cost for each quantity TABLE 6.4 Total Cost Computations for Brass Department Store DISCOUNT NUMBER UNIT PRICE (C) ORDER QUANTITY (Q) ANNUAL MATERIAL COST ($) = DC ANNUAL ORDERING COST ($) = (D/Q)C o ANNUAL CARRYING COST ($) = (Q/2)C h TOTAL ($) 1 $ , , ,000 24, , ,000 23, , Step 4 Choose the alternative with the lowest total cost Copyright 2015 Pearson Education, Inc Use of Safety Stock If demand or the lead time are uncertain, the exact ROP will not be known with certainty Safety stock can help prevent stockouts Can be implemented by adjusting the ROP Average demand ROP = + during lead time ROP = where Average demand during lead time SS = safety stock + SS Safety stock Copyright 2015 Pearson Education, Inc FIGURE 6.7 Use of Safety Stock on Hand Stockout on Hand Use of Safety Stock Objective is to choose a safety stock amount the minimizes total holding and stockout costs If variation in demand and holding and stockout costs are known, payoff/cost tables could be used to determine safety stock More general approach is to choose a desired service level based on satisfying customer demand Safety Stock, SS Stockout is avoided 0 Units Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Use of Safety Stock Set safety stock to achieve a desired service level Service level = 1 Probability of a stockout or Probability of a stockout = 1 Service level Safety Stock with the Normal Distribution ROP = (Average demand during lead time) + Zσ dlt where Z = number of standard deviations for a given service level σ dlt = standard deviation of demand during the lead time Thus Safety stock = Zσ dlt Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 54

10 Hinsdale Company Item A3378 has normally distributed demand during lead time Mean = 350 units, standard deviation = 10 Stockouts should occur only 5% of the time µ = Mean demand = 350 σ dlt = Standard deviation = 10 X = Mean demand + Safety stock SS = Safety stock = X µ = Zσ Z = X µ σ SS µ = 350 X =? FIGURE 6.8 5% Area of Normal Curve Hinsdale Company From Appendix A we find Z = 1.65 = X µ = SS σ σ ROP = (Average demand during lead time) + Zσ dlt = (10) = = units (or about 367 units) SS = 16.5 µ = 350 X = % Area of Normal Curve Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Calculating Lead Demand and Standard Deviation Three situations to consider Demand is variable but lead time is constant Demand is constant but lead time is variable Both demand and lead time are variable Calculating Lead Demand and Standard Deviation 1. Demand is variable but lead time is constant where ROP = dl + Z ( σ d L) d = average daily demand σ d = standard deviation of daily demand L = lead time in days Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Calculating Lead Demand and Standard Deviation 2. Demand is constant but lead time is variable ROP = dl + Z ( dσ L ) Calculating Lead Demand and Standard Deviation 3. Both demand and lead time are variable ROP = dl + Z Lσ d 2 + d 2 σ L 2 where L = average lead time σ L = standard deviation of lead time d = daily demand The most general case Can be simplified to the earlier equations Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 60

11 Hinsdale Company Determine safety stock for three other items For SKU F5402, d = 15, σ d = 3, L = 4 Desired service level = 97% For a 97% service level, Z = 1.88 ROP = dl + Z ( σ d L) =15(4) (3 4) =15(4) (6) = = Hinsdale Company For SKU B7319, d = 25, L = 6, σ L = 3 Desired service level = 98% For a 98% service level, Z = 2.05 ROP = dl + Z ( dσ L ) = 25(6) (25)(3) = (75) = = Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Hinsdale Company For SKU F9004, d = 20, σ d = 4, L = 5, σ L = 2 Desired service level = 94% For a 94% service level, Z = 1.55 ROP = dl + Z Lσ d 2 + d 2 σ L 2 = (20)(5) (4) 2 + (20) 2 (2) 2 = = (40.99) = = Service Levels, Safety Stock, and Holding Costs As service levels increase Safety stock increases at an increasing rate As safety stock increases Annual holding costs increase Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc SERVICE LEVEL (%) Hinsdale Company TABLE 6.5 Safety Stock for SKU A3378 at Different Service Levels Z VALUE FROM NORMAL CURVE TABLE SAFETY STOCK (UNITS) Copyright 2015 Pearson Education, Inc Calculating Annual Holding Cost with Safety Stock Under standard assumptions of EOQ Average inventory = Q/2 Annual holding cost = (Q/2)C h With safety stock Total annual holding cost Holding cost = of regular + inventory THC = Q 2 C h +(SS)C h Holding cost of safety stock where THC = total annual holding cost Q = order quantity C h = holding cost per unit per year SS = safety stock Copyright 2015 Pearson Education, Inc. 6 66

12 Hinsdale Company Hinsdale Company FIGURE 6.9 Service Level Versus Annual Carrying Costs (%) FIGURE 6.9 Service Level Versus Annual Carrying Costs (%) This graph was developed for a specific case, but the general shape of the curve is the same for all cases Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Single-Period Models Some products have no future value beyond the current period News vendor problems or single-period inventory models Marginal analysis uses marginal profit (MP) and marginal loss (ML) With a manageable number of states of nature and alternatives, use discrete distributions When there are a large number of alternatives or states of nature, use normal distribution Marginal Analysis with Discrete Distributions Stock an additional unit only if the expected marginal profit for that unit exceeds the expected marginal loss P = probability that demand will be greater than or equal to a given supply (or the probability of selling at least one additional unit) 1 P = probability that demand will be less than supply (or the probability that one additional unit will not sell) Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Marginal Analysis with Discrete Distributions The expected marginal profit = P(MP) The expected marginal loss = (1 P)(ML) The optimal decision rule Stock the additional unit if P(MP) (1 P)ML With some basic manipulation P(MP) ML P(ML) P(MP) + P(ML) ML P(MP + ML) ML or ML P ML + MP Steps of Marginal Analysis with Discrete Distributions ML 1. Determine the value of for the ML + MP problem 2. Construct a probability table and add a cumulative probability column 3. Keep ordering inventory as long as the probability (P) of selling at least one ML additional unit is greater than ML + MP Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 72

13 Café du Donut Café buys donuts each day for $4 per carton of 2 dozen donuts Cartons not sold are thrown away at the end of the day If a carton is sold, the total revenue is $6 The marginal profit per carton is MP = Marginal profit = $6 $4 = $2 Marginal loss ML = $4 since doughnuts cannot be returned or salvaged DAILY SALES (CARTONS OF DOUGHNUTS) Café du Donut TABLE 6.6 Café du Donut s Probability Distribution PROBABILITY (P) THAT DEMAND WILL BE AT THIS LEVEL Total 1.00 Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Café du Donut Step 1. Determine the value of decision rule ML ML + MP ML P ML + MP = $4 $4 + $2 = 4 6 = 0.67 P 0.67 for the Step 2. Add a new column to the table to reflect the probability that doughnut sales will be at each level or greater Café du Donut TABLE 6.7 Marginal Analysis for Café du Donut DAILY SALES (CARTONS OF DOUGHNUTS) PROBABILITY (P) THAT DEMAND WILL BE AT THIS LEVEL PROBABILITY (P) THAT DEMAND WILL BE AT THIS LEVEL OR GREATER Total 1.00 Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Café du Donut Step 3. Keep ordering additional cartons as long as the probability of selling at least one additional carton is greater than P, the indifference probability P at 6 cartons = 0.80 > 0.67 Marginal Analysis with the Normal Distribution Find four values 1. The average or mean sales for the product, µ 2. The standard deviation of sales, σ 3. The marginal profit for the product, MP 4. The marginal loss for the product, ML X * = optimal stocking level Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 78

14 Steps of Marginal Analysis with the Normal Distributions ML 1. Determine the value of for the ML + MP problem 2. Locate P on the normal distribution (Appendix A) and find the associated Z-value 3. Find X * using the relationship Z = X * µ σ to solve for the resulting stocking policy X * = µ + Zσ Newspaper Example Chicago Tribune µ = 60 papers a day, σ = 10 Marginal loss ML = 20 cents Marginal profit MP = 30 cents Step 1. Stock the Tribune as long as the probability of selling the last unit is at least ML/(ML + MP) ML ML + MP = 20 cents 20 cents + 30 cents = = 0.40 Let P = 0.40 Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Newspaper Example Step 2. Using the normal distribution in Figure 6.10 find the appropriate Z value Z = 0.25 standard deviations from the mean Area under the Curve is = 0.60 (Z = 0.25) Mean Daily Sales Newspaper Example Chicago Tribune µ = 60 papers a day, σ = 10 Step 3. or 0.25 = X * X * = (10) = 62.5, or 62 newspapers FIGURE 6.10 Area under the Curve is 0.40 µ = 60 X * X = Demand Joe should order 62 newspapers since the probability of selling 63 newspapers is slightly less than 0.40 Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Newspaper Example Area under the Curve is = 0.60 (Z = 0.25) Mean Daily Sales Newspaper Example The procedure is the same when P > 0.50 Chicago Sun-s ML = 40 cents, MP = 10 cents, µ = 100, σ = 10 FIGURE 6.10 µ = 60 X = Demand X * = 62.5 Area under the Curve is 0.40 Step 1. ML ML + MP = 40 cents 40 cents + 10 cents = = 0.80 Optimal Stocking Policy (62 Newspapers) Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 84

15 Newspaper Example Step 2. Using the normal distribution in Figure 6.11 find the appropriate Z value for 0.80 and multiply by 1 Z = 0.84 standard deviations from the mean Area under the Curve is 0.80 (Z = 0.84) Newspaper Example Chicago Sun-s µ = 100 papers a day, σ = 10 Step 3. or 0.84 = X * X * = (10) = 91.6, or 91 newspapers Figure 6.11 X * µ = 100 X = Demand Joe should order 91 copies of the Chicago Sun-s every day Optimal Stocking Policy (91 Newspapers) Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc ABC Analysis The purpose is to divide the inventory into three groups based on the overall inventory value of the items Group A items account for the major portion of inventory costs Typically 70% of the dollar value but only 10% of the quantity of items Forecasting and inventory management must be done carefully Mistakes can be expensive ABC Analysis Group B items are more moderately priced May represent 20% of the cost and 20% of the quantity Moderate levels of control Group C items are very low cost but high volume It is not cost effective to spend a lot of time managing these items Simple control policies and loose control Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc TABLE 6.8 INVENTORY GROUP ABC Analysis DOLLAR USAGE (%) INVENTORY ITEMS (%) ARE QUANTITATIVE CONTROL TECHNIQUES USED? A Yes B In some cases C No Dependent Demand: The Case for Material Requirements Planning models discussed so far have assumed item demand was independent In many situations items demand is dependent on demand for one or more other items In these situations material requirements planning (MRP) can be employed effectively Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 90

16 Dependent Demand: The Case for Material Requirements Planning Benefits of MRP 1. Increased customer service levels 2. Reduced inventory costs 3. Better inventory planning and scheduling 4. Higher total sales 5. Faster response to market changes and shifts 6. Reduced inventory levels without reduced customer service Material Structure Tree The first step is to develop a bill of materials (BOM) BOM identifies components, descriptions, and the number required for production of one unit of the final product Material structure tree developed from the BOM Demand for product A is 50 units Each A requires 2 units of B and 3 units of C Each B requires 2 units of D and 3 units of E Each C requires 1 unit of E and 2 units of F Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Material Structure Tree Material Structure Tree Level Material Structure Tree for Item A B(2) A C(3) D(2) E(3) E(1) F(2) The demand for B, C, D, E, and F is completely dependent on the demand for A The material structure tree has three levels Items above a level are called parents Items below any level are called components The number in parenthesis beside each item shows how many are required for each unit of the parent FIGURE 6.12 Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Material Structure Tree We can use the material structure tree and the demand for Item A to compute demands for the other items Part B: 2 number of A s = 2 50 = 100 Part C: 3 number of A s = 3 50 = 150 Part D: 2 number of B s = = 200 Part E: 3 number of B s + 1 number of C s = = 450 Part F: 2 number of C s = = 300 Gross and Net Material Requirements Plan A gross material requirements plan is constructed after the materials structure tree is complete schedule Shows when an item must be ordered Shows when there is no inventory on hand Shows when the production of an item must be started in order to satisfy the demand for the finished product at a particular date Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc. 6 96

17 Gross and Net Material Requirements Plan Lead times are required for each item Item A 1 week Item D 1 week Item B 2 weeks Item E 2 weeks Item C 1 week Item F 3 weeks Gross Material Requirements Plan FIGURE 6.13 Gross Material Requirements Plan for 50 Units of A Week Required Date 50 A Lead = 1 Week Order Release 50 Every part A requires 2 part B s in week 5 Required Date 100 B Lead = 2 Weeks Order Release 100 Required Date 150 C Lead = 1 Week Order Release 150 D E F Required Date 200 Order Release 200 Required Date Order Release Required Date 300 Order Release 300 Lead = 1 Week Lead = 2 Weeks Lead = 3 Weeks Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Gross and Net Material Requirements Plan A net material requirements plan can be constructed from the gross materials requirements plan and on-hand inventory information TABLE 6.9 ITEM ON-HAND INVENTORY A 10 B 15 C 20 D 10 E 10 F 5 Copyright 2015 Pearson Education, Inc Gross and Net Material Requirements Plan Using this data we can construct a plan that includes: Gross requirements On-hand inventory Net requirements Planned-order receipts Planned-order releases The net requirements plan is constructed like the gross requirements plan Copyright 2015 Pearson Education, Inc Net Material Requirements Plan Figure 6.14(a) Net Material Requirements Plan Figure 6.14(b) Week Item A Gross 50 1 On-Hand Net 40 Order Receipt 40 Order Release 40 B Gross 80 A 2 On-Hand Net 65 Order Receipt 65 Order Release 65 Lead Week Item C Gross 120 A 1 On-Hand Net 100 Order Receipt 100 Order Release 100 D Gross 130 B 1 On-Hand Net 120 Order Receipt 120 Order Release 120 Lead Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc

18 Net Material Requirements Plan Figure 6.14(c) Week Item E Gross 195 B 100 C 2 On-Hand Net Order Receipt Order Release F Gross 200 C 3 On-Hand 5 5 Net 195 Order Receipt 195 Order Release 195 Lead Two or More End Products Most manufacturing companies have more than one end item AA A second product AA has this material structure tree D(3) If we require 10 units of AA, the gross requirements for parts D and F are Part D: 3 x number of AA s = 3 x 10 = 30 Part F: 2 x number of AA s = 2 x 10 = 20 F(2) Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Two or More End Products The lead time for AA is one week The gross requirement for AA is 10 units in week 6 and there are no units on hand This new product can be added to the MRP process The addition of AA will only change the MRP schedules for the parts contained in AA MRP can also schedule spare parts and components These have to be included as gross requirements Net Material Requirements Plan Figure 6.15(a) Including AA Week Item AA Gross 10 1 On-Hand 0 0 Net 10 Order Receipt 10 Order Release 10 A Gross 50 1 On-Hand Net 40 Order Receipt 40 Order Release 40 Lead Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Net Material Requirements Plan Figure 6.15(b) Including AA Net Material Requirements Plan Figure 6.15(c) Including AA Week Item B Gross 80 A 2 On-Hand Net 65 Order Receipt 65 Order Release 65 C Gross 120 A 1 On-Hand Net 100 Order Receipt 100 Order Release 100 Lead Week Item D Gross 130 B 30 AA 1 On-Hand Net Order Receipt Order Release E Gross 195 B 100 C 2 On-Hand Net Order Receipt Order Release Lead Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc

19 Net Material Requirements Plan Figure 6.14(d) Including AA Week Item F Gross 200 C 20 AA 3 On-Hand Net Order Receipt Order Release Lead Just-in- Control Organizations have tried to have less inprocess inventory on hand to achieve greater efficiency in the production process This is known as JIT inventory The inventory arrives just in time to be used during the manufacturing process One technique of implementing JIT is a manual procedure called kanban Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Just-in- Control The Kanban System Kanban in Japanese means card Dual-card kanban system Conveyance, or C-kanban Production, or P-kanban Simple systems but require considerable discipline Little inventory to cover variability Schedule must be followed exactly FIGURE 6.16 Producer Area P-kanban and Container 4 Storage Area C-kanban and Container User Area Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Steps of Kanban P-kanban and Container C-kanban and Container 4 Steps of Kanban P-kanban and Container C-kanban and Container 1. Full containers along with their C-kanban card are taken from the storage area to a user area, Producer Area Storage Area typically on a manufacturing line (arrow 1). 2. During the manufacturing process, parts in the container are used up by the user. When the container is empty, the empty container along with the same C-kanban card is taken back to the storage area (arrow 2). Here the user picks up a new full container, detaches the P-kanban card from it, attaches his or her C-kanban card to it, and returns with it to the user area User Area 3. The detached P-kanban card is then attached to an empty Producer Area Storage Area container in the storage area and then and only then is the empty container taken back to the upstream producer area (arrow 3). 4. This empty container is then refilled with parts and taken with its P-kanban card back to the storage area (arrow 4). This kanban process continuously cycles throughout the day. Kanban is sometimes known as a pull production system User Area Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc

20 Some Kanban Rules Minimum of two containers are required No containers are filled without the appropriate P-kanban Each container must hold exactly the specified number of parts or items Only those parts that are needed are produced Enterprise Resource Planning MRP has evolved to include Labor hours Material cost Other resources related to production Refered to as MRP II and resource replaces the word requirements Sophisticated software was developed, systems became known as enterprise resource planning (ERP) systems Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Enterprise Resource Planning Objective of ERP System is to reduce costs by integrating all of the operations of a firm From supplier of materials needed through the organization to invoicing the customer Data entered only once Central database quickly and easily accessed by anyone in the organization Benefits include Reduced transaction costs Increased speed and accuracy of information Enterprise Resource Planning Drawbacks to ERP Software is expensive to buy and costly to customize The implementation of an ERP system may require a company to change its normal operations Employees are often resistant to change Training employees on the use of the new software can be expensive Copyright 2015 Pearson Education, Inc Copyright 2015 Pearson Education, Inc Remember Chapter 3: Where Prices Come From: The Interaction of Demand and Supply Read Quantitative Methods-module guide. Any questions please olivier.edu@gmail.com and make notes as you do so, in whatever way works best for you in terms of remembering information (your performance on this course is only assessed by exam). Copyright 2010 Pearson Education, Inc. Economics R. Glenn Hubbard, Anthony Patrick O Brien, 3e. 119 of 46