Inventory Management

Chapter 12 Independent Demand Inventory ManagementOperations ManagementbyR. Dan Reid & Nada R. Sanders2nd Edition Wiley 2005

PowerPoint Presentation by R.B. Clough - UNH

Inventories in the Supply Chain

Independent vs. Dependent DemandIndependent demand items are finished goods or other items sold to someone outside the companyDependent demand items are materials or component parts used in the production of another item (e.g., finished product)

Types of Inventory:How Inventory is UsedAnticipation or seasonal inventorySafety stock: buffer demand fluctuationsLot-size or cycle stock: take advantage of quantity discounts or purchasing efficienciesPipeline or transportation inventorySpeculative or hedge inventory protects against some future event, e.g. labor strikeMaintenance, repair, and operating (MRO) inventories

Objectives of Inventory ManagementProvide acceptable level of customer service (on-time delivery)Allow cost-efficient operationsMinimize inventory investment

Relevant Inventory Costs

Order Quantity Strategies

Examples of Ordering Approaches

Three Mathematical Models for Determining Order QuantityEconomic Order Quantity (EOQ or Q System)An optimizing method used for determining order quantity and reorder pointsPart of continuous review system which tracks on-hand inventory each time a withdrawal is madeEconomic Production Quantity (EPQ)A model that allows for incremental product deliveryQuantity Discount ModelModifies the EOQ process to consider cases where quantity discounts are available

Economic Order QuantityEOQ Assumptions:Demand is known & constant - no safety stock is requiredLead time is known & constantNo quantity discounts are availableOrdering (or setup) costs are constantAll demand is satisfied (no shortages)The order quantity arrives in a single shipment

EOQ: Total Cost Equation

EOQ Total CostsTotal annual costs = annual ordering costs + annual holding costs

The EOQ FormulaMinimize the TC by ordering the EOQ:

When to Order:The Reorder PointWithout safety stock:

With safety stock:

EOQ ExampleWeekly demand = 240 unitsNo. of weeks per year = 52Ordering cost = $50Unit cost = $15Annual carrying charge = 20%Lead time = 2 weeks

EOQ Example Solution

EPQ (Economic Production Quantity) AssumptionsSame as the EOQ except: inventory arrives in increments & is drawn down as it arrives

EPQ EquationsAdjusted total cost:

Maximum inventory:

Adjusted order quantity:

EPQ ExampleAnnual demand = 18,000 unitsProduction rate = 2500 units/monthSetup cost = $800Annual holding cost = $18 per unitLead time = 5 daysNo. of operating days per month = 20

EPQ Example Solution

EPQ Example Solution (cont.)The reorder point:

With safety stock of 200 units:

Quantity Discount Model AssumptionsSame as the EOQ, except:Unit price depends upon the quantity orderedAdjusted total cost equation:

Quantity Discount ProcedureCalculate the EOQ at the lowest priceDetermine whether the EOQ is feasible at that price Will the vendor sell that quantity at that price?If yes, stop if no, continueCheck the feasibility of EOQ at the next higher price

Continue to the next slide ...

QD Procedure (continued)Continue until you identify a feasible EOQCalculate the total costs (including total item cost) for the feasible EOQ modelCalculate the total costs of buying at the minimum quantity required for each of the cheaper unit pricesCompare the total cost of each option & choose the lowest cost alternativeAny other issues to consider?

QD ExampleAnnual Demand = 5000 unitsOrdering cost = $49Annual carrying charge = 20%Unit price schedule:

Sheet1

QuantityUnit Price

0 to 999$5.00

1000 to 1999$4.80

2000 and over$4.75

Sheet2

Sheet3

QD Example SolutionStep 1

QD Example Solution (Cont.)Step 2

What if Demand is Uncertain?

Safety Stock and Service LevelOrder-cycle service level is the probability that demand during lead time wont exceed on-hand inventory.Risk of a stockout = 1 (service level)More safety stock means greater service level and smaller risk of stockout

Safety Stock and Reorder PointWithout safety stock:

With safety stock:

Reorder Point DeterminationR = reorder pointd = average daily demandL = lead time in daysz = number of standard deviations associated with desired service levels = standard deviation of demand during lead time

Safety Stock ExampleDaily demand = 20 unitsLead time = 10 daysS.D. of lead time demand = 50 unitsService level = 90%Determine:Safety stockReorder point

Safety Stock SolutionStep 1 determine z

Step 2 determine safety stock

Step 3 determine reorder point

ABC Inventory ClassificationABC classification is a method for determining level of control and frequency of review of inventory itemsA Pareto analysis can be done to segment items into value categories depending on annual dollar volumeA Items typically 20% of the items accounting for 80% of the inventory value-use Q systemB Items typically an additional 30% of the items accounting for 15% of the inventory value-use Q or PC Items Typically the remaining 50% of the items accounting for only 5% of the inventory value-use P

ABC Example: the table below shows a solution to an ABC analysis. The information that is required to do the analysis is: Item #, Unit $ Value, and Annual Unit Usage. The analysis requires a calculation of Annual Usage $ and sorting that column from highest to lowest $ value, calculating the cumulative annual $ volume, and grouping into typical ABC classifications.

Sheet1

ItemAnnual Usage ($)Percentage of Total $Cumulative Percentage of Total $Item Classification

10616,50034.434.4A

11012,50026.160.5A

11545009.469.9B

10532006.776.6B

11122504.781.3B

10420004.285.5B

11412002.588C

10710002.190.1C

101960292.1C

1138751.893.9C

1037501.695.5C

1086001.396.8C

1126001.398.1C

102500199.1C

1095001100.1C

Sheet2

Sheet3

Inventory Record AccuracyInaccurate inventory records can cause:Lost salesDisrupted operationsPoor customer serviceLower productivityPlanning errors and expediting

Two methods are available for checking record accuracyPeriodic counting-physical inventoryCycle counting-daily counting of pre-specified items provides the following advantages:Timely detection and correction of inaccurate recordsElimination of lost production time due to unexpected stock outsStructured approach using employees trained in cycle counting

Chapter 12 HW AssignmentProblems 6, 7, 9 13, 16, 17, 22 24.