Foreign Trade University

ContentDefinition and purpose of inventoryInventory costsInventory systemsEconomic order quantity (EOQ) modelsA-B-C approachInventory control

Learning ObjectivesDefine the term inventory and list the major reasons for holding inventories; and list the main requirements for effective inventory management. Discuss periodic and perpetual review systems. Discuss the objectives of inventory management. Describe the A-B-C approach and explain how it is useful.

Learning ObjectivesDescribe the basic EOQ model and its assumptions and solve typical problems. Describe the EPQ model and solve typical problems. Describe the quantity discount model and solve typical problems. Describe reorder point models and solve typical problems. Describe situations in which the single-period model would be appropriate, and solve typical problems.

Examples:Parts in a factoryPaper towels in your cupboardCustomers on holdPaperwork in secretarys in-boxNot limited to physical products

Inventory is DELAY in business process.What is inventory?

What is inventory?TransformationInputOutputRaw materialsMaterials receivedCustomers waiting in a bankPaperwork in in-boxWork-in-ProcessSemi-finished productsCustomers at the counterPaperwork on deskFinished goodsProducts waiting to be shippedCustomers leaving the bankPaperwork in out-boxWithin organization:Between organizations: Goods-in-transit

Inventory: a stock or store of goodsInventory

DefinitionInventory is the stock of any item or resource used in an organization.

An inventory system is the set of policies and controls that monitor levels of inventory and determine what levels should be maintained, when stock should be replenished, and how large order should be.

Inventory: Manufacturing vs. ServiceManufacturing inventory: raw materials, finished products, component parts, supplies, and work-in- progress.

Inventory in service: tangible goods to be sold and the supplies necessary to administer the service.

Purposes of InventoryTo maintain independence of operationsTo meet variation in product demandTo allow flexibility in production schedulingTo provide a safeguard for variation in raw material delivery timeTo take advantage of economic purchase order size

Objective of Inventory ControlTo achieve satisfactory levels of customer service while keeping inventory costs within reasonable boundsLevel of customer serviceCosts of ordering and carrying inventoryInventory turnover is the ratio of annual cost of goods sold to average inventory investment.

A system to keep track of inventoryA reliable forecast of demandKnowledge of lead timesReasonable estimates ofHolding costsOrdering costsShortage costsA classification systemEffective Inventory Management

Lead time: time interval between ordering and receiving the orderHolding (carrying) costs: cost to carry an item in inventory for a length of time, usually a yearOrdering (set-up) costs: costs of ordering and receiving inventoryShortage costs: costs when demand exceeds supplyReorder point (ROP): when the quantity on hand of an item drops to this amount, the item is reordered.Safety stock (Ss): level that reduces risk of stock-out during lead time or random variation. Lead time service level (LTSL): probability that demand will not exceed supply during lead time.Key Inventory Terms

Inventory CostsHolding (carrying) costsOrdering (set-up)costsShortage costs

Inventory CostsHolding (carrying) costs Relate to physically having items in storage, including:- Costs for storage facilities: rent, rate, utility costs, equipments- Costs of handling, breakage, obsolescence, spoilage;- Costs of insurance, taxes;- Opportunity cost of capital: associates with having funds which could be used elsewhere tied up in inventoryTo reduce holding costs, keep low inventory levels (order small quantity in each time and increase order times)

Inventory CostsOrdering costsThe costs of ordering and receiving inventory:- Costs for determining how much is needed,- Costs for preparing invoices, goods inspection,- Costs for shipping, moving goods to temporary storage.

To reduce ordering costs, reduce the number of order times and increase the quantity in each order.

Inventory CostsHolding costs vs. Ordering costs

How to achieve optimal inventory costs?

Inventory Costs = holding costs + ordering costs min

Inventory CostsShortage costsWhen demand exceeds the supply of inventory on hand

Opportunity cost of not making a sale, loss of customer goodwill;Cost of lost production, downtime.

Difficult to measure, subjectively estimated

Inventory SystemsProvides the organizational structure and the operating policies for maintaining and controlling goods to be stocked.Two main questions:When to order? (Inventory Counting Systems: Fixed-time period model (P-model) and Fixed-order quantity model (Q-model)

How much to order? (EOQ, EPQ, and Quantity Discount Models)

Fixed-time Period Model (P-model)Periodic system, in which inventory is counted only at particular times (every week, every month)Order quantity varies each time order is placedOrder when the review period arrivesRecordkeeping is counted at review periodSize of inventory is larger than fixed-order quantity model (Q-model).

Fixed-time Period Model (P-model) Q

Q1Q2 Q3 Place order

SafetyStockt

t 1t2t3t1 = t2= t3; Q1 Q2 Q3

Fixed- order Quantity Model (Q-model)Perpetual system, which requires that every time a withdrawal from inventory or an addition to inventory is made, records must be updated to reflect whether the reorder point (Q0) has been reached.Order quantity is constant at each time order.Order when inventory position drops to reorder level.Recordkeeping when a withdrawal or addition is made.Size of inventory is less than P-model.

Fixed-order Quantity Model (Q-model) Q

Q1Q2 Q3 Place order Q0Safetystock tt 1t2t3Q1 = Q2= Q3; t1 t2 t3

Reorder point

Requirements for Effective Inventory ManagementKeep track of the inventory on hand and on order;Forecast demand precisely and reliably;Understand and control lead times;Estimates the inventory costs in reasonable manner;Use bar code for tracking inventory

Economic Order Quantity (EOQ) ModelsIdentify the optimal order quantity by minimizing the sum of certain annual costs that vary with order size

The basic economic order quantity modelThe economic production quantity modelThe quantity discount model

Basic Economic Order Quantity (EOQ) ModelDetermine the optimal order sizePurpose: minimize the sum of annual costs of holding and ordering inventory.AssumptionOnly 1 product is involved.Annual demand requirements are known.Demand rate is reasonably constant.Lead time does not vary.Each order is received in a single delivery.There are no quantity discounts.

Basic Economic Order Quantity (EOQ) ModelD: Demand given in time t (per year)Q: Order quantity H: Holding cost per unitS: Ordering cost per orderTSC (total annual stocking costs): include holding costs and ordering costs

Annual ordering costs = D/Q * SNumber of orders (D/Q) * Ordering cost per order (S)

Annual holding costs = Q/2 * HAn average amount of inventory (Q/2) * Holding cost per unit (H)

Total annual stocking costs:

Determine Q to minimize total annual stocking costsd(TSC)/d(Q) = H/2 + (- DS/Q2) = 0

n: number of orders in given time tn = D/QOptimal number of orders:

Optimal inventory costs:

ExampleA company sells one product to the market. The annual demand of this product is10000 tons. Holding cost per unit is 4USD/year. Ordering cost per order is 55USD. Determine the optimal order quantity and the number of orders per year.

Advantages of basic EOQ model

+ Simple, easy to calculate.

+ Can be applied for different products and inventory costs which are suitable for different types of businesses.

+ Can avoid errors from a given data set when determine EOQ.

Economic Production Quantity (EPQ) ModelA company makes and uses its products itself.Batch production used whereas the capacity to produce a part exceeds the demand rate.Assumptions:- Only one item is involved.- Annual demand is known.- The usage rate is constant.- Usage occurs continually, production occurs periodically.-The production rate is constant.- Lead time does not vary- No quantity discounts

Economic Production Quantity (EPQ) ModelS: Setup costs are used (no ordering cost)p = production rateu = usage rate=>To meet demand: u< p

Total annual stocking costs = holding cost + setup cost

Economic Production Quantity (EPQ) Model- The economic run quantity (EPQ):

Cycle time = Q/uRun time = Q/pMaximum inventory level = Q/p.(p-u) = Q.(1-u/p)Average inventory level = Q/2.(1-u/p)

Economic Production Quantity (EPQ) ModelExample: Annual demand of a product is 14400 tons. The holding cost per unit is 4USD/ year. The setup cost per run is 55 USD. The production rate of this product is 120 tons/day. The usage rate is 40 tons. Determine the EPQ

Quantity Discount ModelPrice reductions for large orders, which induce customers to buy in large quantitiesConsider:- Potential benefits of reduced purchase price and fewer orders in large quantities.- Increase in carrying costs of higher average inventories.

Quantity Discount Model

P: purchase price per unitTMC (total annual material cost):

TMC =TSC +D.P TMC = (Q/2)H + (D/Q)S + D.P

Quantity Discount ModelExample: A shop imports and resells one product to the market. Annual demand of this product is D =10000 tons. Holding cost is 0.2P (P is purchase cost per unit) USD/year. Ordering cost per order is 5.5USD. The shop is offered a price policy as follow:Quantity (tons) Price (USD/ton) 1-399 2.2 400-699 2 >700 1.8Finding the optimal solution for this shop?

A-B-C ApproachClassify inventory based on some measure of importance, then locate control efforts accordingly

Class A: very important (15-20% of number of items, 70-80% of total inventory value)Class B: moderately important (30% of number of items, 15-25% of total inventory value)Class C: least important (50-55% number of items, only 5% of total inventory value)

A-B-C ApproachA items: close attentions with regular reviews of amount on hand and withdrawals => ensure customer service levels are attained.B items: managed by applying EOQ modelC items: loose control, periodical review

ExampleThere are 10 different materials A, B, C, D, E, F, G, H, I, J stocked in a company. The annual demand of each material and their prices are as below. Classify the inventory items as A, B, C based on annual dollar value.

MaterialABCDEFGHIJDemand10005001550350100060020001001200250Price (USD)901541742.8612.514.170.68.50.420.6

Inventory ControlObjectives: to manage and achieve cost effectivenessDetermine * Reorder point (ROP) * Safety stock (Ss)* Lead time service level (LTSL) * Lead time (LT)

Inventory Control- X: expected demand during lead time- X : average value of X- z: number of standard deviations- : standard deviation of lead time demand

ROP = Expected demand during LT + Safety stockSafety Stock = z.

Exercises

1. D = 500000 units/year, H = 40% of product value; S = 59.5 USD and P = 5.5 USD/unit.

a. Determine EOQ, TSC

b. If we increase Q by 6000 units per order to fit the container, how much does TSC increase?

2. A company stocks one type of product and its price is 800 USD/unit. Its annual demand is 2400 units. The ordering cost is 1200 USD per order. The holding cost per unit annually is 50% of the product value. The supplier of the company offered them a price reduction of 5% if the quantity per each order is equal to and more than 250 units. Find out the optimal solution for the company.

3. Every year a company imports 2 types of products with following quantities and prices:Product A: 2400 units at 800 USD/unitProduct B: 600 units 360 USD/unitThe holding cost per unit annually is equal to 50% value of the product. The ordering cost for both products is 2000 USD/order.Determine the optimal number of order and EOQ.

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