Inventory Management

Amazon.comAmazon.com started as a virtual retailer no inventory, no warehouses, no overhead; just computers taking orders to be filled by othersGrowth has forced Amazon.com to become a world leader in warehousing and inventory management

InventoryOne of the most expensive assets of many companies representing as much as 50% of total invested capitalOperations managers must balance inventory investment and customer service

What Is Inventory?Stock of items kept to meet future demandWorking CapitalDef. - A physical resource that a firm holds in stock with the intent of selling it or transforming it into a more valuable state.

Inventory by Nature of MaterialRaw MaterialsWorks-in-Process Finished GoodsMaintenance, Repair and Operating (MRO)

Inventory (Uses of Material)Transaction InventorySpeculative InventoryPrecautionary Inventory

Functional Classification Of InventoryBased on utility, all inventory can be in one or more of the following categoriesWorking stockSafety stockAnticipation stockPipeline stockDecoupling stockPsychic stock

Inventory CostsCarrying costcost of holding an item in inventoryOrdering /Procurement costcost of replenishing inventoryShortage costtemporary or permanent loss of sales when demand cannot be met

Procurement CostsOrder processingShippingHandling

Carrying CostsWorking Capital (opportunity) costsInventory risk costs( spoilage, breakage, detoriation,obsolescence)Space costsInventory service costsInsurance & Taxes

Out-of-Stock CostsLost sales costBack-order cost

Inventory ManagementIf company holds too little Inventorytoo frequent orderingloss of quantity discounthigher transportation chargeslikely shortage in futureIf company holds too much Inventorycarrying/holding chargesstorageobsolescence, depreciationInvolvement of working capital

Objectives of Inventory Managment1) Maximize the level of customer service by avoiding under stocking.(How much to order?)2) Promote efficiency in production and purchasing by minimizing the cost of providing an adequate level of customer service.(When to order?)

Design of Inventory Mgmt. Systems: Micro IssuesOrder QuantityEconomic Order QuantityOrder TimingReorder Point

Inventory SystemsSingle-Period Inventory ModelOne time purchasing decision (Example: vendor selling t-shirts at a football game)Seeks to balance the costs of inventory overstock and under stock

Multi-Period Inventory ModelsFixed-Order Quantity ModelsEvent triggered (Example: running out of stock)

Fixed Order Quantity SystemsBehavior of Economic Order Quantity (EOQ) SystemsDetermining Order QuantitiesDetermining Order Points

Behavior of EOQ SystemsAs demand for the inventoried item occurs, the inventory level dropsWhen the inventory level drops to a critical point, the order point, the ordering process is triggered The amount ordered each time an order is placed is fixed or constantWhen the ordered quantity is received, the inventory level increases. . . more

Basic Fixed-Order Quantity Model and Reorder Point Behavior

Inventory Order Cycle

Determining Order QuantitiesBasic EOQEOQ for Production LotsEOQ with Quantity Discounts

Assumptions of Basic EOQ ModelDemand is known with certainty and is constant over timeNo shortages are allowedLead time for the receipt of orders is constantOrder quantity is received all at onceQuantity Discount does not existAverage Invenory is half of total inventory

EOQ Cost Model

EOQ Cost Model

Cost Minimization GoalOrdering CostsHoldingCostsOrder Quantity (Q)COSTBy adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs

Example: Electronic Village stocks and sells a particular brand of personal computer. It costs the store Rs450 each time it places an order with the manufacturer for the personal computers. The annual cost of carrying the PCs in inventory is Rs170. The store manager estimates that annual demand for the PCs will be 1200 units. Determine the optimal order quantity and the total minimum inventory cost.

Example: Basic EOQZartex Co. produces fertilizer to sell to wholesalers. One raw material calcium nitrate is purchased from a nearby supplier at $22.50 per ton. Zartex estimates it will need 5,750,000 tons of calcium nitrate next year.The annual carrying cost for this material is 40% of the acquisition cost, and the ordering cost is $595. a) What is the most economical order quantity?b) How many orders will be placed per year?c) How much time will elapse between orders?

Example 10.2 Electronic Village stocks and sells a particular brand of personal computer. It costs the store Rs450 each time it places an order with the manufacturer for the personal computers. The annual cost of carrying the PCs in inventory is Rs170. The store

manager estimates that annual demand for the PCs will be 1200 units. Determine the optimal order quantity and the total minimum inventory cost.

Reorder PointQuantity to which inventory is allowed to drop before replenishment order is made

Need to order EOQ at the Reorder Point:

ROP = D X LTD = Demand rate per periodLT = lead time in periods

ExampleThe I-75 Discount Carpet Store is open 311 days per year. If annual demand is 10,000 yards of Super Shag Carpet and the lead time to receive an order is 10 days, determine the reorder point for carpet.

ExampleItem X is a standard item stocked in a companys inventory of component parts. Each year the firm, on a random basis, uses about 2000 of item X, which costs Rs25 each. Storage costs, which include insurance and cost of capital, amount to Rs5 per unit of average inventory. Every time an order is placed for more item X, it costs Rs10. (a) Whenever item X is ordered, what should the order size be? (b) What is the annual cost for ordering item X? (c) What is the annual cost for storing item X?

Production Quantity Model(EOQ for lot)An inventory system in which an order is received gradually, as inventory is simultaneously being depletedNon-instantaneous receipt modelassumption that Q is received all at once is relaxedp - daily rate at which an order is received over time, production rated - daily rate at which inventory is demanded

Assumptions of Production Quantity ModelDemand is known with certainty and is constant over timeNo safety stockNo shortages are allowedLead time for the receipt of orders is constantGoods are supplied (p)at and consumed (d)at uniform rate,Supply rate is greater than usage rate.Quantity Discount does not exist

Production Quantity Model (cont.)Annual carrying cost= 1 -Q2dpCc

Production Quantity Model (cont.)CoDQ

Production Quantity Model (cont.)(p-d)

Production Quantity Model: ExampleCc = $0.75 per yardCo = $150D = 10,000 yardsd = 10,000/311 = 32.2 yards per dayp = 150 yards per day

Production Quantity Model: Example (cont.)

Example I-75 Outlet Store has its own manufacturing facility in which it produces Super Shag carpet. The ordering cost is the cost of setting up the production process to make Super Shag carpet. Estimated annual demand is 10,000 meters of carpet, and annual carrying cost is Rs0.75 per meter. The manufacturing facility operates the same days the store is open (i.e., 311 days) and produces 150 meters of the carpet per day. Determine the optimal order size, total inventory cost, the length of time to receive an order, the number of orders per year, and the maximum inventory level.

Example: EOQ for Production LotsHighland Electric Co. buys coal from Cedar Creek Coal Co. to generate electricity. CCCC can supply coal at the rate of 3,500 tons per day for $10.50 per ton. HEC uses the coal at a rate of 800 tons per day and operates 365 days per year.HECs annual carrying cost for coal is 20% of the acquisition cost, and the ordering cost is $5,000.a) What is the economical production lot size?b) What is HECs maximum inventory level for coal?

Quantity DiscountsPrice per unit decreases as order quantity increasesPO= if Q

Quantity DiscountsPrice per unit decreases as order quantity increasesPO= if Q

Quantity Discount Model (cont.)

Price-Break Example Problem Data (Part 1)A company has a chance to reduce their inventory ordering costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an e-mail ordering cost of Rs4, a carrying cost rate of 2% of the inventory cost of the item, and an annual demand of 10,000 units?Order Quantity(units)Price/unit(Rs)0 to 2,499 Rs1.202,500 to 3,999 1.004,000 or more .98

Price-Break Example Solution (Part 2)Annual Demand (D)= 10,000 unitsCost to place an order (S)= Rs4First, plug data into formula for each price-break value of CCarrying cost % of total cost (i)= 2%Cost per unit (C) = $1.20, $1.00, $0.98Interval from 0 to 2499, the Qopt value is feasibleInterval from 2500-3999, the Qopt value is not feasible Interval from 4000 & more, the Qopt value is not feasible Next, determine if the computed Qopt values are feasible or not

Price-Break Example Solution (Part 4)Next, we plug the true Qopt values into the total cost annual cost function to determine the total cost under each price-breakTC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = Rs12,043.82TC(2500-3999)= Rs10,041TC(4000&more)= Rs9,949.20Finally, we select the least costly Qopt, which is this problem occurs in the 4000 & more interval. In summary, our optimal order quantity is 4000 units

Quantity Discount: ExampleA hardware store procures and sells hardware items.Information on a item s give here:Expected annual sales=8,000 unitsOrdering cost=Rs.180 per orderHolding cost=10% of the average inventory value.Items can be purchased to the following schedule:LOT SIZEUNIT PRICE(In Rs.)1-999Rs 22.001,000-1,499Rs.20.001,500-1999Rs.19.002,000 and aboveRs. 18.50We are require to determine the best order size.

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