opma 5361 chapter 14

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  • Chapter 14Inventory Management

  • Independent vs. Dependent Demand ItemsIndependent demand inventory itemsdemand cannot be computed, it is random (uncertain)items such as finished goods or end items

    Dependent demand inventory itemsdemand is directly related to that of another itemitems like raw materials or subcomponents (related to end item)

    Big Question When and how much to order?every day |-----------------------------------------------------| once a year

  • 2 Basic Approaches to Ordering InventoryFixed order quantityalways order same quantityorder whenever inventory level gets low (order point)

    Fixed order periodalways order every n daysorder a different quantity each time

    Economic Order Quantity (EOQ) model is most common fixed order quantity approach

  • Inventory CostsOrdering Costsclerical costs, postage, material handling costs, etc.setup or changeover cost

    # orders/year = D/Q

    Annual ordering cost = S(D/Q)

    where D = annual units demanded (forecast)Q = quantity of one orderS = average cost of processing one order

  • Carrying Costs-- costs incurred to keep items in storage

    average inventory level = Q/2(for basic EOQ model)

    Annual carrying cost = C(Q/2)

    where C = carrying cost rate ($ per unit per year)

  • Acquisition Costscost to purchase or produce the items

    Annual acquisition cost = D(ac)

    whereac = cost to purchase or produce one unit of the item

    Stockout Costsestimated per unit cost of a stockout (running out of items)extra paperwork, lost sales, late fees, lost goodwill, etc.

  • Cost of CapitalInterest paid to bank to borrow money to finance inventoryExample:8% annual interest rate60,000 units annual demand$20 per unitcostorder size = 5000 unitsaverage inventory on hand = 2500 unitsHow much interest should they expect to pay next year?

  • xxEOQAnnual Ordering CostsAnnual Carrying CostsTotal Annual Stocking CostsMinimumTotal AnnualStocking Costs

  • Time Graph of Inventory

  • Time Graph of Inventory

  • EOQ AssumptionsDemand, ordering cost rate, carrying cost rate, unit cost, and lead time are known constantsAn order arrives all at onceNo stockouts occurNo safety stock is carried

    Total annual inventory cost = ordering + carrying + acquisition costs

    TC = S(D/Q) + C(Q/2) + D(ac)

    We want to find the order quantity that results in the minimum total annual inventory cost.

  • At the minimum total cost, the slope of the total cost curve is zero, so the derivative of TC with respect to Q is zero.TC = S(D/Q) + C(Q/2) + D(ac)

    Solve for Q to get:

  • Basic EOQ ExampleAnnual demand = 6000 unitsOrdering cost rate = $100 per orderAcquisition cost = $24 per unitCarrying cost rate = 25% of unit value per year250 work days per year

    What quantity should be ordered to minimize total annual inventory cost?

    EOQ =

  • What is the total annual inventory cost with this order quantity?TC = S(D/Q) + C(Q/2) + D(ac)TC =TC =

    On average, how many orders per year should be expected?

    On average, how many work days should one order last?

    What is the expected minimum, maximum, and average inventory level?

  • EOQ with Quantity Discounts

    Step 1: Calculate EOQ for each priceStep 2: For feasible EOQs, calculate total annual costStep 3: Calculate total annual cost at the lowest allowable quantity for each lower priceStep 4: Pick quantity with lowest total annual cost

    Graph of EOQs and price break quantities

  • Example: An office supplies wholesaler sells copier paper by the ream. Ordering cost is $20/order. Carrying cost rate is 30% of the dollar value per year. Annual demand is 1000 reams.#Reams Cost/Ream 1-493.90 50-1993.75200-4993.65500+3.60

    EOQ3.90 =EOQ3.75 =EOQ3.65 =EOQ3.60 =

  • Calculate TC for:189 reams @ $3.75200 reams @ $3.65500 reams @ $3.60TC = SD/Q + CQ/2 + D(ac)

    TC3.75 =

    TC3.65 =

    TC3.60 =

  • Order PointPerpetual inventory accounting inventory records are updated anytime inventory levels change (typically used with fixed order quantity inventory systems)Order point the inventory level that triggers an orderLead time lead time is the amount of time between when a replenishment order is placed until it is receivedStockout inventory level drops to zeroFor most fixed order quantity systems, stockouts can only occur during the lead timeIf demand is constant, set the order point equal to the expected demand during the lead timeOP = EDDLT

  • Stockouts and Safety Stock2 main reasons for a stockout:-- demand during lead time is greater than expected-- lead time is longer than expected

    Safety stock is extra inventory held during the lead time (beyond EDDLT amount) and is the most common approach to reducing stockouts

    OP = EDDLT + SS

    What are the disadvantages of:-- too little safety stock?-- too much safety stock?

  • Setting Order PointsProblem: What inv. level should order point be set at?2 common approaches-- set OP to achieve a desired customer service level-- set OP to minimize costs of to much or too little inv.

    There are many ways to measure customer service.We will define customer service level as:-- the % of DDLT filled with stock on hand

    (What is safety lead time?)

  • Order Point ExampleAnnual demand = 8000 unitsLead time = 4 working days260 working days per yearSafety stock = 200 unitsWhat inv. level should the order point be at?

  • Two-Bin System (for inventory control)

  • 4 Examples of Setting the OPAchieve a desired service level Example#discrete demand (small numbers) 1 & 2continuous demand (normal distr.) 3

    Minimize stockout and carrying costspayoff table 4

  • 1. Sues Jewelry orders 20 mens Rolex watches (style #41B) each time the inventory level of this item gets low. There is a two week lead time once the order is placed with the supplier. Sues records show that for the past 20 times an order has been placed, the demand during the 2-week lead time has always been 3, 4, 5, 6, or 7 watches. The number of occurrences of these demands has been 4, 7, 6, 2, or 1, respectively (a total of 20 DDLT observations). Since the carrying cost for Rolex watches is quite high, Sue wants to determine what order point to use so that there are enough watches on hand during the lead time to sell to 80% of the customers who request one.

  • Sues Jewelry DDLT Frequency Prob.Service Level3 4 4 75 66 27 1 20

    Find OP for an 80% service level

  • 2. So that it can get a volume discount, Kendall Ford orders 20 F-150 extended cab pickup trucks each time it places an order from the manufacturer. The lead time to receive the trucks is 22 days. The frequency of different demands during the lead time has been 3, 4, 7, 8, 9, 12, and 5 occurrences for demands of 9, 10, 11, 12, 13, 14, and 15 trucks, respectively. Due to the cost of having extra trucks on hand, management has decided it is not cost effective to try to avoid all stockouts during the lead time. They would like to set the order point for the F-150 so that it is out of stock for no more than 30% of the customers who would buy this truck. Kendall Ford should place a new order when how many trucks are left on the lot? How many trucks should they expect to sell during the new lead time?

  • Kendall Ford TrucksDDLT Occurrences Prob.Service Level9 3 10 4 11 7 12 8 13 9 14 12 15 5 48

  • 3. A distributor of aircraft jet fuel orders 180,000 gallons each time its supply gets low. The lead time is 3 days. The average daily demand for jet fuel is 18,500 gallons. Past records show that the standard deviation of demand during the lead time is 12,500 gallons. Because of stiff competition from another distributor, it is desired to have enough fuel on hand so that a stockout occurs no more than 5% of the times that customers place orders during the lead time. What should the level of safety stock be? How many gallons should be on hand when an order is placed?

  • Payoff Table:Long cost the cost of one unit left over on hand when an order arrivesShort cost the cost of being one unit short during the lead time (stockout cost)

    4. Each year the Payless Drug Store on Coburg road places orders for cases of natural Christmas wreaths and pays $20 for a case of ten wreaths. The sales price is $5 per wreath. Records for the past 20 orders show that demand during the lead time has been 6 cases on 2 occasions, 7 cases on 6 occasions, 8 cases on 10 occasions, and 9 cases on 2 occasions. Any wreath left on hand when a new order arrives will be all dried out and must be thrown away. What is the long cost and short cost? What should the order point be? What service level would this order point provide?

  • Payoff TableLong cost = Short cost =

    DDLT Freq. Prob.6 27 68 109 2 20

    Next, fill in payoff table and compute expected costs (EC)

  • OPactual DDLT(Long cost or shortcost in table)

  • Reducing Lot SizesCutting setup costs is key to reducing production lot sizes.Setup reduction examples

    Summary of Benefits of Reduced Lot Sizesshorter lead timesless inventory investmentdefectives are caught quicker less scrap, rework, & future errorsneed less floor space employees closer together better communicationprocesses more closely linked encourages joint problem solvingsimplified inventory managementlower material handling costsavoid lumpy workloads

  • Processing Schedule

  • Processing Schedule