Cycle Inventory in a Supply Chain

Cycle Inventoryin a Supply Chain2Role of Inventory in the Supply ChainOverstocking: Amount available exceeds demandLiquidation, Obsolescence, HoldingUnderstocking: Demand exceeds amount availableLost margin Future salesConsistent understocking reduces the customer demand

Goal: Matching supply and demand2Notes:Role of Cycle Inventoryin a Supply ChainLot or batch size is the quantity that a stage of a supply chain either produces or purchases at a timeCycle inventory is the average inventory in a supply chain due to either production or purchases in lot sizes that are larger than those demanded by the customerQ: Quantity in a lot or batch sizeD: Demand per unit time4Batch or Lot sizeBatch = Lot = quantity of products bought / produced togetherBut not simultaneously, since most production can not be simultaneousQ: Lot size. D: Demand per time.Consider sales at a Jeans retailer with demand of 100 jeans per day and an order size of 1000 jeans.Q=1000. D=100/day.QInventoryTimeOrderOrderOrder0Cycle4Notes:Role of Cycle Inventoryin a Supply Chain

Average flow time resulting from cycle inventory

Role of Cycle Inventoryin a Supply ChainLower cycle inventory hasShorter average flow timeLower working capital requirementsLower inventory holding costsCycle inventory is held toTake advantage of economies of scaleReduce costs in the supply chainRole of Cycle Inventoryin a Supply ChainAverage price paid per unit purchased is a key cost in the lot-sizing decisionMaterial cost = CFixed ordering cost includes all costs that do not vary with the size of the order but are incurred each time an order is placedFixed ordering cost = SHolding cost is the cost of carrying one unit in inventory for a specified period of timeHolding cost = H = hCRole of Cycle Inventoryin a Supply ChainPrimary role of cycle inventory is to allow different stages to purchase product in lot sizes that minimize the sum of material, ordering, and holding costsIdeally, cycle inventory decisions should consider costs across the entire supply chainIn practice, each stage generally makes its own supply chain decisionsIncreases total cycle inventory and total costs in the supply chainEstimating Cycle Inventory Related Costs in PracticeInventory Holding CostObsolescence costHandling costOccupancy costMiscellaneous costsTheft, security, damage, tax, insuranceEstimating Cycle Inventory Related Costs in PracticeOrdering CostBuyer timeTransportation costsReceiving costsOther costs

Economies of Scaleto Exploit Fixed CostsLot sizing for a single product (EOQ)D=Annual demand of the productS=Fixed cost incurred per orderC=Cost per unitH=Holding cost per year as a fraction of product costBasic assumptionsDemand is steady at D units per unit timeNo shortages are allowedReplenishment lead time is fixedEconomies of Scaleto Exploit Fixed CostsMinimizeAnnual material costAnnual ordering costAnnual holding costLot Sizing for a Single Product

14Economic Order Quantity - EOQAnnualcarryingcostPurchasingcostTC =+Q2hC DQSTC = ++AnnualorderingcostCD +Total cost is simple function of the lot size Q. 15Cost Minimization GoalOrder Quantity (Q)The Total-Cost Curve is U-ShapedOrdering CostsQ Annual Cost(optimal order quantity)

Holding costsLot Sizing for a Single Product

The economic order quantity (EOQ)

The optimal ordering frequencyEOQ ExampleAnnual demand, D = 1,000 x 12 = 12,000 unitsOrder cost per lot, S = $4,000Unit cost per computer, C = $500Holding cost per year as a fraction of unit cost, h = 0.217Notes:EOQ Example

18Notes:EOQ Example

19Notes:EOQ Example

Lot size reduced to Q = 200 units20Notes:Lot Size and Ordering CostIf the lot size Q* = 200, how much should the ordering cost be reduced?Desired lot size, Q* = 200Annual demand, D = 1,000 12 = 12,000 unitsUnit cost per computer, C = $500Holding cost per year as a fraction of inventory value, h = 0.2

Aggregating Multiple Productsin a Single OrderSavings in transportation costsReduces fixed cost for each productLot size for each product can be reducedCycle inventory is reducedSingle delivery from multiple suppliers or single truck delivering to multiple retailersReceiving and loading costs reducedLot Sizing with MultipleProducts or CustomersOrdering, transportation, and receiving costs grow with the variety of products or pickup pointsObjective is to arrive at Lot sizes and ordering policy that minimize total costDi:Annual demand for product i S:Order cost incurred each time an order is placed, independent of the variety of products in the order si:Additional order cost incurred if product i is included in the orderLot Sizing with MultipleProducts or CustomersThree approaches to lot sizing decisions:Each product manager orders his or her model independently.The product managers jointly order every product in each lot.Product managers order jointly but not every order contains every product; that is, each lot contains a selected subset of the products.Multiple Products Ordered and Delivered IndependentlyDemand DL = 12,000/yr, DM = 1,200/yr, DH = 120/yrCommon order costS = $4,000Product-specific order costsL = $1,000, sM = $1,000, sH = $1,000Holding costh = 0.2Unit costCL = $500, CM = $500, CH = $50025Notes:Multiple Products Ordered and Delivered IndependentlyLiteproMedproHeavyproDemand per year12,0001,200120Fixed cost/order$5,000 $5,000$5,000Optimal order size1,095346110Cycle inventory54817355Annual holding cost$54,772$17,321$5,477Order frequency11.0/year3.5/year1.1/yearAnnual ordering cost$54,772$17,321$5,477Average flow time2.4 weeks7.5 weeks23.7 weeksAnnual cost$109,544$34,642$10,954 Total annual cost = $155,14026Notes:Lots Ordered and Delivered Jointly

Products Ordered and Delivered Jointly

Annual order cost = 9.75 x 7,000 = $68,250Annual ordering and holding cost= $61,512 + $6,151 + $615 + $68,250 = $136,528Products Ordered and Delivered JointlyLiteproMedproHeavyproDemand per year (D)12,0001,200120Order frequency (n)9.75/year9.75/year9.75/yearOptimal order size (D/n)1,23012312.3Cycle inventory61561.56.15Annual holding cost$61,512$6,151$615Average flow time2.67 weeks2.67 weeks2.67 weeksAggregation with Capacity ConstraintW.W. Grainger exampleDemand per product, Di = 10,000Holding cost, h = 0.2 Unit cost per product, Ci = $50 Common order cost, S = $500 Supplier-specific order cost, si = $10030Notes:Aggregation with Capacity Constraint

Annual holding cost per supplier31Notes:Aggregation with Capacity ConstraintTotal required capacity per truck = 4 x 671 = 2,684 unitsTruck capacity = 2,500 units Order quantity from each supplier = 2,500/4 = 625Order frequency increased to 10,000/625 = 16Annual order cost per supplier increases to $3,600Annual holding cost per supplier decreases to $3,125.32Notes:33Tailored Aggregation: Ordering Selected SubsetsExample: Orders may look like (L,M); (L,H); (L,M); (L,H).Most frequently ordered product: LM and H are ordered in every other delivery.We can associate fixed order cost S with product L because it is ordered every time there is an order.Products other than L, the rest are associated only with their incremental order costs (s values).

An Algorithm:Step 1: Identify most frequently ordered productStep 2: Identify frequency of other products as a relative multipleStep 3: Recalculate ordering frequency of most frequently ordered productStep 4: Identify ordering frequency of all products33Notes:Lots Ordered and Delivered Jointly for a Selected SubsetStep 1:Identify the most frequently ordered product assuming each product is ordered independently

The frequency of the most frequently ordered item will be modified later. This is an approximate computation.Lots Ordered and Delivered Jointly for a Selected SubsetStep 2:For all products i i*, evaluate the ordering frequency

i*= most frequently ordered products which is included each time an order is placed.Lots Ordered and Delivered Jointly for a Selected SubsetStep 3:For all i i*, evaluate the frequency of product i relative to the most frequently ordered product i* to be mi

Step 4:Recalculate the ordering frequency of the most frequently ordered product i* to be n

Ordered and Delivered Jointly Frequency Varies by OrderApplying Step 1

ThusOrdered and Delivered Jointly Frequency Varies by OrderApplying Step 2

Applying Step 3

Ordered and Delivered Jointly Frequency Varies by OrderLiteproMedproHeavyproDemand per year (D)12,0001,200120Order frequency (n)11.47/year5.74/year2.29/yearOptimal order size (D/n)1,04620952Cycle inventory523104.526Annual holding cost$52,307$10,461$2,615Average flow time2.27 weeks4.53 weeks11.35 weeksOrdered and Delivered Jointly Frequency Varies by OrderApplying Step 4

Applying Step 5

Annual order costTotal annual cost

$130,767Economies of Scale toExploit Quantity DiscountsLot size-based discount discounts based on quantity ordered in a single lotVolume based discount discount is based on total quantity purchased over a given periodTwo common lot size-based discount schemesAll-unit quantity discountsMarginal unit quantity discount or multi-block tariffsQuantity DiscountsTwo basic questionsWhat is the optimal purchasing decision for a buyer seeking to maximize profits? How does this decision affect the supply chain in terms of lot sizes, cycle inventories, and flow times?Under what conditions should a supplier offer quantity discounts? What are appropriate pricing schedules that a supplier seeking to maximize profits should offer?All-Unit Quantity DiscountsPricing schedule has specified quantity break points q0, q1, , qr, where q0 = 0If an order is placed that is at least as large as qi but smaller than qi+1, then each unit has an average unit cost of CiUnit cost generally decreases as the quantity increases, i.e., C0 > C1 > > Cr Objective is to decide on a lot size that will minimize the sum of material, order, and holding costsAll-Unit Quantity Discounts

All-Unit Quantity DiscountsStep 1:Evaluate the optimal lot size for each price Ci,0 i r as follows

All-Unit Quantity DiscountsStep 2:We next select the order quantity Q*i for each price Ci

1.2.3.Case 3 can be ignored as it is considered for Qi+1For Case 1 if then set Q*i = QiIf , then a discount is not possibleSet Q*i = qi to qualify for the discounted price of Ci

All-Unit Quantity DiscountsStep 3:Calculate the total annual cost of ordering Q*i units

All-Unit Quantity DiscountsStep 4:Select Q*i with the lowest total cost TCi

Cutoff priceAll-Unit Quantity Discount ExampleOrder QuantityUnit Price04,999$3.005,0009,999$2.9610,000 or more$2.92q0 = 0, q1 = 5,000, q2 = 10,000 C0 = $3.00, C1 = $2.96, C2 = $2.92D = 120,000/year, S = $100/lot, h = 0.2All-Unit Quantity Discount ExampleStep 1

Step 2Ignore i = 0 because Q0 = 6,324 > q1 = 5,000For i = 1, 2

All-Unit Quantity Discount ExampleStep 3

Lowest total cost is for i = 2Order bottles per lot at $2.92 per bottle

Marginal Unit Quantity DiscountsMulti-block tariffs the marginal cost of a unit that decreases at a breakpoint

Vi be the cost of ordering qi unitsFor each value of i, Define V0 =0 and Vi for 0 i r, as follows

Marginal Unit Quantity Discounts

Marginal Unit Quantity DiscountsMaterial cost of each order Q is Vi + (Q qi)Ci

Total annual costMarginal Unit Quantity DiscountsStep 1:Evaluate the optimal lot size for each price Ci

Marginal Unit Quantity DiscountsStep 2:Select the order quantity Qi* for each price Ci

1.2.3.Marginal Unit Quantity DiscountsStep 3:Calculate the total annual cost of ordering Qi*

Step 4:Select the order size Qi* with the lowest total cost TCiMarginal Unit Quantity Discount ExampleOriginal data now a marginal discount Order QuantityUnit Price04,999$3.005,0009,999$2.9610,000 or more$2.92q0 = 0, q1 = 5,000, q2 = 10,000 C0 = $3.00, C1 = $2.96, C2 = $2.92D = 120,000/year, S = $100/lot, h = 0.2Marginal Unit Quantity Discount Example

Step 1

Marginal Unit Quantity Discount ExampleStep 2

Step 3

Short-Term Discounting: Trade PromotionsTrade promotions are price discounts for a limited period of timeKey goalsInduce retailers to use price discounts, displays, or advertising to spur salesShift inventory from the manufacturer to the retailer and the customerDefend a brand against competitionShort-Term Discounting: Trade PromotionsImpact on the behavior of the retailer and supply chain performanceRetailer has two primary optionsPass through some or all of the promotion to customers to spur salesPass through very little of the promotion to customers but purchase in greater quantity during the promotion period to exploit the temporary reduction in price (forward buy)Forward Buying Inventory Profile

Forward BuyCosts to be considered material cost, holding cost, and order costThree assumptionsThe discount is offered once, with no future discountsThe retailer takes no action to influence customer demandAnalyze a period over which the demand is an integer multiple of Q*Forward BuyOptimal order quantity

Retailers are often aware of the timing of the next promotion

Impact of Trade Promotions on Lot SizesQ* = 6,324 bottles, C = $3 per bottled = $0.15, D = 120,000, h = 0.2Cycle inventory at DO= Q*/2 = 6,324/2 = 3,162 bottles Average flow time= Q*/2D = 6,324/(2D) = 0.3162 months

66Notes:Optimal order quantity =

Impact of Trade Promotions on Lot SizesCycle inventory at DO= Qd/2 = 38,236/2 = 19,118 bottlesAverage flow time= Qd/2D = 38,236/(20,000) = 1.9118 monthsWith trade promotionsForward buy = Qd Q* = 38,236 6,324 = 31,912 bottles67Notes:Optimal order quantity =

How Much of a Discount Should the Retailer Pass Through?Profits for the retailerProfR = (300,000 60,000p)p (300,000 60,000p)CROptimal pricep = (300,000 + 60,000CR)/120,000Demand with no promotionDR = 30,000 60,000p = 60,000Optimal price with discountp = (300,000 + 60,000 x 2.85)/120,000 = $3.925DR = 300,000 - 60,000p = 64,500Demand with promotionTrade PromotionsTrade promotions generally increase cycle inventory in a supply chain and hurt performanceCounter measuresEDLP (every day low pricing)Discount applies to items sold to customers (sell-through) not the quantity purchased by the retailer (sell-in)Scan based promotions69Notes:Managing MultiechelonCycle InventoryMulti-echelon supply chains have multiple stages with possibly many players at each stage Lack of coordination in lot sizing decisions across the supply chain results in high costs and more cycle inventory than requiredThe goal is to decrease total costs by coordinating orders across the supply chainManaging MultiechelonCycle Inventory

Integer Replenishment PolicyDivide all parties within a stage into groups such that all parties within a group order from the same supplier and have the same reorder intervalSet reorder intervals across stages such that the receipt of a replenishment order at any stage is synchronized with the shipment of a replenishment order to at least one of its customersFor customers with a longer reorder interval than the supplier, make the customers reorder interval an integer multiple of the suppliers interval and synchronize replenishment at the two stages to facilitate cross-dockingInteger Replenishment PolicyFor customers with a shorter reorder interval than the supplier, make the suppliers reorder interval an integer multiple of the customers interval and synchronize replenishment at the two stages to facilitate cross-dockingThe relative frequency of reordering depends on the setup cost, holding cost, and demand at different parties

These polices make the most sense for supply chains in which cycle inventories are large and demand is relatively predictableInteger Replenishment PolicyFigure 11-7

Integer Replenishment Policy