Managing Economies of Scale in the Supply Chain: Cycle Inventory

Learning ObjectivesUnderstand the role of cycle inventory in a supply chainDefine the effects of quantity discounts on lot size and cycle inventoryIdentify the appropriate discounting schemes for the supply chain, taking into account cycle inventoryUnderstand the effects of trade promotions on lot size and cycle inventory

Role of Inventory in the Supply Chain

Safety Inventory

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Cycle Inventory

Seasonal Variability

Supply / Demand Variability

Economies of Scale

Reduce Buffer Inventory

Reduce Waiting Time

Reduce Material Flow Time

Improved Forecasting

Improve Matching of Supply and Demand

Seasonal Inventory

Role of Cycle Inventoryin a Supply ChainLot, or batch size: quantity that a supply chain stage either produces or orders at a given timeCycle inventory: average inventory that builds up in the supply chain because a supply chain stage either produces or purchases in lots that are larger than those demanded by the customerQ = lot or batch size of an orderD = demand per unit timeInventory profile: plot of the inventory level over time Cycle inventory = Q/2 (depends directly on lot size)Average flow time = Avg inventory / Avg flow rateAverage flow time from cycle inventory = Q/(2D)

Role of Cycle Inventoryin a Supply Chain: Example Jean-MartThe demand for jeans at Jean-Mart, a department store, is relatively stable at D= 100 pairs of jeans per day. The store manager at Jean-Mart currently purchases in lots of Q = 1000 pairs. Calculate the cycle inventory and average flow time for jeans.

Cycle inventory = lot size/2 = Q/2 = 1000/2 = 500 Avg flow time = avg inventory / avg flow rate = cycle inventory / demand = Q/2D = 1000/(2)(100) = 5 days

Cycle inventory adds 5 days to the time a unit spends in the supply chainLower cycle inventory is better because:Average flow time is lowerWorking capital requirements are lowerLower inventory holding costs

Role of Cycle Inventoryin a Supply Chain [2]Cycle inventory is held primarily to take advantage of economies of scale in the supply chainSupply chain costs influenced by lot size:Material cost = C ($C/unit)Fixed ordering cost = S ($S/lot)Holding cost = H = hC (h = cost of holding $1 in inventory for one year or denoted by $H/unit/year)Primary 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 chain, but in practice, each stage generally makes its own supply chain decisions increases total cycle inventory and total costs in the supply chain

Estimating Cycle Inventory Related Costs in PracticeInventory Holding CostCost of capital: holding cost for products that do not become obsolete quicklyObsolescence or spoilage cost: estimate the rate at which the value of the stored product drops because of its market value or quality falls (e.g. perishable products)Handling costs: include only incremental receiving and storage costs that vary with the quantity of product receivedOccupancy costs: reflect the incremental change in space cost due to changing cycle inventory Miscellaneous costs: theft, security, damage, tax, insuranceOrdering CostBuyer time: incremental time of the buyer placing the extra orderTransportation costs: a fixed transportation cost if often incurred regardless of the size of the orderReceiving costs: e.g. administration work cost such as purchase order matching and any effort associated with updating inventory records

Economies of Scaleto Exploit Fixed Costs [2]Annual demand = DNumber of orders per year = D/QAnnual material cost = CDAnnual order cost = (D/Q)SAnnual holding cost = (Q/2)H = (Q/2)hCTotal annual cost = TC = CD + (D/Q)S + (Q/2)hC

Fixed Costs: Optimal Lot Sizeand Reorder Interval (EOQ) D:Annual demand S:Setup or Order CostC:Cost per unith:Holding cost per year as a fraction of product costH:Holding cost per unit per yearQ:Lot SizeQ*: Optimal Lot Size (Economic Order Quantity or EOQ)n*: Optimal order frequencyMaterial cost is constant and therefore is not considered in this model

Example Economic Order QuantityMr. Fu is the manager at Allied Electrics. He is planning to manage the stores inventory costs more efficiently. In a pilot study, he asked the planning team to apply the EOQ model to a particular model of Samsung television. Annual demand for that product is 12000 units, with a monthly demand of 1000. Administrative, transportation and receiving form the fixed cost of $4000 each time an order is placed. Each television costs the wholesaler $500 to buy and 20 percent of the value of the item to hold each year. What would be the EOQ in this case?

Solution:Demand, D = 1000 x 12 = 12,000 computers per yearUnit cost per television, C = $500Holding cost per year as a fraction of unit cost, h = 0.2Order cost per lot, S = $4,000Q* = Sqrt[2DS/hC] = Sqrt[(2)(12000)(4000)/(0.2)(500)] = 980 computers Cycle inventory = Q*/2 = 490Average Flow time = Q*/2D = 980/(2)(12000) = 0.041 year = 0.49 monthOptimal order frequency = n* = Sqrt[(12000)(0.2)(500)/(2)(4000)] = 12.24 ordersAnnual ordering and holding cost = = (12000/980)(4000) + (980/2)(0.2)(500) = $97,980

Example Economic Order Quantity [2]Suppose lot size is reduced to Q=200, which would reduce flow time:Annual ordering and holding cost = = (12000/200)(4000) + (200/2)(0.2)(500) = $250,000

To make it economically feasible to reduce lot size, the fixed cost associated with each lot would have to be reduced

Example Relationship between Lot Size and Ordering CostIf desired lot size = Q* = 200 units, what would S (order cost) have to be?

Desired lot size = Q* = 200Annual demand = D = 12000 unitsUnit cost per television = C = $500Holding cost per year as a fraction of inventory value = h = 0.2

Use EOQ equation and solve for S:S = [hC(Q*)2]/2D = [(0.2)(500)(200)2]/(2)(12000) = $166.67KEY POINT: To reduce optimal lot size by a factor of k, the fixed order cost must be reduced by a factor of k2

Key Points from EOQ ModelIn deciding the optimal lot size, the tradeoff is between setup (order) cost and holding cost.

If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often. Cycle inventory (in days of demand) should decrease as demand increases.

If lot size is to be reduced, one has to reduce fixed order cost. To reduce lot size by a factor of 2, order cost has to be reduced by a factor of 4.

Aggregating Multiple Productsin a Single OrderTransportation is a significant contributor to the fixed cost per orderCan possibly combine shipments of different products from the same suppliersame overall fixed costshared over more than one producteffective fixed cost is reduced for each productlot size for each product can be reducedCan also have a single delivery coming from multiple suppliers or a single truck delivering to multiple retailersAggregating across products, retailers, or suppliers in a single order allows for a reduction in lot size for individual products because fixed ordering and transportation costs are now spread across multiple products, retailers, or suppliers

Example: Aggregating Multiple Products in a Single OrderSuppose there are 4 computer products in the previous example: Deskpro, Litepro, Medpro, and HeavproAssume demand for each is 1000 units per monthIf each product is ordered separately:Q* = 980 units for each productTotal cycle inventory = 4(Q/2) = (4)(980)/2 = 1960 unitsAggregate orders of all four products:Combined Q* = 1960 unitsFor each product: Q* = 1960/4 = 490Cycle inventory for each product is reduced to 490/2 = 245Total cycle inventory = 1960/2 = 980 unitsAverage flow time, inventory holding costs will be reduced

Lot Sizing with MultipleProducts or CustomersIn practice, the fixed ordering cost is dependent at least in part on the variety associated with an order of multiple models A portion of the cost is related to transportation (independent of variety)A portion of the cost is related to loading and receiving (not independent of variety)Three scenarios:Lots are ordered and delivered independently for each productLots are ordered and delivered jointly for all three modelsLots are ordered and delivered jointly for a selected subset of models

Lot Sizing with Multiple ProductsApplied Electrics, the electrical wholesaler, wants to expand inventory ordering system to 3 models of its Samsung televisions: L, M, H.

Demand per yearDL = 12,000; DM = 1,200; DH = 120Common transportation cost, S = $4,000Product specific order costsL = $1,000; sM = $1,000; sH = $1,000Holding cost, h = 0.2Unit costCL = $500; CM = $500; CH = $500

Delivery OptionsNo Aggregation: Each product ordered separatelyComplete Aggregation: All products delivered on each truckTailored Aggregation: Selected subsets of products on each truck

No Aggregation: Order Each Product Independently Total cost = $155,140

Litepro

Medpro

Heavypro

Demand per year

12,000

1,200

120

Fixed cost / order

$5,000

$5,000

$5,000

Optimal order size

1,095

346

110

Order frequency

11.0 / year

3.5 / year

1.1 / year

Annual cost

$109,544

$34,642

$10,954

Aggregation: Order AllProducts JointlyCombined order cost = S* = S + sL + sM + sH = 4000+1000+1000+1000 = $7000Optimal order frequency = n* = Sqrt[(DLhCL+ DMhCM+ DHhCH)/2S*] = 9.75Optimal order size:QL = DL/n* = 12000/9.75 = 1230QM = DM/n* = 1200/9.75 = 123QH = DH/n* = 120/9.75 = 12.3

Cycle inventory = Q/2 Average flow time = (Q/2)/(weekly demand)Annual holding cost = QhC / 2

Complete Aggregation:Order All Products JointlyAnnual order cost = 9.75 $7,000 = $68,250Annual total cost = $136,528

Litepro

Medpro

Heavypro

Demand per year

12,000

1,200

120

Order frequency

9.75/year

9.75/year

9.75/year

Optimal order size

1,230

123

12.3

Annual holding cost

$61,512

$6,151

$615

Lessons from AggregationAggregation allows firms to lower lot size without increasing costComplete aggregation is effective if product specific fixed cost is a small fraction of joint fixed costTailored aggregation is effective if product specific fixed cost is a large fraction of joint fixed cost

Exercise 1 pg 320Harley-Davidson has its engine assembly plant in Milwaukee and its motorcycle assembly plant in Pennsylvania. Engines are transported between the two plants using trucks, with each trip costing $1,000. The motorcycle plant assembles and sells 300 motorcycles each day. Each engine costs $500, and Harley incurs a holding cost of 20 percent per year. How many engines should Harley load onto each truck? What is the cycle inventory of engines at Harley?As part of its initiative to implement just-in-time(JIT) manufacturing at the motorcycle assembly plant in Question 1, Harley has reduced the number of engines loaded on each truck to 100. If each truck still costs $1,000, how does this decision impact annual inventory costs at Harley? What should the cost of each truck be if a load of 100 engines it to be optimal for Harley?

Exercise - 2Harley purchases components from three suppliers. Components purchased from Supplier A are priced at $5 each and used at the rate of 20,000 units per month. Components purchased from Supplier B are priced at $4 each and are used at the rate of 2,500 units per month. Components purchased from Supplier C are priced at $5 each and used at the rate of 900 units per month. Currently Harley purchases a separate truckload from each supplier. As part of its JIT drive, Harley has decided to aggregate purchases from the three suppliers. The trucking company charges a fixed cost of $400 for the truck with an additional charge of $100 for each stop. Thus, if Harley asks for a pickup from only one supplier, the trucking company charges $500; from two suppliers it charges $600;and from three suppliers it charges $700. Suggest a replenishment strategy for Harley that minimizes annual cost. Compare the cost of your strategy with Harleys current strategy of ordering separately from each supplier. What is the cycle inventory of each component at Harley?

DiscountsLot size basedDiscounts based on the quantity ordered in a single lotVolume basedDiscounts based on the total quantity purchased over a given period, regardless of the number of lots purchased over that period

How should buyer react?What are appropriate discounting schemes?

What is the appropriate discounting schemes?For commodity products for which price is set by the market, manufacturers with large fixed costs per lot can use lot size-based quantity discounts to maximize total supply chain profitsThis however, increase cycle inventory in the supply chainFor products for which the firm has market power (product has demand curve), two-part tariffs or volume-based quantity discounts can be used to achieve coordination in the supply chain and maximize supply chain profits

Economies of Scale toExploit Quantity DiscountsAll-unit quantity discountsMarginal unit quantity discounts

Why quantity discounts?Improved coordination to increase total supply chain profitsExtraction of surplus through price discrimination

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 CiThe unit cost generally decreases as the quantity increases, i.e., C0>C1>>Cr The objective for the company (a retailer in our example) is to decide on a lot size that will minimize the sum of material, order, and holding costs

All-Unit Quantity Discount ProcedureStep 1: Calculate the EOQ for the lowest price. If it is feasible (i.e., this order quantity is in the range for that price), then stop. This is the optimal lot size. Calculate total cost (TC ) for this lot size.Step 2: If the EOQ is not feasible, calculate the TC for this price and the smallest quantity for that price.Step 3: Calculate the EOQ for the next lowest price. If it is feasible, stop and calculate the TC for that quantity and price.Step 4: Compare the TC for Steps 2 and 3. Choose the quantity corresponding to the lowest TC. Step 5: If the EOQ in Step 3 is not feasible, repeat Steps 2, 3, and 4 until a feasible EOQ is found.

All-Unit Quantity Discount: ExampleDrugs Online (DO) is an online retailer of prescription drugs and health supplements. Vitamins represent a significant percentage of its sales. Demand for vitamins is 10,000 bottles per month. The price charged by the manufacturer is as follows:

Order quantityUnit Price0-4,999$3.005,000-9,999$2.9610,000-$2.92

q0 = 0, q1 = 5,000, q2 = 10,000C0 = $3.00, C1 = $2.96, C2 = $2.92D = 120,000 units/year, S = $100/lot, h = 0.2

All-Unit Quantity Discount: ExampleStep 1: Calculate Q2* = Sqrt[(2DS)/hC2] = Sqrt[(2)(120,000)(100)/(0.2)(2.92)]=6,410Not feasible (6,410 < 10,000)

Calculate TC2 using C2 = $2.92 and q2 = 10,000TC2 = (D/Q2)S + (Q2/2)hC2 + DC2 =(120,000/10,000)(100)+(10,000/2)(0.2)(2.92)+(120,000)(2.92) = 1,200 + 2,920 + 350,400 = $354,520

Step 2: Calculate Q1* = Sqrt[(2DS)/hC1] = Sqrt[(2)(120,000)(100)/(0.2)(2.96)]=6,367Feasible (5,000

All-Unit Quantity DiscountsWhat is the effect of such a discount schedule?Retailers are encouraged to increase the size of their ordersAverage inventory (cycle inventory) in the supply chain is increasedAverage flow time is increasedIs an all-unit quantity discount an advantage in the supply chain?

Marginal Quantity Discount: Example (optional)Drugs online is an online retailer of prescription drugs and health supplements. Vitamins represent a significant percentage of its sales. Demand for vitamins is 10,000 bottles per month. The price charged by the manufacturer is as follows:

Order quantityUnit Price0-5000$3.005001-10000$2.9610001-$2.92

q0 = 0, q1 = 5,000, q2 = 10,000C0 = $3.00, C1 = $2.96, C2 = $2.92D = 120,000 units/year, S = $100/lot, h = 0.2

Let Vi be the cost of ordering qi units; Vi = C0(q1-q0) + C1(q2-q1) + + ci-1(qi-q0-1)

Marginal Quantity Discount: Example (optional)Let Vi be the cost of ordering qi units; Vi = C0(q1-q0) + C1(q2-q1) + + ci-1(qi-q0-1)

Optimal lot size for price, Ci, is Qi =

TCi = (D/Qi)S+[Vi+(Qi-qi)Ci]h/2 + D/Qi[Vi+(Qi-qi)Ci]

V0 = 0; V1 = 3(5,000-0)=15,000; V2 = 3(5,000-0)+2.96(10,000-5,000)=29,800

Start with i=2

Marginal Quantity Discount: Example (optional)Step 1: Calculate Q2* = Sqrt[(2D(S+V2-q2C2))/hC2] = Sqrt[(2)(120,000)(100+29,800-29,200)/(0.2)(2.92)] = 16,961Feasible ( 16,961 > 10,000) Stop

Calculate TC2 using C2 = $2.92 and Q2 = 16,961; q2 = 10,000

TC2 = (D/Q2)S+[V2+(Q2-q2)C2]h/2 + D/Q2[V2+(Q2-q2)C2] = $ 360,365

Volume-based DiscountsIn the case of Drug Online (DO), consider the scenario in which the manufacturer has invented a new vitamin pill, Vitaherb, which is derived from herbal ingredients, so it can be argued that the price at which DO sells Vitaherb influences demand given by demand curve 360,000 60,000p; where p is price at which DO sells Vitaherb.The manufacturer incurs a production cost of CS = $2 per bottle. The manufacturer must decide on the price to charge DO and DO in turn must decide on the price to charge the customer.

Volume-based DiscountsWhen the two make their decisions independently, it is optional for DO to charge a price of p $5 and for the manufacturer to charge DO a price of CR $4. The total market demand for this case is 360,000 60,000p = 60,000 bottles of VitaherbThe profit at DO = (ProfR)60,000 (p-CR) = 60,000 x 1= $ 60,000The profit at the manufacturer = (ProfM)60,000 (CRCS) = 60,000 x 2 = $ 120,000Total SC profit = $ 180,000

Volume-based DiscountsIf the two stages coordinate and DO prices at p = $4, market demand is 120,000Total SC profit will be 120,000 x (4 2) = $ 240,000As a result of each stage settings its price independently, the supply chain thus loses $60,000This is called double marginalization

There are two pricing schemes that the manufacturer may use to achieve the coordinated solution: two-part tariff and volume-based quantity discount

Two-part tariffIn this case, the manufacturer charges its entire profit as an up-front franchise fee and then sells to the retailers at its suppliers costDO case: the manufacturer charges DO an up-front fee of $180,000 and gives DO CR = $2 DO maximizes its profit if it prices the vitamins at p=$4It has annual sales of 120,000Profits = $ 60,000Recall: the manufacturer makes a profit of $180,000Observe that two-part tariff is really a volume-based quantity discount

Volume-based DiscountDO case:The average material cost for DO declines as it increases the quantity it purchases per yearThis observation can be made explicit by designing a volume-based discount scheme that also achieves coordinationThe objective here is to price in such a way that the retailer buys the total volume sold when the two stages coordinate pricing. Recall that 120,000 bottles are sold per year when the supply chain is coordinatedThe manufacturer must offer DO a volume discount to encourage DO to purchase this quantity

Volume-based DiscountThe manufacturer thus offers a price of CR$4 per bottle if the quantity of DO purchases per year is less than 120,000$3.5 if the total volume in the year is 120,000 or higherIt is then optimal for DO to order 120,000 and price at p = $4 to the customers.

Total profit earned by DO = $ 60,000Total profit earned by the manufacturer = $ 180,000Total SC profit = $ 240,000

Quantity vs Volume-based DiscountsLot size-based discounts tend to raise the cycle inventory in the supply chain by encouraging retailers to increase the size of each lot.Volume-based discounts in contrast, are compatible with small lots that reduce cycle inventory.

Lot size-based discounts make sense only when the manufacturer incurs very high fixed cost per order. Otherwise, it is better to have volume-based discounts

Short-Term Discounting: Trade PromotionsTrade promotions are price discounts for a limited period of time (also may require specific actions from retailers, such as displays, advertising, etc.)Key goals for promotions from a manufacturers perspective:Induce retailers to use price discounts, displays, advertising to increase salesShift inventory from the manufacturer to the retailer and customerDefend a brand against competitionWhat is the impact on the behavior of the retailer and on the performance of the supply chain?Retailer has two primary options in response to a promotion:Pass through some or all of the promotion to customers to spur salesPurchase in greater quantity during promotion period to take advantage of temporary price reduction, but pass through very little of savings to customers FORWARD BUYING

Short-Term Discounting: Trade PromotionsWhen the retailer takes the second option i.e., forward buyingAnd the following assumptions hold:Discount is offered once, with no future discountsRetailer takes no action to influence customer demand customer demand remain unchangedIn a period over which demand is an integer multiply of Q*, then, the optimal order quantity at the discounted price is given by

Qd =

Forward buy = Qd Q*

Q*: Normal order quantityC: Normal unit costd: Short term discountD: Annual demandh: Cost of holding $1 per yearQd: Short term order quantity

Short Term Discounts:Forward BuyingDO is retailer that sells Vitaherb, a popular vitamin diet supplement. Annual demand, D = 120,000Normal cost, C = $3 per bottleHolding cost, h = 0.2Normal order size, Q* = 6,324 bottles Discount per tube, d = $0.15

Optimal lot size during promotion:Qd = dD/(C-d)h + CQ*/(c-d) = [(0.15)(120000)/(3.00-0.15)(0.2)] + [(3)(6324)/(3.00-0.15)] = 38,236 bottles Forward buy = Qd Q* = 38,236 6,324 = 31,912 bottles

Trade PromotionsWhen a manufacturer offers a promotion, the goal for the manufacturer is to take actions (countermeasures) to discourage forward buying in the supply chainCounter measuresEDLP (every day low pricing): price is fixed over time and no short-term discounts are offeredEliminates any incentive for forward buyingAs a result, all stages of the supply chain purchase in quantities that match demandScan based promotions: e.g. retailer receives credit for the promotion discount for every unit sold Customer coupons

Exercise pg 322Number 11Number 12 Number 13

ReferencesChopra S. and P. Meindl, Supply Chain Management, 5e, Prentice Hall, 2013Handfield, Monczka, Giunipero and Patterson, Sourcing and Supply Chain Management, 4e, South-Western, 2009Cachon and Terwiesch, An Introduction to Operations Management, 2e, McGraw-Hill, 2009

*Notes:*Notes:*Notes:*Notes:*Notes:*Notes:*Notes:Optimal order quantity = *Notes:*Notes: