1Recap{ Feb 12 & 19, 2008z Supply chainsz Coordination with Revenue Sharing (RS)z RS with competing retailers or sales effort{Today1{Todayz Quantity Discount detailsz Buyback contractz Supply chains under uncertaintyDrawbacks of Revenue Sharing{ Revenue sharing requires it i monitoring { Contracts with multiple retailers may have legal issues{ Retailers may sell competing goods and have ability to set prices2{ Revenue sharing can impact sales effort2Revenue Sharing with Sales Effort (CSC){ Revenue depends on quantity and effort: R(q e)effort: R(q,e){ CSC: Π*= R(q,e) – cq – g(e)z g(e) is an increasing, differentiable, convex function with g(0) = 0{ Optimal effort:z∂Π/∂e = ∂R(q,e)/∂e –g’(e) =0 …… (1)3∂Π/∂e ∂R(q,e)/∂e g (e) 0 …… (1){ Optimal quantity: z ∂Π/∂q = ∂R(q,e)/∂q –c =0 …… (2)Revenue Sharing with Sales Effort (DSC){ Retailer’s profit zΠ(q) = αR(q e) wq g(e)zΠ(q) = αR(q,e) –wq –g(e){ Optimal effort:z ∂Π/∂e = α∂R(q,e)/∂e –g’(e) =0 ….. (3)z Implications?{ Optimal quantity: z ∂Π/∂q = α∂R(q,e)/∂q –w =0 4z At optimal alpha:z ∂R(q,e)/∂q –w =0 …..(4)z Implications?{ Overall conclusion?3Two-part tariff{ Supplier charges ffz a fixed fee Fz a wholesale price w per unitExample:For travelers who value flexibility and the increased security of knowing everyoneon the flight, there is a compelling incentive for opting for fractional ownership. [...]5g, p g p g p[]Under NetJets’ scheme, a one-sixteenth share of a small Cessna Encore, which seatsseven passengers, costs $487,500 plus a monthly management fee of $6,350 and anoccupied hourly fee of $1,390 for each of the allotted 50 hours.” (Financial Times,December 12, 2001)Quantity Discounts{ “We offer a quantity discount for orders of 10 pieces and more of the same products” (www decor24 com)products. (www.decor24.com){ “Server quantity discounts start at 10 units, with further breaks at 25, 50, 100, 250 and above.” (www.greyware.com){“Quantity discounts on miscellaneous 6{Quantity discounts on miscellaneous accessories:” (www.frye.com)z 0 - 4 = 0%z 5 - 9 = 5% z 10 - 24 = 10%z 25 - 49 = 15%z 50 - up = 20%4Quantity Discounts{ “We offer a quantity discount for orders of 10 pieces and more of the same products.” (www.decor24.com){ “Server quantity discounts start at 10 units, with further breaks at 25, 50, 100, 250 and above.” (www.greyware.com){ “Quantity discounts on miscellaneous accessories:” (www frye com)7accessories:” (www.frye.com)z 0 - 4 = 0%z 5 - 9 = 5% z 10 - 24 = 10%z 25 - 49 = 15%z 50 - up = 20%Quantity Discounts{ CSC: Π = R(q) – cq{ DSC: ΠR= R(q) – (w(q) + cR)qz where w(q) is a continuous differentiable, decreasing function of q{ Can we coordinate the chain?85Additional Calculations9Revenue Sharing vs QD{ Retailer’s revenue?{ If demand is uncertain, who bears the risk?106Buy-back (return) contract{ The retailer can return any unsold units at the end of the selling season to the supplier SupplierRetailerp: sales priceS(q): (expected) sales quantityR(q) = pS(q)c: unit costw: wholesale priceb: buyback priceq: order qty11the end of the selling season to the supplier and receive b<w{ Buyback contract allocates the risk of excess inventory between the supplier and the retailerCoordinating with buy-back contracts{ SupplierEach unit costs cto the supplierzEach unit costs cSto the supplierz Supplier sells items to a retailer at wper unitz Purchases left-over units at the end of the selling season for b per unit, b<w{ Retailer12z Let R(q) = pS(q)z Price is given, not a decision variablez S(q) is a sales functionz Faces costs cR7Buy-back calculations13Buy-back (cont)148Buy-back (return) contract{ To “coordinate” the supply chain and receive (1α) fraction of total supply chain receive (1-α) fraction of total supply chain profits, supplier must setz w = p(1-α)+αc-cRz b = p(1-α){ Buyback contract allows for “flexible”division of profits between the supplier 15division of profits between the supplier and the retailer z Æ Can choose contract parameters for win-win!!Comparison of Buy-back with RS{ Compare to Revenue Sharing:z wRS=αc – cR169Wholesale price contract c=25, p=50, Demand~Uniform[0,100], w=30Supply chain’s (expected) profitSupplier’s profitRetailer’s (expected) profitFor any w>c, retailer’s order quantity in the17qq*=50order quantity in the decentralized supply chain is less than q*Buy-back (return) contract c=25, p=50, Demand~Uniform[0,100], w=33.5, b=17Centralized supply chain’s (expected) profitRetailer’s (expected) profitFor this combination of w and b:•q ↑(40Æ50)↑18Supplier’s (expected) profit• SC profit ↑(600Æ625)• Supplier’s profit ↑ (200Æ212.5)• Retailer’s profit ↑ (400Æ412.5)• Decentralized SC behaves same as the centralized SC • Win-win for the players!10Example: Simple supply chain with demand uncertainty{ Demand > q Æ lost salesDd Æ iSupplierRetailerp: sales priceRandom demand c: unit costw: wholesale priceq: order qty19{Demand < q Æexcess inventoryNewsvendor Model{ Π(q) = Exp (Revenue + Salvage – PurchaseCost)2011Newsvendor (Alternative Way){ Π(q) = Exp (Revenue + Salvage – PurchaseCost)21Buy-back Contracts under Uncertainty{ Simple modelzSingle selling period, retail price pzSingle selling period, retail price pz Random demand with probability distribution F(x){ Retailer’s expected profitP(q,w,b)= pS(q) + bI(q) – wqp(q- ∫0→qF(x)dx) + b ∫0→qF(x)dx - wqOptimal q:F(q)=(p-w)/(p-b){The profit of the integrated system22{The profit of the integrated systemP(q) = pS(q) – cq = p(q- ∫0→qF(x)dx)-cqOptimum qI:F(qI)=(p-c)/p12Buy-back contracts{ F(q)=(p-w)/(p-b){F(q)=(p-c)/p in the integrated system{F(qI)=(p-c)/p in the integrated systemF(qI)=F(q) if (p-c)/p = (p-w)/(p-b) w=? b=?Set b=p(1- α), w=p(1- α)+αc (0< α <1)23(p-w) =p - p + αp - αc = α(p-c)(p-b) = p - p + αp = αpF(q)=(p-w)/(p-b) = α(p-c)/αp = (p-c)/p = F(qI)Price as a Decision{ Do the contracts still coordinate?{ Revenue Sharing{ Quantity Discount{ Buy-back 2413Voluntary vs. Forced Compliance{ Forced compliance: Supplier delivers exactly the amount zSupplier delivers exactly the amount ordered by the retailer{ Voluntary compliance: z Supplier delivers an amount (not to exceed q) to maximize her profits{ How do the quantities and 25qcoordination differ under these schemes?Compliance Scenarios{ Wholesale price