11Recap{ Feb 12 & 19, 2008z Supply chainsz Coordination with Revenue Sharing (RS)z RS with competing retailers or sales effort{ Todayz Quantity Discount detailsz Buyback contractz Supply chains under uncertainty2Quantity 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)z 0 - 4 = 0%z 5 - 9 = 5% z 10 - 24 = 10%z 25 - 49 = 15%z 50 - up = 20%23Quantity 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?4Additional Calculations35Revenue Sharing vs QD{ Retailer’s revenue?{ If demand is uncertain, who bears the risk?6Buy-back (return) contract{ The retailer can return any unsold units at the 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 retailerSupplierRetailerp: sales priceS(q): (expected) sales quantityR(q) = pS(q)c: unit costw: wholesale priceb: buyback priceq: order qty47Coordinating with buy-back contracts{ Supplierz Each 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{ Retailerz Let R(q) = pS(q)z Price is given, not a decision variablez S(q) is a sales functionz Faces costs cR8Buy-back calculations59Buy-back (cont)10Buy-back (return) contract{ To “coordinate” the supply chain and 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 and the retailer z Æ Can choose contract parameters for win-win!!611Comparison of Buy-back with RS{ Compare to Revenue Sharing:z wRS=αc – cR12qWholesale price contract c=25, p=50, Demand~Uniform[0,100], w=30Supply chain’s (expected) profitSupplier’s profitRetailer’s (expected) profitq*=50For any w>c, retailer’s order quantity in the decentralized supply chain is less than q*713Buy-back (return) contract c=25, p=50, Demand~Uniform[0,100], w=33.5, b=17Centralized supply chain’s (expected) profitRetailer’s (expected) profitSupplier’s (expected) profitFor this combination of w and b:•q ↑(40Æ50)• 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!14Example: Simple supply chain with demand uncertainty{ Demand > q Æ lost sales{ Demand < q Æ excess inventorySupplierRetailerp: sales priceRandom demand c: unit costw: wholesale priceq: order qty815Newsvendor Model{ Π(q) = Exp (Revenue + Salvage – PurchaseCost)16Newsvendor (Alternative Way){ Π(q) = Exp (Revenue + Salvage – PurchaseCost)917Buy-back Contracts under Uncertainty{ Simple modelz Single 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 systemP(q) = pS(q) – cq = p(q- ∫0→qF(x)dx)-cqOptimum qI:F(qI)=(p-c)/p18Buy-back contracts{ F(q)=(p-w)/(p-b){ 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)(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)1019Price as a Decision{ Do the contracts still coordinate?{ Revenue Sharing{ Quantity Discount{ Buy-back 20Voluntary vs. Forced Compliance{ Forced compliance: z Supplier 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 coordination differ under these schemes?1121Compliance Scenarios{ Wholesale price contractz ΠS= (w-cS)q{ Revenue sharing contractz Supplier’s profit is affine transformation of CSC profitz Implications?{ Buy-back, Quantity
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