Impact of Returns on Supply Chain Coordination Ana Muriel Department of Mechanical and Industrial Engineering, University of Massachusetts In collaboration with Rocio Ruiz-Benitez

Outline Motivation Model Analysis Computational Study Conclusions

Motivation The value of commercial product returns now exceeds $100 billion annually in the US (Stock, Speck and Shear (2002)) Commercial product returns: Products returned for any reason within 90 days of purchase. Hewlett Packard recently estimated the cost of consumer returns for North America exceeded 2% of their total outbound sales revenue. Returns ~ 6% of sales Reason% of returns Defective20% Could not install27.5% Performance40% Convenience12.5% Ferguson, Guide and Souza (2005)

Motivation Policy of most US retailers: Full returns no question asked!! Return rates: 6% to 15% (Dekker and Van der Laan (2003)) Mail order companies and e-tailers: as high as 35% Largely ignored in supply chain coordination and contracts literature Most research on consumer returns concerns inventory policies, production planning and reverse logistics ( Fleischmann and Kuik (2003), Kiesmuller (2003))

Literature Review Wood (2001), “Remote Purchase Environments: The influence of Return Policy Leniency on Two-Stage Decision Processes”, Journal of Marketing Research 38, Dekker and Van der Laan (2003), “Inventory control in reverse logistics”, chapter in Business Aspects of Closed-Loop Supply Chains, V.D. Guide Jr., L.N. Van Wassenhove, editors. Carnegie Mellon University Press, Pittsburgh, PA Fleischmann M. and Kuik R. (2003), “On optimal inventory control with independent stochastic items returns”, European Journal of Operational Research 151, Kiesmuller, G.P. (2003), “Optimal control of a one product recovery system with leadtimes”, International journal of Production Economics 81-82, Ferguson, Guide and Souza (2005), “Supply Chain Coordination for False Failure Returns”, working paper. Georgia Institute of Technology. Souza, Guide, van Wassenhove and Blackburn (2005), “Time Value of Commercial Product Returns”, working paper. University of Maryland.

Research Questions: What is the profit impact of incorporating consumer returns in our decision models? Centralized system Decentralized system How does it affect retail prices and quantities ordered? How does this depend on the magnitude of logistics costs? the relative share between retailer and manufacturer? the proportion of product that is returned?

Classical Model Two-echelon supply chain Stochastic and price dependent demand y Manufacturer’s decision variables: wholesale price w repurchase price s Retailer’s decision variables: order quantity Q selling price r Single replenishment opportunity Manufacturer Retailer rSwQwQcQcQ Sales S = min(y,Q) s(Q-S)s(Q-S)

Returns Model A percentage of sales is returned Returns R =  S Manufacturer’s returns logistics cost:l 1 Retailer’s returns handling cost: l 2 This costs include inspection, shipping, sorting, repackaging, remanufacturing, disposal Average salvage value of returned item v ManufacturerRetailer rRrR rS wQwQ cQcQ wRwR l1Rl1Rl2Rl2R vRvR s(Q-S)s(Q-S)

Costs Associated with Returns System costs:  = r - v + l Manufacturer costs  1 = w - v + l 1 Retailer costs  2 = r – w + l 2

Demand Distribution y = stochastic and price dependent demand faced by the retailer: y=xD(r) x= positive r. v. with mean 1 and density function f() D(r) = expected demand quantity, decreasing in retail price Demand density function

Profit Functions and Optimal Decision Variables: Centralized System  C = rS – cQ –  R Decentralized System  T =  R +  M Retailer  R = rS +s(Q-S)– wQ –  2 R Manufacturer  M = (w-c)Q – s(Q-S) –  1 R

Policy IR: Ignores customer returns when optimizing Q IR, r IR, w IR, s IR Customer returns considered a posteriori, to calculate respective profits Expected profit:  IR Policy CR: Considers customer returns when optimizing Q CR, r CR, w CR, s CR Expected profit:  CR Analysis Objective: Compare the following decision rules

Analysis: Centralized System Proposition: Under deterministic and price dependent demand, the optimal retail price increases and the order quantity decreases when considering consumer returns. That is, Q CR r IR Intuitive since the profit margin is reduced by consumer returns.

Analysis: Centralized System Theorem: Under stochastic and price dependent demand we have that 1. For fixed r, Q CR (r)< Q IR (r) 2. For fixed Q, r CR (Q)> r IR (Q) 3. Under mild conditions, Q CR r IR C1: For all r> r IR, Q IR (r) Q IR (r IR ) C2: For all Q<Q IR, r IR (Q) r IR (Q IR )

Analysis: Decentralized System Corollary: Given w, the retailer’s optimal decisions satisfy: 1. For fixed r, Q CR (r)< Q IR (r) 2. For fixed Q, r CR (Q)> r IR (Q) 3. Under mild conditions, Q CR r IR C1: For all r> r IR, Q IR (r) Q IR (r IR ) C2: For all Q<Q IR, r IR (Q) r IR (Q IR )

Question Will consumer returns always result in higher prices and lower quantities in a decentralized supply chain?

Analysis: System Coordination Under Buy-Back Contracts Theorem: Under consumer returns, a policy that allows for unlimited returns at a partial credit s will lead to supply chain coordination for appropriate values of s and w. In particular, Allowing no returns is system suboptimal Extension of Pasternack(1985), demand is not price dependent

Computational Study Assumptions: f(x) ~ uniform distribution in [0,2] Linear demand model D(r)=b(r-k) where b 0 constants b=-3, k=5 (Emmons and Gilbert (1998))

Centralized System We observe: Q CR r IR Q CR decreases as l increases Profit difference increases with l and  10% returns and l=1, the difference is 6.33% Percent improvement increases with  and l l=1 l=2 l=3 CR IR

Decentralized System We observe: Q CR < Q IR r CR > r IR For fixed value of w,  R CR >  R IR But for optimal w,  R IR >  R CR Q* r* CR IR Manuf. Retail. Total

Retail. Total Manuf. Profit Functions at optimal w CR IR Percent Savings Manufacturer: up to 10% Retailer: 9% to 66% Total: 6% to 37%

Sensitivity Analysis With respect to: 1) Share of logistic cost faced by retailer (  ) 2) Percentage of consumer returns (  )

Under policy IR… Q IR, r IR and w IR constant logistics costs do not intervene in the decision making process Under policy CR… Q CR and r CR increase with  ; Manufacturer decreases w CR as incentive for retailer to increase order quantity Ends up bearing all logistics cost If  > 70% =>  R IR* <  R CR* Q* r* w* CR IR Manuf. Retail. Total

 =.06  =.2  =.35 CR IR

Conclusions When considering returns … Centralized system: 1) Lower quantities and higher retail prices 2) Significant profit increase Decentralized system: 1) Lower quantities and higher retail prices 2) Poor coordination of the supply chain All members worse off in general Ignoring returns reduces double marginalization 3) The manufacturer bears the returns logistics costs: Higher percentage manufacturer decreases incurred by retailer wholesale price to compensate