Supply chain coordination Chain-to-chain competition IM 2010: Operations Research, Spring 2014 Supply Chain Management Ling-Chieh Kung Department of Information Management National Taiwan University May 29, 20141 Supply Chain Management 1 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Supply chain management ◮ In operations research or management science, a subfield is called supply chain management . ◮ A supply chain is a collection of firms such as suppliers, manufacturers, distributors, wholesalers, retailers, and salespeople that together deliver products to end consumers. → → → http://servagya.com http://www.hvsystems.co.uk ◮ An extension of operations management (focusing on manufacturers). ◮ Strategic decisions: distribution channel structure, supplier selection, collaborative forecasting, etc. Supply Chain Management 2 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Supply chain contracting ◮ Some firms operate its own supply chain. ◮ In most cases, a supply chain is decentralized . ◮ Firms interact through contracting . ◮ Firms in a supply chain are teammates but also competitors. ◮ A firm does not act for the chain’s profit or other firms’ profits. ◮ A firm acts for its own profit. ◮ Game theory helps! ◮ Key issues: incentives and information . ◮ A supply chain is also called a distribution channel . Supply Chain Management 3 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Road map ◮ Supply chain coordination . ◮ Chain-to-chain competition. Supply Chain Management 4 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Pricing in a supply chain ◮ Recall our supply chain pricing game: C w r Manufacturer Retailer D ( r ) = A − Br ✲ ✲ ✲ ◮ Suppose the supply chain is decentralized : ◮ The retail price r ∗ = BC +3 A . 4 B R = ( A − BC ) 2 ◮ The retailer earns π ∗ . 16 B M = ( A − BC ) 2 ◮ The manufacturer earns π ∗ . 8 B M = 3( A − BC ) 2 ◮ In total, they earn π ∗ C = π ∗ R + π ∗ . 16 B ◮ Suppose the two firms integrate : ◮ The optimal solution is r FB = BC + A < r ∗ . 2 B = ( A − BC ) 2 ◮ In total, they earn π FB > π ∗ C . C 4 B Supply Chain Management 5 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Double marginalization ◮ Decentralization introduces inefficiency. ◮ Double marginalization : The retail price is marked up twice . ◮ The sales volume is smaller under decentralization. ◮ the “total pie” becomes smaller. ◮ There is incentive misalignment in the supply chain. ◮ Inefficiency can be eliminated if the manufacturer chooses w = C . ◮ This is impossible! ◮ Any solution? ◮ Changing the game rules. ◮ Using a different contract format. Supply Chain Management 6 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Two-part tariffs ◮ A two-part tariff consists of a per-unit price w and a lump-sum fee t . ◮ Buying q units requires wq + t dollars. ◮ In this case, the retailer’s behavior is identical. . It earns ( A − Bw ) 2 ◮ The optimal retail price is still r ∗∗ ( w ) = Bw + A − t . 2 B 4 B ◮ The manufacturer solves � A − Bw � π ∗∗ M = max ( w − C ) + t 2 w ≥ 0 ,t ≥ 0 (1) ( A − Bw ) 2 s.t. − t ≥ 0 . 4 B Proposition 1 For the problem in (1), the optimal solution is t ∗∗ = ( A − BC ) 2 and 4 B w ∗∗ = C . The associated objective value is π ∗∗ M = ( A − BC ) 2 . 4 B Supply Chain Management 7 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Supply chain coordination ◮ A two-part tariff can coordinate the supply chain. ◮ The equilibrium outcome is (socially) efficient . ◮ The manufacturer provides enough incentives to induce the retailer to choose the efficient retail price. ◮ In equilibrium, the manufacturer takes all; the retailer gets nothing. ◮ But win-win can be achieved! ◮ t may be adjusted to make the retailer profitable. R = ( A − BC ) 2 ◮ E.g., t > π ∗ is attractive. 16 B Supply Chain Management 8 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Indirect newsvendor ◮ How about the indirect newsvendor channel? c ( w ) p Manufacturer Retailer D ∼ F, f ✲ ✲ ✲ ( q ) ◮ They try to maximize: ◮ The retailer: π R ( q ) = p E [min { D, q } ] − wq . ◮ The manufacturer: π M ( w ) = ( w − c ) q ∗ , where q ∗ ∈ argmax q { π R ( q ) } . ◮ If the supply chain is decentralized: ◮ w ∗ > c and F ( q ∗ ) = 1 − w ∗ p . ◮ If the two firms integrate: p ; q ∗ < q FB . ◮ F ( q FB ) = 1 − c ◮ Any contract to coordinate the supply chain? Supply Chain Management 9 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Risk-sharing contracts ◮ The retailer orders too few because w > c . ◮ Overage is too costly. ◮ The risk of overage is too high. ◮ The retailer takes all the risk while the manufacturer is risk-free. ◮ A risk-sharing contract helps. ◮ In particular, a return (buy-back) contract works. ◮ The retailer is allowed to return (all or some) unsold products to get (full or partial) credits. ◮ Contractual terms: ◮ w is the wholesale price. ◮ r is the return credit (buy-back price). ◮ ( w, r ) = ( w, 0) reduces to the wholesale contract; ◮ ( w, r ) = ( w, w ) is a full return contract. Supply Chain Management 10 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Expected profits ◮ Under a return contract ( w, r ), the retailer’s expected profit is � q � ∞ � � π R ( q ) = xp + ( q − x ) r f ( x ) dx + qpf ( x ) dx. 0 q ◮ Let q ∗ ∈ argmax q ≥ 0 π R ( q ). The manufacturer’s expected profit is � q ∗ ( q ∗ − x ) rf ( x ) dx. π M ( w, r ) = q ∗ ( w − c ) − 0 ◮ The expected supply chain profit is � q � ∞ π C ( q ) = − cq + xpf ( x ) dx + qpf ( x ) dx. 0 q Supply Chain Management 11 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Efficient inventory level ◮ From the supply chain’s perspective, this is still the same problem. ◮ The efficient inventory level q FB satisfies F ( q FB ) = 1 − c p . ◮ Questions: ◮ Is there a contract ( w, r ) that induces the retailer to order q FB ? ◮ Does that contract benefit both players (compared with the optimal wholesale contract)? Supply Chain Management 12 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Retailer’s ordering strategy ◮ Under a return contract, the retailer’s expected profit is � q � ∞ � � π R ( q ) = xp + ( q − x ) r f ( x ) dx + qpf ( x ) dx. 0 q ◮ We then have � q � ∞ π ′ R ( q ) = − w + rf ( x ) dx + pf ( x ) dx 0 q = − w + p − ( p − r ) F ( q ) . and π ′′ R ( q ) ≤ 0. ◮ To induce the retailer to order q FB , we need π ′ R ( q FB ) = 0, i.e., R ( q FB ) = − w + p − ( p − r ) F ( q FB ) = − w + p − ( p − c )( p − r ) π ′ = 0 . p Supply Chain Management 13 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Coordinating return contracts ◮ Is there a coordinating return contract? Proposition 2 R ( q FB ) = 0 if and only if w = p − ( p − c )( p − r ) ◮ π ′ . p ◮ For any p and c , a pair of w ∈ [ c, p ] and r ∈ [0 , w ] exist to satisfy the above equation. Proof. The first part is immediate. According to the equation, we need r = p ( w − c ) p − c . Then w ≤ p implies r = p ( w − c ) ≤ w and c ≤ w implies p − c r = p ( w − c ) ≥ 0. Such an r thus exists. p − c ◮ How about profit splitting? Supply Chain Management 14 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Profit splitting ◮ Under a return contract, channel coordination requires w = p − ( p − c )( p − r ) � p − c � = c + r. p p ◮ When w = c , we need r = 0. In this case, π ∗ M = 0 and π ∗ R = π ∗ C . ◮ When w = p , we need r = p . In this case, π ∗ M = π ∗ C and π ∗ R = 0. ◮ And these functions are all continuous ! ◮ The supply chain expected profit may be split arbitrarily. ◮ Win-win is possible. Supply Chain Management 15 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Remarks ◮ For this problem, there are other coordinating contracts. ◮ E.g., revenue-sharing contracts. ◮ Key: incentives. ◮ In practice, the manufacturer may pay the retailer without asking for the physical goods. ◮ Two-part tariffs and return contracts may be actually win-win-win . ◮ Consumers also benefit from supply chain coordination. ◮ In general, a coordinating contract is not always win-win. Supply Chain Management 16 / 36 Ling-Chieh Kung (NTU IM)
Supply chain coordination Chain-to-chain competition Road map ◮ Supply chain coordination. ◮ Chain-to-chain competition . Supply Chain Management 17 / 36 Ling-Chieh Kung (NTU IM)
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