Supply chain coordination under option contracts with joint pricing under price-dependent demand

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We consider a coordination problem under option contracts in a two-echelon supply chain, where the product retail price, option price, option exercise price, and order quantity are optimized. The market demand is random and sensitive to product retail price. Our analyses consider two types of contracts. One is a conventional option contract, where the supplier determines the option price and exercise price, and the retailer determines the product retail price and order quantity. Two cases are studied in terms of the supplier's decisions: (1) the supplier has option exercise price as its decision variable, and (2) has both the option price and option exercise price as its decision variables. The other type of contract is an option contract with a joint pricing mechanism, for which two supply chain players determine a relationship between the option exercise price and product retail price. For both types of contracts, we develop a newsvendor model to examine how joint pricing impacts supply chain coordination and decisions. We use sequential procedures to derive the optimal decisions for the supply chain players, including the retailer's order quantity and product retail price and the option exercise price set by the supplier. We then show that a conventional option contract cannot coordinate the supply chain on its own. We propose introducing joint pricing to option contacts and prove that it would benefit both supply chain players and induce them to voluntarily achieve coordination.