When Yield Is Not the Only Supply Uncertainty: Newsvendor Model of a Trade Agent

Problem definition: We study the procurement decisions of a trade agent: The agent chooses a bid (unit price to pay) to procure the goods available from seller(s). If the agent wins the bid, the supply is used to meet the buyer’s demand. Methodology/results: The trade agent’s single-period, single-product problem is a new type of newsvendor problem. We analyze the agent’s optimal bid for a seller with yield uncertainty. We show that the bid outcome distribution needs to satisfy an easy-to-check condition but no conditions on the yield distribution are needed for a unique optimal bid to exist. We also show that the expected sales-to-supply ratio that measures scarcity affects the optimal bid. We investigate the monotonicity of the optimal bid with respect to economic parameters, demand, and distributions of bid outcome and yield. The agent’s problem with multiple sellers is also a novel newsvendor network problem. For the two-seller case, we show when diversification is optimal for the agent. We show that working with both sellers may not always be optimal despite the opportunity for risk pooling and bidding only at the unreliable seller may be optimal even when the other seller is reliable. Managerial implications: We make the following recommendations for the agent: (i) bid at a seller only when the expected sales-to-supply ratio for a seller is higher than the critical ratio, considering the agent’s cost of underage and overage, (ii) increase the bid if the bid outcome distribution increases in the reversed hazard rate order, and (iii) increase or decrease the bid depending on the demand-to-supply ratio when a seller’s expected yield increases. Inclusion of additional sellers lowers the optimal bids across the seller network, but it may not be optimal to bid at all sellers. For the two-seller problem, whether to diversify is a decision easily made by computing the expected benefit of bidding at each seller.