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

Özden Engin Çakıcı, Itir Karaesmen
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Abstract

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.Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.0190 .
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当产量不是唯一的供应不确定性时:贸易代理的新闻供应商模型
问题定义:我们研究贸易代理的采购决策:代理商选择一个出价(支付单价)来采购卖方提供的货物。如果代理中标,则供应将用于满足买方的需求。方法/结果:贸易代理的单周期、单产品问题是一种新型的新闻供应商问题。我们分析了代理对具有产量不确定性的卖方的最优出价。我们证明,出价结果分布需要满足一个易于检查的条件,但不需要产量分布的条件,就能得到唯一的最优出价。我们还证明,衡量稀缺性的预期销售供应比会影响最优出价。我们研究了最优出价在经济参数、需求以及出价结果和收益分布方面的单调性。有多个卖家的代理问题也是一个新颖的新闻供应商网络问题。对于两个卖家的情况,我们展示了什么时候对代理商来说多样化是最优的。我们表明,尽管有机会分散风险,但与两个卖家合作并不总是最优的;即使另一个卖家是可靠的,只向不可靠的卖家投标也可能是最优的。管理意义:我们为代理商提出以下建议:(i) 考虑到代理商的低价和高价成本,只有当卖家的预期供销比高于临界供销比时,才向卖家投标;(ii) 如果投标结果分布按反向危险率顺序增加,则增加投标;(iii) 当卖家的预期收益增加时,根据供销比增加或减少投标。加入更多卖家会降低整个卖家网络的最优出价,但对所有卖家出价未必是最优的。对于双卖家问题,通过计算在每个卖家处出价的预期收益,就可以轻松做出是否分散出价的决定:在线附录见 https://doi.org/10.1287/msom.2023.0190 。
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