Complementarity analysis of a multi‐item inventory model with leading product pricing
研究了一个联合库存补货与定价问题，卖家控制主导产品价格并补货所有产品，发现最优策略是订单至库存水平与标价政策，并揭示了产品间经济关系的分歧。
Our research investigates a joint inventory replenishment and pricing problem, where a seller controls the price of a leading product while restocking for all the products. We demonstrate that the seller's expected value functions present an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:semantics definitionURL="" encoding=""> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mo>♮</mml:mo> </mml:msup> <mml:mtext>-concave</mml:mtext> </mml:mrow> <mml:annotation encoding="">$L^\natural \text{-concave}$</mml:annotation> </mml:semantics> </mml:math> structure, recommending an optimal order‐up‐to inventory‐level and list‐price policy. Our findings reveal divergent economic relationships between products from the seller's and customer's perspectives, suggesting managers broaden their strategies beyond customer viewpoints. We extend the pricing and inventory analysis to scenarios involving three substitute products under both price and inventory control. In these situations, we further reveal that sellers and customers uniformly view product inventories as substitutes, and the corresponding value functions are submodular and mutually diagonally dominant.