Optimal inventory control with cyclic fixed order costs
研究随机需求下周期性固定订货成本的库存模型，发现最优策略是周期依赖的(s,S)策略，并证明其基于K-凸性，数值实验显示前向购买效应是主要驱动力。
We consider a periodic review single‐item inventory model under stochastic demand. Every m periods, in the regular order period, fixed order costs are K . In the periods in‐between, the intraperiods, higher fixed order costs of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:semantics definitionURL="" encoding=""> <mml:mrow> <mml:mi>L</mml:mi> <mml:mo>></mml:mo> <mml:mi>K</mml:mi> </mml:mrow> <mml:annotation encoding="">$L&#62;K$</mml:annotation> </mml:semantics> </mml:math> apply. The literature on optimal inventory policies under fixed order costs does not account for these time‐dependent fixed order costs. By generalizing existing proofs for optimal inventory policies, we close this gap in inventory theory. The optimal inventory policy is complex in the regular order period and in the intraperiods, a period‐dependent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:semantics definitionURL="" encoding=""> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>S</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="">$(s,S)$</mml:annotation> </mml:semantics> </mml:math> policy is optimal. We describe and prove this optimal policy based on the notion of K ‐convexity and the optimal ordering behavior in the presence of non– K ‐convex cost functions. In a numerical study, we find that a major driver of the optimal policy is a forward‐buying effect that shifts the probability of ordering from the intraperiods to the regular order period. The cost differences between the optimal and a pure period‐dependent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:semantics definitionURL="" encoding=""> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>,</mml:mo> <mml:mi>S</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="">$(s,S)$</mml:annotation> </mml:semantics> </mml:math> policy are, however, small.