This article presents a tangible vendor-buyer cooperative strategy that benefits both, the vendor and the buyer where the demand is deterministic constant, and the delivery lead time follows a general distribution. To build a realistic coordination mechanism, a delivery tolerance time range is specified beyond which two different types of nonlinear penalty costs termed as an early delivery penalty cost and late delivery penalty cost are assessed. Shortages are allowed for a short time-span. The penalty costs are taken as a product of a linear function of delivery lead time and a nonlinear function of the delivery lot size. The problem is formulated as a multi-variable mixed-integer nonlinear programming (MINLP) problem and the objective of this research is to achieve the minimum integrated expected cost where decision variables are: reorder point, delivery lot size, number of deliveries, and delivery time thresholds. Since closed-form solutions are not immediately obtained, different search procedures are employed to resolve issues relating to an integer solution. Numerical results are provided for uniform, exponential and normal distributions of delivery lead time to establish the general model.

本文提出了一种切实可行的供应商-买方合作策略，在需求确定性不变且交货提前期遵循一般分布的情况下，该战略对卖方和买方都有利。为了建立一个现实的协调机制，指定了一个交付容忍时间范围，超过该范围的两种不同类型的非线性惩罚成本，称为提前交付惩罚成本和延迟交付惩罚成本被评估。短时间允许短缺。惩罚成本被视为交货提前期的线性函数和交货批量大小的非线性函数的乘积。该问题被表述为多变量混合整数非线性规划 (MINLP) 问题，本研究的目标是实现最小综合预期成本，其中决策变量为：再订货点、交货批次大小、交货数量和交货时间阈值。由于不能立即获得封闭形式的解决方案，因此采用不同的搜索程序来解决与整数解决方案相关的问题。提供了交货提前期的均匀分布、指数分布和正态分布的数值结果，以建立通用模型。