We consider a serial supply chain consisting of a raw material supplier, a manufacturer, a distribution centre and a retailer in the presence of time-varying delivery between manufacturer facility and the retailer warehouse. Delivery time functions are developed based on practical data analysis and the cost models for both linear and non-linear delivery time functions are derived. Analytic solution for system with linear delivery times is derived and a search algorithm for system with non-linear delivery times is established. Finally, sensitivity analysis is made to help decision makers achieve a lower total cost in practice.

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The fluctuation of the seasonal variable delivery time significantly impacts the operating costs of production and distribution systems. This paper finds that a non-linear deliver time function which has a non-zero second derivative can simulate the practical situation more than linear function which has a zero second derivative based on practical data. And this paper focuses on a supply chain in which the retailer requires a small-lot at a fixed interval, the manufacturer sets up a distribution center to satisfy the demand, and the manufacture facility is far from the retailer. A search algorithm for finding the optimal production lot and ordering quantity in a system of non-linear deliver times is proposed. The sensitivity analysis shows that cost savings can be achieved by planning production cycles according to the acceleration of deliver time changes and in-transit costs.