# Incorporating transportation costs into the single and multiple items newsvendor problems

## TL;DR

This paper explores how transportation costs affect inventory and truck fleet decisions in supply chains, showing that flexible truck usage can reduce costs.

## Contribution

The paper introduces a new lower breakeven point for fixed transportation costs and proposes an optimal solution for multi-product shipping.

## Key findings

- A lower breakeven point for fixed transportation costs was identified compared to prior research.
- Using a mix of truck types can reduce overall supply chain costs.
- Joint replenishment of multiple products improves truck capacity utilization and saves costs.

## Abstract

The efficiency and responsiveness of supply chains are vitally dependent on inventory replenishment and transportation decisions. In this paper, we study a supply chain consisting of a single retailer ordering seasonal products within the newsvendor framework. The primary objective of the paper is to investigate the retailer’s decision-making process, aimed at determining the optimal replenishment quantities and selecting the appropriate mix and size of the truck fleet. Initially, we formulate a mathematical model where the retailer exclusively manages a limited fleet of its own trucks for inbound transportation of a single seasonal product. In this context, we determine a lower breakeven point for the fixed transportation cost than what has been previously proposed in the literature. Subsequently, we examine a commonly encountered transportation scenario where the retailer has the opportunity to expand its fleet size by leasing trucks from the external market. The outcomes of the numerical example indicates that the flexibility resulting from the utilization of different types of trucks can lead to reduced overall costs. We also address the practical transportation problem of efficiently shipping various seasonal products solely with the retailer’s own trucks. For this complex problem, we propose an optimal solution procedure based on Lagrangian method. We show that the joint replenishment of multiple products results in cost savings and enhances utilization of the trucks’ capacities.