Application of Linear Programming on Transportation and Transshipment Problems

Application of Linear Programming on Transportation and Transshipment Problems

1. Introduction

    Linear programming (LP) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. LP technique and LP extensions have been widely used in business situations, such as Aggregate Production Planning, Product Mix and Multiperiod Scheduling. This report focus on the application of LP and LP extension, with the help of Solver function in Excel, on transportation and transshipment problems. Firstly, a transportation operation problem is stated. The second part describes the LP solutions and relevant sensitivity analysis. Finally, the limitations on LP in general and in the specific problem are assessed.

1. Problem description

Orange is a Chinese technology company headquartered in Shenzhen, China that designs, develops, manufactures and sells consumer electronics. The best seller of Orange company is Orange Phone. In China, Orange has 4 plants and 10 retail stores, and Orange phones are produced in plants and then shipped to the retail stores. The CEO of Orange wants to keep a smooth, steady and adequate flow of Orange Phone from plants to retail stores to meet customers’ demand while at the same time minimize the transport cost.

The simplest transportation system for Orange is to ship the required demand of phone to retail stores directly from plants. In reality, however, there is hardly absolute input and output at each plant. To optimize freight efficiency and reduce cost, company often transship its products by transshipment points. In this case, retail stores can be used as transshipment points. Therefore, two transport solutions will be discussed in the following parts:  

• Cost minimization of direct shipment from plants to retail stores
• Cost minimization of indirect shipment from plant to retail stores (one transshipment via retails store)

Each plant has a minimum production volume to gain a profit and a maximum capacity because of facilities and labor limitations, as shown in table 1 (data from: Huawei, 2016). The distances from each plant to each retail store and between each retail store are in table 1 and 2 (data from: google map). If transport distance > 500 km, the phone would be shipped by air and the average cost is £0.04 per unit per 10 kilometers; if transport distance < 500 km, the phone would be shipped by road freight and the average cost is £0.02 per unit per 10 kilometers (data from: Shunfeng). Finally, the Orange company have estimated the weekly demand of Orange Phones in each retail store (data from: Huawei, 2016). All these estimates are in table 1.