On the mathematical modeling of green one-to-one pickup and delivery problem with road segmentation

Highlights

• A mixed integer programming model is presented for the green one-to-one PDP.

• The model accounts for explicit fuel consumption (emissions), variable vehicle speed and road categorization.

• Numerical analyses show that the investigated factors has a significant impact on operational-level logistics decisions.

• Results suggest that the model can achieve significant savings in total transportation cost.

• A case study from the Netherlands shows the applicability of the model in practice.

Abstract

This paper presents a green one-to-one pickup and delivery problem including a set of new features in the domain of green vehicle routing. The objective here is to enhance the traditional models for the one-to-one pickup and delivery problem by considering several important factors, such as explicit fuel consumption (which can be translated into emissions), variable vehicle speed and road categorization (i.e., urban, non-urban). Accordingly, the paper proposes a mixed integer programming model for the problem. A case study from the Netherlands shows the applicability of the model in practice. The numerical analyses show that the investigated factors has a significant impact on operational-level logistics decisions and the selected key performance indicators. The results suggest that the proposed green model can achieve significant savings in terms of total transportation cost. The total cost reduction is found to be (i) 3.03% by the use of explicit fuel consumption estimation, (ii) up to 10.7% by accounting for variable vehicle speed and (iii) up to 10.5% by considering road categorization. As total cost involves explicit energy usage estimation, the proposed model has potential to offer a better support to aid sustainable logistics decision-making process.

Introduction

Logistics is one of the focal sectors in European economy as it contributes to the economic growth and plays a key role in international competitiveness. In the upcoming decades, a steady increase is expected in freight movements throughout Europe mainly due to the population growth and internationalization of trade flows. European Union (EU) policy has been accordingly focusing on improving freight logistics efficiency and mitigating logistics related environmental and social externalities to achieve sustainable logistics (Demir et al., 2015, TRIP, 2015). Apart from several economic goals (e.g., maximizing profit or achieving on-time delivery), sustainable logistics is, therefore, concerned with environmental (e.g., greenhouse gases (GHGs), air pollution, noise pollution, energy use/energy efficiency, renewable energy use, land usage and waste from packaging or shipping) and social (e.g., mobility of citizens, accessibility, employment level and conditions, health and safety incidents) issues as well. Among the aforementioned issues, transportation energy use and GHG emissions are treated as the main key performance indicators (KPIs) in logistics management literature for evaluating sustainability performance of logistics operations (see e.g., Kellner and Igl, 2015, Soysal et al., 2012, Soysal, 2015, Xiao and Konak, 2017, Zhu et al., 2014, Zaman and Shamsuddin, 2017).

According to a projection made by the EU on transport sector, oil scarcity and climate change issues are listed as the major challenges of any transport system (Commission, 2011). In this context, the EU has recently adopted a climate and energy package that sets a target of reducing GHG emissions in the EU by 20% with respect to 1990 (Commission, 2009). Private transport sector has the same attitude towards achieving carbon efficient logistics (see e.g., Colicchia et al. (2013)). For instance, the Deutsche Post DHL claims that providing a product or a service to the customer at the right time, at the right cost, at the right place does not mean that your responsibility as a producer or service provider is over (DHL, 2010). The logistics industry should be also responsible for its own environmental impact on human health. According to the company, some of the future trends in sustainable logistics will be as follows: (i) CO₂ labeling will become standardized and these labels will allow customers to compare “green” products while making climate-friendly choices (see e.g., Acquaye et al. (2015)), (ii) Carbon emissions will have a price tag (see e.g., Choudhary et al. (2015)), and (iii) Carbon pricing will lead to more strict regulatory measures (see e.g., Fahimnia et al. (2015)). These developments present the importance of considering more than just economic aspects in current logistics problems.

The vehicle routing problem (VRP) is one of the core problems at operational-level logistics management, since thousands of companies and organizations engaged in the delivery and collection of goods (or people) are confronted with this problem every day (Toth and Vigo, 2014). The classical VRP comprises a vendor (depot) responsible for delivering products to a set of customers and aims to determine vehicle routes of which total travel costs are minimized. The main constraints are as follows (i) each customer is visited exactly once, (ii) each route starts and ends at the depot, and (iii) the total demand of the customers served by a route does not exceed the vehicle capacity.

An important extension of the VRP is named as the VRP with time windows in which service at each customer must start within a given time window. Another related and important extension of the VRP is called as pickup and delivery problem (PDP) in which a set of pickup and delivery requests between location pairs are satisfied. In this study, we address one-to-one PDP with time windows where the objective is to design a set of least cost vehicle routes starting and ending at a common depot in order to satisfy pickup and delivery requests within given time windows, subject to side constraints (Cordeau et al., 2008). In one-to-one PDP, each origin is associated with a single destination, making up a pickup and delivery (a and b) pair (Şahin et al., 2013). A generic representation of the one-to-one PDP is presented in Fig. 1.

In the VRP literature, the traditional quantitative models for pickup and delivery problems (PDPs) aim to minimize transportation costs with optimal routes for a fleet of vehicles to visit the pickup and drop-off locations in order. The traditional costs often comprise the total distance traveled or total time spent by vehicles (Qu and Bard, 2012). However, we are aware from the green vehicle routing literature that nontraditional green vehicle routing models exploit from the advanced fuel consumption estimation approaches to enhance the environmental sustainability and efficiency of the logistics chain and to better benefit from the real life applications. First, these green models do not rely on only travel distance while estimating fuel consumption, but also consider vehicle load, vehicle speed and other vehicle characteristics. Second, these models often regard travel speed as a decision variable rather than a known parameter, which means that travel speed is not constant and can take any value within given limits. For a detailed information on the studies proposing green models, the interested reader is referred to the reviews by Dekker et al., 2012, Hassini et al., 2012, Erdogan and Miller-Hooks, 2012, Lin et al., 2014, or Bektaş et al. (2016). As far as we know, prior to our research, the one-to-one PDP with environmental concerns has not been addressed in the literature.

Apart from these two main concerns addressed in the green VRP literature, traditional models for PDPs assume that roads are homogeneous in every arc. These traditional models, therefore, ignore potential road segmentation in arcs, which can be regarded as a strong assumption in terms of practical implementability in real life. It has been also observed that road categorization is a fact that the green VRP literature tends to overlook.

From this point of view, this paper aims to enhance the traditional one-to-one PDP models, to make them more useful for decision makers in logistics management. In order to achieve this improvement, we develop a decision support model for the one-to-one PDP that accounts for the above mentioned key issues simultaneously. The proposed model accounts for (i) an explicit calculation of fuel consumption cost based on travel distance, vehicle load, vehicle speed and other vehicle characteristics, (ii) variable vehicle speed that can take any value within given limits, and (iii) road categorization as urban and non-urban roads. The enhanced decision support model can be used by decision makers to improve the sustainability performance of the delivery operations in one-to-one PDPs in terms of logistics cost, transportation energy use and carbon emissions. To the best of our knowledge, this is the first attempt to develop a mathematical model for one-to-one PDP with the above mentioned characteristics.

The rest of the paper is structured as follows. Section 2 presents a brief literature review on the topic to highlight the contributions to the related literature. Section 3 presents a formal description of the studied problem, whereas Section 4 discusses the proposed decision support model. Section 5 provides computational results on a case study. The last section presents conclusions and future research directions.