Optimization of City Logistic Goods Transport - A Use Case from the Capital Region of Denmark

Optimization of City Logistic Goods Transport - A Use Case from the Capital Region of Denmark


This case study focuses on the optimization of an existing fleet of electric vehicles for the collection of blood samples in the public sector. The aim is to decide the fleet size and mix the Capital Region of Denmark should invest in.

Region Hovedstaden (Capital Region of Denmark) is a regional authority that performs various functions for ensuring that health and growth thrive in the Greater Copenhagen area. Running the healthcare system is one of the primary responsibilities. This system is organized in the following manner: there are several private physicians and a few major hospitals. While the physicians carry out non-emergent consultation, hospitals cater to emergencies, surgeries, and diagnostic services such as biomedical sample testing, X-rays, etc. As part of diagnostic services, private physicians conduct blood tests on patients in their clinics. The Region must collect these blood samples from all the clinics to a specific testing laboratory in a hospital in a timely manner.

From a freight logistics planning perspective, on the demand side of this supply chain, the clinics must be specified by the quantity of demand, the time window, and the duration of service. The time window and service duration are given by the region from previous data. The quantity of demand is given by the number of vials of blood samples that must be collected from the clinic.

The demand quantity clearly depends on the number of patients visiting the clinic on each day, which is not usually known with certainty beforehand. However, based on interactions with physicians, it was found that the variability of the estimate of demand is very low given the day of the week and the time of the year – summer or non-summer. Since these estimates are not readily available, a survey was conducted targeting all the physicians in the region of interest and obtained reasonable estimates for all days of the week and both periods of the year.

In the current setup a fleet of electric vans is used. The Capital Region of Denmark is considering the deployment of smaller vehicles (cargo scooters) on this service as they are more flexible in traffic e.g. easier to park. The two types of electric vehicles were the TRIPL cargo bike and the mid-sized pickup van Renault Kangoo ZE, both is seen on the picture.

Figure 1 - The TRIPL Cargo Bike third from the left and the Renault Kangoo ZE fourth from the left.

Source: Capital Region of Denmark

Table 1 - Vehicles considered in the Capital Region of Denmark

Source: Malladi et al. (2019) DTU Management

So far, the Region has been using fixed routes based on the full set of clinics. However, this resulted in a variety of operational issues including running out of driving range, not serving many clinics, and missing time windows. Two main reasons for these operational issues were:

  1. The previous fleet mix and the fixed routes were not optimized for serving subsets of customers and a spectrum of requests. The previous fleet mix decision used by the Region did not consider uncertainty and variability in operational request profiles at the strategic planning stage.
  2. The energy consumed for climate control (which depends on temperature that cannot be known with certainty at the strategic planning stage) and powering auxiliary external devices has not been accounted for so far in the literature and thus in the planning methods. This results in an overestimation of the energy available to execute routes, leading to missed service at some clinics.

We are thus investigating a stochastic fleet size and mix problem aiming to minimize Total Cost of Ownership (TCO), considering uncertainty in the requests and temperature in every operational period at the strategic planning stage.


The main result in Figure 1, shows the composition of the ten best fleet mixes, their associated Total Cost of Ownership and average fill rate. The results show the best fleet mix consists of one pickup van and four cargo bikes. Comparing the best fleet mix with the second-best fleet mix, we see that the single pickup van from the best fleet mix is substituted with two cargo bikes. This results in a lower average fill rate, but a higher Total Cost of Ownership. The difference in Total Cost of Ownership between the best and the tenth best solution is 40,000 US dollars (equivalent to 25% of the best solution’s TCO).

Figure 2 - The ten best fleet mix solutions, their TCO and average fill rates.

Source: Malladi et al. (2019) DTU Management

Figure 2 is based on the current demand characterization, but as we are considering an operational period of 10 years, we must take into consideration what might happen in the future as well. Evaluating different scenarios, decision makers often prefer a slightly costlier solution if it means it is more robust and has a built-in resilience against future changes in the logistic systems. In Figure 2, such an analysis is presented. Figure 3 shows the Total Cost of Ownership for the top eight fleet mixes, when varying the demand factor. Varying the demand factor means all doctors have their demand scaled by a multiplier. The previous best fleet mix ([1,4 means 1 pick-up van and 4 cargo bikes]), remains the preferred solution for the demand scaling interval 0.95 to 1.15. If the demand were to increase by more than 20%, the best fleet mixes would be [2,3] and [1,5], as they have an increased capacity to cope with the increased demand. However, the demand in blood samples is expected to be relatively stable over a 10-year period, but for another organization og company such an analysis could be vital, if they are preparing an expansion.

Figure 3 - Sensitivity analysis on the top eight fleet mix solutions to variation of scaling demand at all doctors. A legend entry [a, b] refers to a fleet mix with [a] vans and [b] cargo bikes.

Source: Malladi et al. (2019) DTU Management

Figure 4 shows the importance of including the climate control power in the vehicle energy consumption model for the best fleet mix [1,4]. The data for this plot comes from varying the outside temperature, and for each temperature setting, executing the Adaptive Large Neighborhood Search on the same operational instances. The left axis shows the average operational cost per shift for different outside temperatures with (green line) and without the climate control (red line). The right axis shows the cost difference in percentage (blue line). It is assumed that 20 degrees Celsius is the desired cabin temperature, and thus the cost with and without inclusion of climate control is equal here. The average cost without climate control stays constant, whereas it varies a lot for the case with climate control. This means that auxiliary consumers in an electric vehicle (e.g. air conditioning) can reduce the range to such an extent that under certain circumstances the tours are not completed. Therefore, it is important that auxiliary consumers are taken into account in the energy consumption of the vehicles in order to carry out all tours. Even if this leads to higher average energy/operational costs as shown in figure 4.

Figure 4 - Average operational cost per shift in USD (left axis) and percentage cost difference over the case of no cabin climate control (right axis) with varying ambient temperature for the best fleet mix solution with 1 van and 4 TRIPL Cargo Bikes.

Source: Malladi et al. (2019) DTU Management


Malladi et al. (2019). DTU Management. Stochastic Fleet Mix Optimization: Evaluating Electromobility in Urban Logistics

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