1. Introduction
The sudden outbreak of the novel coronavirus thrust the issue of pharmaceutical cold chain logistics into the spotlight. The pharmaceutical cold chain is a crucial link in drug transport, with tremendous potential for industrial development [
1]. Meanwhile, the emergence of “two votes” and the new GSP certification specification, accompanied by stricter supervision over procedures such as procurement, storage, and sale, make the direct distribution from pharmaceutical plants to dealers or hospitals seemingly more profitable and feasible. However, many logistics enterprises cannot meet the requirements of the latest pharmaceutical cold chain logistics; as a result, drug distribution tasks are performed independently by pharmaceutical manufacturers. In addition, since the pharmaceutical cold chain logistics is still in its early stage [
2], the comprehensive cost and carbon emissions are not ideal. Pertaining to this condition, studies showed that the logistics activities of carrier vehicles, especially those involved in cold chain logistics, are a main factor contributing to global warming (see [
3,
4]). Moreover, this goes against the prevalent “low-carbon environmental protection” concept, while being unfavorable toward the battle of pollution prevention and control. Therefore, optimizing the pharmaceutical cold chain logistics path and reducing carbon emissions in logistics management became the focus of research [
3]. Currently, there are three main research topics for cold chain logistics optimization. The first one is the optimization of cold chain logistics efficiency, which involves improving properties, infrastructure maintenance, and management practices [
5]. The second one is the optimization of logistics decision making, such as route optimization and energy optimization [
6]. The last one is about environmentally friendly logistics that reduce carbon emissions and energy consumption [
7].
The contributions of this study are as follows:
- (1)
Proposal of a new medicine cold chain distribution model, which is different from the existing single transport vehicle scheme.
- (2)
Considerations of the influence of spatial and seasonal temperature variations on customers from distinct areas and a further refinement of transportation costs, especially for the issues of consumables in cold zones.
- (3)
Acceleration of the convergence speed, while avoiding local optimal solutions via a nonlinear convergence factor, and further improvements of the traditional Grey Wolf Optimizer algorithm through the introduction of the greedy algorithm principle and the damage repair idea in the large-scale neighborhood search algorithm.
The specific research organization of this paper is as follows:
Section 2 reviews the progress of the related research through a literature review;
Section 3 analyzes the existing problems of the pharmaceutical cold chain and puts forward a cold chain transportation scheme with the dual distribution method;
Section 4 designs the comparison function to determine the distribution mode and establishes a path optimization model;
Section 5 introduces a large-scale neighborhood search algorithm, the Grey Wolf Optimizer (GWO), and our improvements of this algorithm;
Section 6 demonstrates the superiority of our proposed method through an example analysis and an efficiency comparison with existing algorithms;
Section 7 summarizes the research results and plans for future research.
2. Literature Review
Traditionally, cold chain logistics refers to the continuous processes employed to ensure the refrigerated preservation of perishable foodstuffs from production to consumption stages (see Zhao et al. [
1]). This involves various processes such as initial refrigeration, refrigeration during post-harvest, transportation, retail distribution, and home storage. However, pharmaceutical cold chain logistics is significantly different from traditional food cold chain logistics, as improper operations could greatly impact medicine quality, making it much more vulnerable. As a result, the comprehensive cost of pharmaceuticals is considerably high (see Han et al. [
3]), and optimizing pharmaceutical cold chain logistics has become a pressing topic.
The studies on traditional cold chain optimization models are as follows: Wang et al. [
8] took the urban cold chain delivery problem in the case of a time-varying road network as their research object and designed a uniparental genetic algorithm to solve a multi-objective optimization model with multiple factors such as total delivery cost, customer satisfaction, and customer value to provide a reference for urban cold chain delivery decisions. Liu et al. [
9] built a joint distribution–green vehicle path problem (JD–GVRP) model to deliver cold chain products by considering carbon tax policy mutual collaboration. Ma et al. [
10] introduced a safety factor and set up constraints based on the equilibrium of the increase and decrease in customer demand. They established a mathematical model intended to minimize the comprehensive cost to solve the optimization problem of a logistics vehicle path with random demand. In addition, they used an adaptive genetic algorithm to solve the mathematical model to verify the practicality and innovation of the optimization model. For external factors such as road conditions, Ren et al. [
11] incorporated the forbidden search operator and dynamic probabilistic selection of just models under knowledge-based business strategies into the ant colony algorithm to solve the path optimization problem of urban cold chain logistics distribution. Theophilus et al. [
12] introduced a new mixed integer formula, to determine the product decay throughout the service process when the truck arrives, to improve fresh produce distribution efficiency. The situation and a temperature-controlled zone dedicated to fresh products were considered to ensure the lowest total cost of the truck delivery process.
Unlike the general cold chain industry, the whole circulation process of the cold pharmaceutical chain from production to pre-use must be within a specified temperature range; since exceeding this temperature range leads to drug failure, there is no tolerance for cargo loss rate. For this reason, Chen et al. [
13] developed a combined contract coordination model with a quantity discount and revenue-sharing contract under decentralized decision making that was applied to the coordination and optimization of the pharmaceutical supply chain. Xiong et al. [
14] established a mathematical model with the objective function of minimizing the distribution cost based on the new version of the product supply specification standard with the constraints of supply–demand balance and transportation volume for each cycle. They demonstrated the effectiveness of the proposed method through case studies. Setak et al. [
15] proposed a three-level pharmaceutical supply chain model considering competition and integrity under uncertainty and used a two-stage stochastic approach to model the problem. A hybrid genetic algorithm was applied to solve the transportation problem of pharmaceutical companies in the Erbouche Mountains to verify the model’s validity. Meisam et al. [
16] considered a four-level multi-phase supply chain including manufacturers, distribution centers, hospitals, and patients for the multi-objective optimization problem of the cold pharmaceutical chain. They proposed a multi-objective non-dominated ranking genetic algorithm to solve a multi-objective model and used the multi-objective non-dominated ranking genetic algorithm to solve a supply chain problem in the medical sector in Iran, proving that the proposed method can provide a more reliable solution in a real pharmaceutical supply chain. Zahir et al. [
17] proposed a pharmaceutical supply chain network design mathematical model. They discussed a new robust likelihood optimization method to validate the effectiveness of the proposed mathematical model. Wen [
18] constructed a time-reliability calculation method for pharmaceutical cold chain logistics without intersecting the minimum set of paths, established a time-reliability-based optimization model for pharmaceutical cold chain logistics networks, and designed a stochastic simulation genetic algorithm to solve the model to solve the pharmaceutical cold chain logistics distribution problem that satisfies node reliability. Zhang et al. [
19] determined the number of shipments and vessel deployments in a multi-period planning environment with independent perishable product demand to reduce the cost of transporting perishable products such as in the cold pharmaceutical chain. Goodarzian et al. [
20] developed two new meta-heuristic algorithms for the pharmaceutical supply chain network (PSCN) design problem and improved the social engineering optimization (ISEO) and the hybrid firefly and simulated annealing algorithm (HFFA-SA) to solve a new mixed-integer nonlinear programming model. This new mixed-integer nonlinear programming model is solved to minimize the total cost and delivery time of pharmaceutical products to hospitals and pharmacies, while maximizing the reliability of the transportation system.
In addition to the optimization of the path optimization in the pharmaceutical cold chain, many researchers simultaneously studied the refrigeration materials and new devices used in the pharmaceutical cold chain. Cui et al. [
21] proposed a hybrid method based on an improved bidirectional gated cyclic unit (IBGRU) network and unscented Kalman filter (UFK), which achieves battery stability at different temperatures and has good estimation accuracy and robustness. Li et al. [
22] proposed two kinds of Li-ion battery estimation models and a variety of equivalent circuit models for different practical applications and designed an improved particle swarm optimization algorithm (IPSO) to optimize the model. The experimental results show that the proposed method is more flexible for Li-ion battery health state estimation. Cui et al. [
23] proposed a hybrid method based on the CNN-BWGRU network to solve the problem of the accurate estimation of the battery State of Charge (SOC), which provides useful guidance for the safe and stable operation of batteries in the natural environment. Liu et al. [
24] designed a time convolution model of a supercapacitor to more accurately predict its remaining service life. At the same time, they used the Adam convolution algorithm to optimize the time network parameter adjustment process; through the experiment, it is concluded that the time convolution network model has stronger robustness and higher accuracy for the prediction of the residual service life of the supercapacitor. Taher et al. [
25] assessed refrigerators in the air thermal behavior of two kinds of situations; throughout the operation cycle (charging and discharging) used in the different phase change materials, the results show that their study system of the integrated PCM can significantly reduce the consumption of cooling needed for when the door opened, thereby reducing greenhouse gas emissions and providing significant energy savings. Leungtongkum et al. [
26] analyzed the effects of the melting point and position of phase change materials (PCM), the quality and load of PCM, insulation materials, external temperature, and other conditions on product temperature and energy consumption and applied PCM in refrigeration equipment. Zhou et al. [
27] built a high- and low-temperature test chamber test bench, studied the performance comparison of the R404A with or without a heat recovery cycle, studied the refrigeration cycle of the new refrigerant R4484, and proved through experiments that the stability of the R4484 refrigeration system under high-temperature conditions was due to the R404A refrigeration system.
In summary, the domestic and international research on pharmaceutical cold chain distribution still has the following shortcomings:
- (1)
The choice of distribution mode is single, and only refrigerated trucks with refrigeration functions are considered for transportation.
- (2)
The existing research mostly limits the transportation season to spring or autumn, i.e., the external temperature of the truck during the transportation is determined to be in the range of 10–20 °C, without considering seasonal temperature variation.
- (3)
The truck transportation area is located in the same temperature zone, without considering the distribution environment across multiple temperature zones, so it is more instructive to consider the new distribution model in pharmaceutical cold chain logistics and the spatial and seasonal temperatures variations according to the actual customer demand.
3. Problem Analysis
3.1. Problem Description
Pharmaceutical cold chain logistics require more stringent preservation conditions during transportation compared to traditional cold chain logistics. To effectively reduce the total cost and carbon emissions of these logistics, this paper takes into consideration both seasonal and spatial temperature variations. At the beginning of our logistics process, hospitals and first-tier suppliers issue orders. The supply chain department of the pharmaceutical company then determines the mode of transportation according to the order, taking into account the temperature zone and current season of the customer node. Once the decision is made, the goods are transported either by a refrigerated truck or van equipped with a refrigerated box from the pharmaceutical factory to each customer’s location. The specific flowchart is shown in
Figure 1.
3.2. Model Assumptions
To ensure that the problem is solved with the minimum comprehensive cold chain logistics cost under the known customer demand and to maintain the maximum vehicle capacity with fixed cost and carbon emissions in each region, for the actual problem, the following assumptions are made.
- (1)
The information of all customers is known. The locations of the pharmaceutical plant and customers are fixed, and the delivery demand of each customer is provided.
- (2)
Each customer’s order cannot be divided into several delivery missions, and each customer can only be served for once.
- (3)
Road congestion or traffic jams are left out, so the transport vehicle can deliver at a constant speed and reach the area specified by the customer.
- (4)
Excluding the carbon emissions caused by the operation of the pharmaceutical plant, only the carbon emissions generated during transportation are taken into account.
- (5)
The maximum weight of each customer’s demand cannot exceed the loading capacity of the carrier vehicle.
- (6)
Every carrier vehicle departs from the pharmaceutical factory and eventually returns to it after passing through each customer point.
- (7)
The pharmaceutical company has sufficient stock to cope with the demand of every customer.
- (8)
There is no malfunction of the Probability Density Function (PDF) thermometer and no deterioration of the drugs during transportation.
3.3. Model Parameters
For a more intuitive representation of the model, the tables of the setup parameters and variables are shown in
Table 1 and
Table 2, respectively.
3.4. Analysis of Decision Variables
In order to reduce the costs and carbon emissions in the distribution process, we propose a dual distribution model that uses both refrigerated trucks and van-loaded refrigerated containers based on the specific demands of each regional customer point. To determine the most cost-efficient mode of distribution for each customer point, we calculate the costs associated with each option. For example, the total transportation cost for a 1013 km route using a refrigerated truck is RMB 3054, which includes the fixed costs as well as the fuel costs and carbon taxes. The additional costs include the use of reefer boxes, disposable PDF thermometers, refrigerant storage, and vehicle transportation, which total RMB 54.6 per piece of a drug. Based on this calculation, we select refrigerated trucks for transportation when the demand exceeds 56 pieces and vans with refrigerated boxes when the demand is less than or equal to 56 pieces.
We set the cost of transporting refrigerated trucks in the region as
and the cost of transporting refrigerated containers in vans as
; see Equations (1) and (2), respectively.
The choice of distribution method is made after calculating the demand cost in the region, and the decision variable
is expressed as follows:
The pharmacy number is set to 0, and each customer node is denoted by
i,
j (
i,
j = 1, 2, 3, …, N). The decision variables
,
,
, and
are denoted as follows:
Considering the regional and seasonal temperature variance, carrier vans need to place a corresponding quantity of refrigerants. The quantity of refrigerants required is influenced by the annual average and seasonal temperature variations. To clarify this concept, the domestic annual average isotherm map [
28] (
Figure 2) and the refrigerant storage use table (
Table 3) are presented below. The temperature data are collected from the China Meteorological Center Yearbook [
29], and the isotherm is generated by ArcMap.
Taking the values of 0, 1, 2, 3, 4, and 5 for each season of refrigerant storage use in each region in the table, the decision variable
is expressed as follows:
If we use six blocks of refrigerant accumulators, we cover the inner walls of the refrigerator and the upper part and lower part of the medicine. For seven blocks, we add one block to the topside of the refrigerator. For eight blocks, we put two accumulators in the slots of the box and around the whole circumference of the medicine. For nine blocks, we add one block to the topside of the refrigerator. Furthermore, for 10 blocks, we place accumulators in all the slots around the refrigerator and around the whole circumference of the medicine.
As mentioned previously, the number of refrigerant accumulators must be adjusted to accommodate temperature fluctuations. If customers are located in multiple temperature zones, changes in refrigerant storage must be taken into account. Specifically, when a van with a refrigerated box travels from a low-temperature zone to a high-temperature zone, an additional refrigerant accumulator must be added. On the other hand, if the van travels from a high-temperature zone to a low-temperature zone, no additional accumulators are necessary.
3.5. Cost Analysis
3.5.1. Fixed Costs ()
To provide pharmaceutical plant services to each customer point, either refrigerated trucks or vans with refrigerated boxes are used. This method incurs comprehensive costs, including fixed and depreciation costs. If vans with refrigerated boxes are utilized, then additional expenses are incurred for the refrigerated box, including depreciation costs, fixed refrigerant usage costs, and disposable PDF temperature agent usage costs. (The new version of GSP implementation requires thermometer tracking for each box). These costs are shown in Equation (3).
where
,
indicates 1 when the pharmacy uses refrigerated trucks
or vans
, otherwise it indicates 0;
is the choice of refrigerated trucks or vans for distribution, and
indicates the current season and the amount of refrigerant storage used.
3.5.2. Transportation and Carbon Emissions Costs ()
The cost of this segment is divided into two stages: the transportation vehicle transportation cost
and the carbon emissions cost
, where
is the product of the distance traveled by the transportation vehicle and the unit transportation cost of the transportation vehicle, as shown in Equation (4).
The calculation of carbon emissions cost
in this paper is based on the fuel conversion factor in the Greenhouse Gas Inventory Protocol [
30], which is 2.676 kg
/L for analysis, and we set the carbon dioxide emissions as the product of the fuel consumption and fuel conversion factor. Meanwhile, the fuel consumption rate is determined by the distanced traveled and the loading condition of the carrier vehicle, as shown in Equation (5).
Therefore, the cost of the carbon emissions is
7. Conclusions
In this study, we developed an improved mathematical model for pharmaceutical cold chain logistics path optimization that considers both comprehensive cost and carbon emissions reduction. To effectively classify delivery methods, we constructed comparison functions. We optimized the grey wolf algorithm by introducing a nonlinear factor and accounting for seasonal and spatial temperature variations to specify the use of refrigerant accumulators.
Our numerical experiment using full-scale example data verified that our improvements resulted in increased accuracy and efficiency for cold chain logistics. The decision time and route length were algorithmically reduced by 16.88% and 8.11%, respectively. Practically, we saved 7.73% of the conventional comprehensive cost and, remarkably, reduced over one-third of the overall carbon emissions. Therefore, our innovative dual distribution method application was found to be more effective in improving cold chain logistics capacity than the mathematical method optimization.
From a management perspective, the findings of this study hold significant implications for the pharmaceutical industry. The 2030 Agenda for Sustainable Development emphasizes the need to guarantee affordable and high-quality medicines for all. Ensuring the safety and effectiveness of these medicines is crucial, particularly in developing nations where the infrastructure may be inadequate. Therefore, optimizing cold chain logistics using innovative methods, such as the dual distribution approach suggested in this study, can make a substantial contribution toward achieving the Sustainable Development Goals.
However, our research identified several neglected issues and operational limitations in pharmaceutical cold chain logistics. Based on our findings, there are managerial insights for future research within pharmaceutical cold chain logistics:
While the dual distribution method proposed in this study mitigates temperature variation in cold chain logistics, it overlooks other factors that impact logistics quality, such as the human costs associated with loading and unloading longer routes. Future efforts should undertake a more comprehensive analysis that simultaneously evaluates all factors.
Our example data analysis illustrates the effectiveness of our algorithm on a larger scale. However, our distribution method remained unchanged from the original scenario. Therefore, further consideration of the transportation modes is necessary. For instance, we can utilize different types of carrier vehicles in a single long route to dynamically adjust our vehicle type according to customer demand variations.
Our study, along with other current research, assumes that there will be no emergencies during cold chain logistics. However, customer nodes along longer routes can significantly change, leading to massive node variations that can cause systematic inefficiencies in logistics optimization. As such, further optimization of the self-repairing mechanisms is necessary. Dynamic route optimization can be introduced into our model to address possible dynamic customer nodes and demand variations.
In conclusion, this study provides valuable insights into optimizing pharmaceutical cold chain logistics from both cost and carbon emissions reduction perspectives. Nonetheless, additional research is required to create more comprehensive models that consider all relevant variables, including those associated with human factors and emergency situations. Adopting such models will enable the industry to achieve greater efficiency and sustainability and contribute toward achieving the objectives of the 2030 Agenda for Sustainable Development.