Optimizing Cold Chain Logistics with Artificial Intelligence of Things (AIoT): A Model for Reducing Operational and Transportation Costs

Abstract

This paper discusses the modeling and solution of a cold chain logistics (CCL) problem using artificial intelligence of things (AIoT). The presented model aims to reduce the costs of the entire CCL network by maintaining the minimum quality of cold products distributed to customers. This study considers equipping distribution centers and trucks with IoT tools and examines the advantages of using these tools to reduce logistics costs. Also, four algorithms based on artificial intelligence (AI), including Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Gray Wolf Optimizer (GWO), and Emperor Penguin Optimizer (EPO), have been used in solving the mathematical model. The analysis results show that equipping trucks and distribution centers with the Internet of Things has increased the total costs by 15% compared to before. This approach resulted in a 26% reduction in operating costs and a 60% reduction in transportation costs. As a result of using the Internet of Things, total costs have been reduced by 2.78%. Furthermore, the performance of AI algorithms showed that the high speed of these algorithms is guaranteed against the high accuracy of the obtained results. So, EPO has achieved the optimal value of the objective function compared to a 70% reduction in the solution time. Further analyses show the effectiveness of EPO in the indicators of average objective function, average RPD error, and solution time. The results of this paper help managers understand the need to create IoT infrastructure in the distribution of cold products to customers. Because implementing IoT devices can offset a large portion of transportation and energy costs, this paper provides management solutions and insights at the end. As a result, there is a need to deploy IoT tools in other parts of the mathematical model and its application.

1. Introduction

While globalization has made the relative distance between world regions much smaller, the physical separation of these regions is still a very important reality. Physical separation may cause many human and financial losses in transportation operations. Some goods may be damaged during transportation and not kept at a suitable temperature [1]. In this case, this product will be destroyed, and if used again, it will cause loss of life. For a wide range of food, medicines, and vaccines, their quality decreases over time, and therefore, it is necessary to transport them from one point to another with the right vehicles in the right way and at the right time. These transportation operations are summarized and defined in a cold-chain logistics network [2]. A supply chain is defined as a concept for managing the flow of goods from suppliers to customers, which includes all operations, including sourcing raw materials, manufacturing products, and distributing and storing products. In a supply chain, strategic and tactical decisions are usually made simultaneously, which increases its complexity. In these models, each level of supplier, production center, distribution center, and customer can be considered as a node [3].

Transporting such products and goods along a supply chain that mainly includes suppliers, manufacturers, warehouses, and final consumers is very difficult. Especially when there is uncertainty in the amount of product demand, failure to accurately estimate the amount of demand can affect the production and supply of perishable goods and result in high costs due to product destruction. Today, the use of IoT tools has been able to largely estimate the exact amount of demand according to customers’ needs [4].

Due to the perishable nature of these products, their freshness decreases continuously; this model aims to maintain the minimum freshness of food delivered to final consumers during CCL. The most important issue in such networks is achieving the number of decision variables, including the mode of transportation and choosing the right refrigerated truck. Today, with the emergence of new technologies such as the IoT and AI, the cold products industry has also been affected from production to distribution [5]. The IoT means connecting everything to the Internet. CCL actors use IoT tools, such as electronic devices and software, sensors, and actuators, to reduce transportation and production costs, improve quality, increase production efficiency, reduce production errors, reduce delivery time, etc. [6]. The simultaneous use of IoT tools and AI has created a new concept called AIoT, which has improved the performance of the supply chain [7]. This has made a conceptual model for CCL based on the AIoT to be proposed in this paper. The proposed model aims to distribute cold products appropriately while maintaining minimum quality to customers in an AIoT-based supply chain.

The model presented in this research takes strategic and tactical decisions simultaneously. In strategic decisions, the location of distribution centers and deployment of IoT tools in those centers is considered, and in tactical decisions, optimal vehicle routing is important in a way that guarantees minimum product quality. The issue of which product, from which distribution center, with which vehicle, and how it will be delivered to customers shows the importance of this issue. Making the above optimal decisions is aimed at reducing the total costs of the mathematical model. The total costs incurred on the mathematical model in this paper include the costs of locating distribution centers, the costs of establishing the IoT, the costs of vehicle routing, and the savings due to the implementation of IoT tools in the mathematical model.

This paper attempts to answer the question of how to provide a model for cold chain logistics based on the Internet of Things that, in addition to maintaining the quality and freshness of cold items, reduces total costs. In addition, what is the impact of artificial intelligence-based algorithms in the presented mathematical model?

This paper is divided into six sections. The second section covers the literature review and the research gap. The third section presents a conceptual model of a CCL based on the AIoT. In addition to the mathematical model, this section also presents AI algorithms. The fourth section discusses the analysis of different numerical examples and the algorithms’ efficiency. Finally, the fifth and sixth sections discuss the conclusions and management suggestions.

2. Literature Review

Recently, many researches have been conducted in the field of CCL, which can be referred to [8,9] in the field of optimization of CCL efficiency, [10] in the field of cold chain integrity and accurate control, [11,12,13,14] in the field of CCL with IoT; [15,16,17] in the field on location-routing in CCL network.

Daofang et al. [18] designed a CCL distribution network to reduce agricultural product distribution losses and total costs. This paper uses the concept of service radius to convert the transportation time between logistics nodes into the service radius of logistics nodes. The model results showed the effect of cost reduction on the distribution of vegetables. Considering time window constraints, Liu et al. [19] modeled a CCL distribution network. The results of this mathematical model show the effective use of logistics resources, leading to savings in logistics space and human resources and improving distribution capacity. Kogler et al. [20] presented a supply chain optimization model in the wood industry to reduce total costs. They studied distribution and vehicle routing strategies and identified the most optimal mode of transportation and purchasing of items. Matskul et al. [21] designed a real science problem of optimizing the performance of a CCL network. This paper deals with the minimization of total costs and the minimization of environmental costs (along with negative environmental consequences). The results showed that when the Nash equilibrium conditions are met, the mathematical model for optimizing the total costs of the logistics network is reduced to a convex (quadratic) programming problem.

Bai et al. [22] developed a mathematical optimization model considering distribution cost and carbon emissions. They used the modified NSGA II algorithm to form the Pareto front. The results of this study showed that this model can more accurately evaluate the costs of distribution and carbon emission than the models that do not consider the real-time traffic conditions in the actual road network. Nozari et al. [23] addressed optimizing total logistics costs, including fuel consumption, carbon emissions, product disposal, fines, operating warehouses, and fleet rental in a multi-path location routing problem. They used a memetic algorithm. The proposed model and algorithms were applied to real-world cases in Hangzhou, China, and their practical application was demonstrated. Li and Li [24] presented a CCL distribution model considering customer satisfaction, which included a multi-objective model (minimum carbon transaction cost, minimum network cost, and maximum customer satisfaction). They used an NSGA-II and differential mutation. Experimental data show that the proposed approaches effectively increase customer satisfaction, reduce total distribution costs, and promote energy conservation and emission reduction.

Das et al. [25] introduced an intelligent and secure network model aimed at determining the optimal route for cold chain logistics (CCL) to hospitals. Their CCL framework focuses on hospitals that require drugs and vaccines to be stored at specific temperatures. To address this, they applied the bee-ant optimization algorithm and compared its performance against the bee colony optimization and ant colony optimization algorithms. The findings revealed that their proposed algorithm achieved an impressive accuracy of 98.83% in ensuring precise logistics delivery to hospitals. Bathaee et al. [26] explored the design of a CCL network for fresh agricultural products, emphasizing aspects such as cold storage capacity, storage location, and transportation from production sites to cold stores. They developed a two-level planning model accounting for the degradation in agricultural product quality. Using the Karush-Kuhn-Tucker (KKT) method, they transformed the two-level model into a single-level optimization model. Moghaddasi et al. [27] presented a hybrid non-linear scheduling-routing model to enhance CCL network design by integrating Balanced Scorecard (BSC) dimensions. Their approach prioritized maximizing customer satisfaction while minimizing unit costs and greenhouse gas emissions. Fuzzy programming was employed to manage uncertainties in the parameters. The proposed model assists supply chain managers in selecting the optimal number of distribution centers and identifying the most cost-effective routes to minimize overall system expenses.

Kogler and Rauch [28] investigated multimodal routing models for goods distribution, highlighting that deploying up to 25% additional trucking capacity during peak periods could prevent a 73% value reduction. Recent research has also explored the application of machine learning in logistics. Tsolaki et al. [29] reviewed cutting-edge applications in freight transportation, supply chain, and logistics, focusing on areas such as arrival time estimation, demand forecasting, industrial process optimization, traffic flow management, location prediction, vehicle routing problems, and anomaly detection in transportation data. Ma et al. [30] proposed a vehicle routing model utilizing an ant colony algorithm to minimize distribution costs while maximizing customer satisfaction. Their findings demonstrated the model’s effectiveness in supporting China’s sustainable cold chain logistics (CCL) development. Similarly, Rahmanifar et al. [17] introduced an integrated location and routing model for CCL networks, aiming to minimize total costs associated with transportation, facility location, and delivery delays. They applied the epsilon constraint method and multi-objective evolutionary algorithms (MOEA) to construct the Pareto front. Ye [31] developed a cold supply chain demand forecasting framework using deep neural networks. The proposed method, based on Bayesian Multilayer Networks (BNN), forecasted short-term e-commerce demand while incorporating a cold supply chain optimization technique for inventory management. Wan and Zheng [32] optimized CCL network structures using genetic algorithms, confirming the feasibility and effectiveness of their model through case studies. Their research contributes significantly to advancing the CCL industry. He et al. [33] tackled a new electric vehicle routing problem with a soft time window, where goods requiring different temperature layers were distributed simultaneously using insulated cold storage boxes in electric vehicles. The model, leveraging an ant colony optimization algorithm, aimed to reduce transportation costs. Results indicated that distributing multiple temperature-sensitive goods simultaneously improved both cost efficiency and operational effectiveness.

A literature review shows that various models have been presented in the supply chain and total cost reduction. These issues can be seen in various industries such as electronic components, automotive, pharmaceutical, wood, food, etc. What is of great importance, which researchers have paid less attention to today, is the implementation of the Internet of Things in the form of an optimization model. Various studies on machine learning and the Internet of Things have been presented in conceptual models, but what is important is how to apply and use it mathematically effectively. Therefore, relying on this issue and the issue of maintaining the quality of cold items, which is still neglected in mathematical optimization models, this article presents a mathematical model in the field of CCL based on the Internet of Things. On the other hand, various methods have been used in various studies to solve the problem, referred to as exact methods such as branch and bound, figure and price, etc., heuristic and meta-heuristic algorithms. In this article, algorithms based on artificial intelligence have been used to achieve faster and better results due to the NP-hard nature of routing models.

3. Mathematical Model of CCL Based on AIoT

This section presents a mathematical model of CCL based on AIoT. This mathematical model aims to minimize the total costs of delivering items to customers through distribution centers in a location-routing problem where refrigerated trucks and distribution centers can be equipped with different IoT tools. To explain this problem, several distribution centers have been considered, according to Figure 1, and locating and equipping them with IoT tools are strategic decisions. Each distribution center is equipped with several refrigerated trucks that distribute products to customers through the problem of vehicle routing. The second category includes tactical decisions, such as how to route the vehicle and equip it with IoT tools.

One of the most important decisions made in this mathematical model is the distribution of products to customers so that the minimum quality of the products is guaranteed at the moment of delivery. According to the literature on the subject and based on Figure 2, the longer the delivery time of the products to the customers, the lower the quality [34]. Therefore, using IoT tools in vehicle routing is considered an option for faster delivery of products in the mathematical model. Strategic and tactical decisions are made simultaneously and through AI algorithms.

Figure 2 shows that the shorter the shelf life of the products, the lower the quality over time. Therefore, speeding up the delivery time of products in CCL is very important. The mathematical model of CCL based on the IoT is presented based on the following assumptions.

• Equipping distribution centers and refrigerated trucks with IoT tools is possible.
• Equipping trucks with the IoT leads to optimal routing and, of course, reducing transportation costs.
• Equipping distribution centers with the IoT leads to the reduction of operating costs, including (energy costs, human resources costs, etc.).
• The capacity of distribution centers and trucks is already known.
• There is an inverse exponential relationship between quality and delivery time of products.
• At least the minimum quality of the CCL network must be guaranteed.
• Customer demand for different cold products should be estimated.

Based on the above assumptions, the mathematical symbols for modeling the problem are presented as follows.

Sets

$I$	Set of problem nodes
$J\subset I$	Set of distribution centers $j\in \{\mathrm{1,2},\dots ,J\}$
$K\subset I/\left\{J\right\}$	Set of customer $k\in \{J+1,J+2,\dots ,J+K\}$
$P$	Set of perishable products $P\in \{\mathrm{1,2},\dots ,P\}$
$V$	Set of heterogeneous refrigerated trucks $v\in \{\mathrm{1,2},\dots ,V\}$
$T$	Set of IoT tools $t\in \{\mathrm{1,2},\dots ,T\}$

Parameters

$f_j$	$\mathrm{Fixed}\cos \mathrm{t}\mathrm{of}\mathrm{distribution}\mathrm{center}j\in J$
$g_v$	$\mathrm{Fixed}\cos \mathrm{t}\mathrm{of}\mathrm{using}\mathrm{the}\mathrm{truck}v\in V$
$f_{jt}^{\prime }$	$\mathrm{The}\cos \mathrm{t}\mathrm{of}\mathrm{deploying}\mathrm{the}\mathrm{IoT}\mathrm{tool}t\in T\mathrm{in}\mathrm{the}\mathrm{distribution}\mathrm{center}j\in J$
$g_{vt}^{\prime }$	$\mathrm{The}\cos \mathrm{t}\mathrm{of}\mathrm{deploying}\mathrm{the}\mathrm{IoT}\mathrm{device}t\in T\mathrm{in}\mathrm{the}\mathrm{truck}v\in V$
$o_j$	$\mathrm{Operating}\cos \mathrm{ts}\mathrm{of}\mathrm{distribution}\mathrm{center}j\in J$
${\rho }_v$	$\mathrm{Transporting}\cos \mathrm{t}\mathrm{of}\mathrm{products}\mathrm{per}\mathrm{kilometer}\mathrm{by}\mathrm{truck}v\in V$
$s_v$	$\mathrm{The}\mathrm{average}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{truck}\mathrm{is}v\in V$
${\alpha }_{jt}$	$\mathrm{The}\mathrm{operating}\mathrm{cost}\mathrm{reduction}\mathrm{factor}\mathrm{of}\mathrm{the}\mathrm{distribution}\mathrm{center}j\in J$ due to the use of the IoT tool $t\in T$
${\beta }_{vt}$	$\mathrm{The}\mathrm{reduction}\mathrm{factor}\mathrm{of}\mathrm{truck}\mathrm{transportation}\cos \mathrm{t}v\in V$ due to the use of IoT tool $t\in T$
${\phi }_p$	$\mathrm{Shelf}\mathrm{life}\mathrm{of}\mathrm{product}p\in P$
$\psi$	Minimum quality of the CCL network
${\gamma }_{i{i}^{\prime }}$	$\mathrm{Distance}\mathrm{between}\mathrm{node}i\in I\mathrm{and}{i}^{\prime }\in I$
${\theta }_{vp}$	$\mathrm{Truck}\mathrm{capacity}v\in V\mathrm{from}\mathrm{product}p\in P$
${\delta }_{jp}$	$\mathrm{Capacity}\mathrm{of}\mathrm{distribution}\mathrm{center}j\in J\mathrm{of}\mathrm{product}p\in P$
$d_{kp}$	$\mathrm{Demand}\mathrm{of}\mathrm{product}p\in P\mathrm{for}\mathrm{customer}k\in K$

Decision making variables

$Z_j$	1; If the distribution center $j\in J$ is chosen. 0; otherwise.
$R_v$	1; If truck $v\in V$ is selected. 0; otherwise.
$Z_{jt}^{\prime }$	1; If the distribution center $j\in J$ is equipped with the IoT tool $t\in T$. 0; otherwise.
$R_{vt}^{\prime }$	1; If truck $v\in V$ is equipped with IoT device $t\in T$. 0; otherwise.
$X_{i{i}^{\prime }v}$	1; If truck $v\in V$ travels between node $i\in I$ and $i^{\prime }\in I$. 0; otherwise.
$Y_{jkv}$	1; If customer $k\in K$ is assigned to distribution center $j\in J$ and truck $v\in V$. 0; otherwise.
$F_{kp}$	Product quality $p\in P$ at the moment of its delivery to customer $k\in K$

By defining the symbols of the problem, the mathematical model of CCL based on IoT is as follows:

$$\begin{array}{c}MinCost={\displaystyle \sum _{j\in J}}{f}_j{Z}_j+{\displaystyle \sum _{v\in V}}{g}_v{R}_v+{\displaystyle \sum _{j\in J}}{\displaystyle \sum _{t\in T}}{f}_{jt}^{\prime }{Z}_{jt}^{\prime }+{\displaystyle \sum _{v\in V}}{\displaystyle \sum _{t\in T}}{g}_{vt}^{\prime }{R}_{vt}^{\prime }+{\displaystyle \sum _{i\in I}}{\displaystyle \sum _{i^{\prime }\in I}}{\displaystyle \sum _{v\in V}}{\rho }_v{\gamma }_{i{i}^{\prime }}{X}_{i{i}^{\prime }v}\\ +\left({\displaystyle \sum _{j\in J}}{o}_j{Z}_j-{\displaystyle \sum _{j\in J}}{\displaystyle \sum _{t\in T}}{\alpha }_{jt}{o}_j{Z}_{jt}^{\prime }\right)-{\displaystyle \sum _{i\in I}}{\displaystyle \sum _{i^{\prime }\in I}}{\displaystyle \sum _{v\in V}}{\displaystyle \sum _{t\in T}}{\beta }_{vt}{\rho }_v{\gamma }_{i{i}^{\prime }}{XR}_{i{i}^{\prime }vt}\end{array}$$

(1)

$$s.t:$$

$${\displaystyle \sum _{v\in V}}\sum _{i\in I}{X}_{ikv}=1,\forall k\in K$$

(2)

$${\displaystyle \sum _{j\in J}}{\displaystyle \sum _{k\in K}}{X}_{jkv}\le 1,\forall v\in V$$

(3)

$${\displaystyle \sum _{i\in I}}{X}_{jiv}-{\displaystyle \sum _{i\in I}}{X}_{ijv}=0,\forall v\in V,j\in I$$

(4)

$${\displaystyle \sum _{i\in I}}\left(X_{jiv}+X_{ikv}\right)\le 1+Y_{jkv},\forall j\in J,k\in K,v\in V$$

(5)

$${\displaystyle \sum _{k\in K}}{d}_{kp}{Y}_{jkv}\le {\theta }_{vp}{R}_v,\forall j\in J,v\in V,p\in P$$

(6)

$${\displaystyle \sum _{k\in K}}{\displaystyle \sum _{v\in V}}{d}_{kp}{Y}_{jkv}\le {\delta }_{jp}{Z}_j,\forall j\in J,p\in P$$

(7)

$$R_{vt}^{\prime }\le R_v,\forall v\in V,t\in T$$

(8)

$$Z_{jt}^{\prime }\le Z_j,\forall j\in J,t\in T$$

(9)

$$F_{kp}\ge 100e^{-{\displaystyle \frac{{\gamma }_{jk}}{s_v{\phi }_p}}}-M\left(1-Y_{jkv}\right),\forall j\in J,k\in K,v\in V,p\in P$$

(10)

$$F_{k^{\prime }p}\ge F_{kp}-100\left(1-e^{-{\displaystyle \frac{{\gamma }_{k{k}^{\prime }}}{s_v{\phi }_p}}}\right)-M\left(2-X_{k{k}^{\prime }v}-Y_{jkv}\right),\forall j\in J,k,k^{\prime }\in K,v\in V,p\in P$$

(11)

$$F_{kp}\ge \psi ,\forall k\in K,p\in P$$

(12)

$${XR}_{i{i}^{\prime }vt}-X_{i{i}^{\prime }v}-\left(1-R_{vt}^{\prime }\right)\ge -{\displaystyle \frac{3}{2}},\forall i,i^{\prime }\in I,v\in V,p\in P$$

(13)

$${\displaystyle \frac{3}{2}}{XR}_{i{i}^{\prime }vt}-X_{i{i}^{\prime }v}-\left(1-R_{vt}^{\prime }\right)\le 0,\forall i,i^{\prime }\in I,v\in V,p\in P$$

(14)

$$Z_j,R_v,Z_{jt}^{\prime },R_{vt}^{\prime },X_{i{i}^{\prime }v},Y_{jkv}\in \left\{\mathrm{0,1}\right\}$$

(15)

$$F_{kp}\ge 0$$

(16)

Equation (1) shows the total cost function of CCL. The first and second expressions show the fixed costs of choosing the distribution center and the fixed cost of using the truck, respectively. The third and fourth terms show the costs of deploying IoT devices in selected distribution centers and trucks. The fifth term shows the costs of transporting products by trucks. The sixth term shows the operational cost of distribution centers and the reduction of its costs through IoT tools. The seventh term also shows the reduction of transportation costs due to using IoT tools in optimal routing. Equation (2) guarantees that each customer is assigned to only one distribution center and one truck. Equation (3) guarantees that each tour should be assigned to at most one type of truck. Equation (4) shows that if a truck enters a node, it must leave that node to another destination. Equation (5) shows that the truck assigned to a tour returns to the distribution center after visiting customers. Equation (6) guarantees that the amount of product moved by each truck will be less than the total demand of the allocated customers. Equation (7) guarantees that the amount of product distributed by each distribution center will be less than its capacity. Equation (8) shows that if a type of truck is selected, it is possible to equip it with IoT tools. Equation (9) shows that if the distribution center is selected, it can be equipped with IoT tools. Equations (10) and (11) calculate the quality of the distributed product in terms of product durability. Equation (12) shows the minimum quality of the CCL network. Equations (13) and (14) are related to the linearization of the mathematical model. Equations (15) and (16) show the type of decision variables.

The model developed in this paper is location-routing-based in CCL. Therefore, AI algorithms have been used to analyze the model developed in this paper. The AI algorithms used in this paper include GA, PSO, GWO, and EPO.

The proposed AI algorithms are an intelligent technique for solving the optimization problem. These algorithms are based on human behavior, physics, and AI, requiring a basic solution for implementation. The initial solution is used as a string of numbers to form the justified space of the problem and to achieve the optimal value of the objective function. Therefore, the initial solution is a string of random numbers as long as the nodes of the mathematical model (|J|+|K|+|V|). |J| The number of distribution centers, |K| number of customers and |V| The number of trucks is defined. Figure 3 shows an example of the initial solution for three distribution centers, six customers, and three trucks.

Due to the continuous search nature of AI algorithms, random data is first transformed into discrete data. In Figure 3, the smallest random number is selected for each section, and the value one is assigned. Then, the following smallest number is selected, and the value two is assigned to it. This procedure continues until all random numbers have been converted to discrete data. An algorithm, according to Figure 4, is defined to decode the initial solution and convert it into decision variables.

According to the algorithm presented in Figure 4, the initial solution of AI algorithms is decoded. This means that the value of the decision variables of the problem is determined based on this algorithm, and the costs of the entire CCL network are calculated. Based on the operators of each algorithm based on AI, improvement in the value of the objective function and decision variables is possible. Figure 5, Figure 6, Figure 7 and Figure 8 show the flowchart of each AI algorithm used in this paper to solve the CCL problem.

GA: A genetic algorithm evolves a population of candidate solutions to optimize a problem. Starting with a random population, each generation undergoes fitness evaluation, selection of fitter individuals, and genome modifications (recombination and mutation) to create the next generation. The process continues until reaching a defined number of generations or a satisfactory fitness level.

Figure 5. Flowchart of GA algorithm [35].

Figure 5. Flowchart of GA algorithm [35].

Figure 6. Flowchart of PSO algorithm [36].

Figure 6. Flowchart of PSO algorithm [36].

Figure 7. Flowchart of GWO algorithm [37].

Figure 7. Flowchart of GWO algorithm [37].

PSO: article Swarm Optimization (PSO) is an iterative method for solving optimization problems. It uses a population of particles that move through the search space, guided by their local best-known positions and the swarm’s global best position. This process directs the swarm toward optimal solutions.

The velocity of each particle and, consequently, its new position changes according to relations (17) and (18).

$$V_i^{t+1}=w{V}_i^t+c_{1}rand\left({pbest}_i-X_i^t\right)+c_{2}rand({gbest}_i-X_i^t)$$

(17)

$$X_i^{t+1}=X_i^t+V_i^{t+1}$$

(18)

where $V_i^{t+1}$ is the velocity of particle i in the new iteration t, $V_i^t$ is the velocity of particle i in the current iteration t, $X_i^{t+1}$ is the current position of particle t + 1, $X_i^t$ is the particle’s position in the new iteration, pbesti is the best position that particle i has taken so far, and gbesti is the best position of the best particle (the best position that all particles have taken so far). Rand is a random number between zero and one used to maintain the diversity and variety of the group. $C_1$ and $C_2$ are the cognitive and social parameters, respectively. Choosing the right value for these parameters will accelerate the algorithm’s convergence and prevent premature convergence in local optima. The parameter w is called the inertia weight, and it is used to ensure convergence in the particle group.

GWO: The GWO mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. Four types of grey wolves, alpha, beta, delta, and omega, are employed to simulate the leadership hierarchy. In addition, three main steps- hunting, searching for prey, encircling prey, and attacking prey- are implemented to perform optimization. In order to mathematically model the social hierarchy of wolves when designing GWO, we consider the fittest solution as the alpha (α). Consequently, the second and third best solutions are beta (β) and delta (δ), respectively. The remaining candidate solutions are assumed to be omega (ω). The GWO algorithm guides the hunting (optimization) by α, β, and δ. The ω wolves follow these three wolves [37].

As mentioned above, grey wolves encircle prey during the hunt. In order to mathematically model encircling behavior, the following equations are proposed:

$$\overrightarrow{D}=|\overrightarrow{C}·\overrightarrow{X_p}\left(t\right)-\overrightarrow{X}(t)|$$

(19)

$$\overrightarrow{X}\left(t+1\right)=\overrightarrow{X}\left(t\right)-\overrightarrow{A}·\overrightarrow{D}$$

(20)

where t t indicates the current iteration, $\overrightarrow{A}$ A → and $\overrightarrow{C}$ C → are coefficient vectors, $\overrightarrow{X_p}\left(t\right)$ X p → is the position vector of the prey, and $\overrightarrow{X}\left(t\right)$ X → indicates the position vector of a grey wolf. The vectors A → C →, $\overrightarrow{A}$ A → and $\overrightarrow{C}$ are calculated as follows:

$$\overrightarrow{A}=2\overrightarrow{a}·\overrightarrow{r_1}-\overrightarrow{a}$$

(21)

$$\overrightarrow{C}=2\overrightarrow{r_2}$$

(22)

The above equations enable gray wolves to update their position around prey. As a result, the following equations are used to perform hunting.

$${\overrightarrow{D}}_{\alpha }=\left|{\overrightarrow{C}}_1·{\overrightarrow{X}}_{\alpha }-\overrightarrow{X}\right|,{\overrightarrow{D}}_{\beta }=\left|{\overrightarrow{C}}_2·{\overrightarrow{X}}_{\beta }-\overrightarrow{X}\right|,{\overrightarrow{D}}_{\delta }=\left|{\overrightarrow{C}}_1·{\overrightarrow{X}}_{\delta }-\overrightarrow{X}\right|$$

(23)

$${\overrightarrow{X}}_1={\overrightarrow{X}}_{\alpha }-{\overrightarrow{A}}_1·{\overrightarrow{D}}_{\alpha },{\overrightarrow{X}}_2={\overrightarrow{X}}_{\beta }-{\overrightarrow{A}}_2·{\overrightarrow{D}}_{\beta },{\overrightarrow{X}}_3={\overrightarrow{X}}_{\delta }-{\overrightarrow{A}}_3·{\overrightarrow{D}}_{\delta }$$

(24)

$$\overrightarrow{X}\left(t+1\right)={\displaystyle \frac{{\overrightarrow{X}}_1+{\overrightarrow{X}}_2+{\overrightarrow{X}}_3}{3}}$$

(25)

EPO: The emperor penguin, the largest penguin species, is distinguished by its black, white, and yellow plumage. These social birds breed in large colonies during winter, with females laying a single egg and traveling up to 50 miles to hunt. Emperor penguins can dive 1900 feet and remain underwater for over 25 min, using their stiff, flattened wings for swimming.

Emperor penguins are the only species that huddle to survive during the Antarctic winter. The huddling behavior of emperor penguins is decomposed into four phases [38]:

• Generate and determine the huddle boundary of emperor penguins.
• Calculate the temperature profile around the huddle.
• Determine the distance between emperor penguins.
• Relocate the effective mover.

Figure 8. Flowchart of EPO algorithm [39].

Figure 8. Flowchart of EPO algorithm [39].

An important feature of this huddling behavior is that each penguin has an equal opportunity to the warmth of the huddle.

After introducing AI algorithms to solve the mathematical model of CCL, several numerical examples were analyzed, and the efficiency of the algorithms was compared.

4. Analysis of the Mathematical Model Based on the IoT

4.1. Small-Size Numerical Example Analysis

The mathematical model for a cold chain logistics (CCL) network incorporating IoT technology addresses two key challenges: determining the location of capacity facilities and optimizing the routing of heterogeneous vehicles. This model is designed to minimize total costs by making decisions about the placement of distribution centers, the routing of refrigerated vehicles, and the equipping of both distribution centers and vehicles with various IoT tools. A small numerical example has been analyzed to evaluate the outputs and effectiveness of the proposed model.

The numerical example involves six customers, three distribution centers, three truck types, two product categories, and three IoT tool types. As shown in

Table 1. The value of the problem parameters according to the uniform distribution function.

Parameter	Value	Unit	Parameter	Value	Unit
$f_j$	$~U\left(10,000,12,000\right)$	$	${\alpha }_{jt}$	$~U($0.3, 0.6$)$	-
$g_v$	$~U(800,1000)$	$	${\beta }_{vt}$	$~U($0.3, 0.6$)$	-
$f_{jt}^{\prime }$	$~U(1500,2000)$	$	${\phi }_p$	$~U($10, 15$)$	H
$g_{vt}^{\prime }$	$~U(500,1000)$	$	$\psi$	65	%
$o_j$	$~U(200,300)$	$	${\gamma }_{i{i}^{\prime }}$	$~U(40,100)$	km
${\rho }_v$	$~U(5,15)$	$	${\theta }_{vp}$	$~U(1000,2500)$	kg
$s_v$	$~U(30,40)$	Km/h	${\delta }_{jp}$	$~U(10,000,30,000)$	kg
$d_{kp}$	$~U(250,300)$	kg

, the remaining problem parameters are generated randomly using a uniform distribution function. These parameters are derived from published research data and are designed to ensure the creation of a feasible and realistic problem space.

After setting the problem parameters, a small numerical example is run using CPLEX 12 on an Intel(R) Core (TM) i5-3470 CPU @ 3.20 GHz system. The optimal value of the total costs obtained in this example equals 19,253.86 US dollars in 94.45 s. The total costs of the mathematical model include location costs, vehicle selection, IoT infrastructure building, and operating costs. Figure 9 shows the costs of each department and the reduction of costs due to implementing the IoT. These are the outputs of the numerical example obtained from the CPLEC method.

Figure 9 shows that the highest costs incurred on the network are related to the fixed costs of choosing distribution centers. In this numerical example, $2975.51 was spent on equipping the IoT infrastructure, which resulted in a cost reduction of $3526.16. This problem shows that equipping the IoT infrastructure in CCL has included 15.45% of the total costs, which has reduced 26.85% in operating costs and 60% in transportation costs. Although equipping the IoT tool in the CCL network has increased costs, the total costs have decreased by 2.78% compared to not equipping the network with IoT tools.

Based on these analyses, the results of mathematical model decisions are presented in

Table 2. The optimal value of the decision variables of the numerical example of small-size.

Potential DC	Selected DC	Allocated IoT Tools to DC
$j_1,j_2,j_3$	$j_2$	-
	$j_3$	$t_3$
Potential Trucks	Selected Trucks	Allocated IoT tools to Trucks
$v_1,v_2,v_3$	$v_1$	$t_1,t_2$
	$v_2$	$t_2$

.

The results of Table 2 show that the distribution center (2) is not equipped with any IoT tools, while truck number (1) is equipped with two. Figure 10 shows the routing of trucks in the CCL network, and

Table 3. The quality of distributed products in a small numerical example using CPLEX.

Truck	Start Point	Routing $\mathbf{Quality}\mathbf{(}{\mathit{p}}_{\mathbf{1}}\mathbf{,}{\mathit{p}}_{\mathbf{2}}\mathbf{)}\mathbf{|}{\mathit{\phi }}_{\mathbf{1}} \mathbf{=} \mathbf{15}\mathbf{,}{\mathit{\phi }}_{\mathbf{2}} \mathbf{=} \mathbf{10}$					Finish Point
$v_1$	$j_3$	$k_4$ (92.61, 90.86)	$\to$	$k_5$ (81.16, 76.75)	$\to$	$k_3$ (71.19, 65.45)	$j_3$
$v_2$	$j_2$	$k_2$ (94.49, 93.16)	$\to$	$k_1$ (83.47, 79.59)	$\to$	$k_6$ (72.91, 66.56)	$j_2$

shows the quality of products distributed to customers.

According to Figure 10, because distribution center 1 was not chosen, no product distribution has been done through this center.

Table 3 shows that the minimum quality of the CCL network is equal to 65%, and the quality of the products at the moment of distribution is higher than this number. Considering the impact of product shelf life on quality-related equations, this sensitivity analysis is shown in Figure 11. In the results of the mathematical model obtained according to Figure 4, the model is unacceptable if the quality is less than the permissible limit. Re-routing must be done, and if the minimum quality is maintained, the model is acceptable.

The results of Figure 11 show that as the product’s shelf life increases, the product’s minimum quality at the moment of distribution also increases. Due to the limitation of the minimum quality of the entire network, when the product’s shelf life is 10 or 11 h, the quality is less than the limit, and therefore, the network is redesigned, and new truck routing is done. This issue has led to an increase in total costs by 8.21%.

In another analysis, changes in the cost of the entire CCL network under different amounts of demand have been investigated. Based on this, the amount of demand changes by ±10%, ±20%, and ±30%, and the total costs of the network are shown in Figure 12.

By examining the results of Figure 12, it can be seen that with the increase in demand, the total costs have increased due to the number of trucks and transportation costs. This analysis shows that with a 30% increase in demand, total costs have increased by 11.33%.

4.2. Analyzing a Small Numerical Example with Algorithms Based on AI

After reviewing the logistics model of the cold chain based on the IoT and its analysis, this section investigates AI algorithms such as (GA, PSO, GWO, and EPO) to solve the mathematical model. Therefore, before implementing the mathematical model and solving it with algorithms based on AI, the initial parameters of the algorithms have been adjusted.

Algorithm parameters have been adjusted using the Taguchi method to increase AI algorithms’ efficiency in achieving the objective function’s optimal value (the total costs of CCL based on the IoT). In this method, for each parameter, three levels are proposed by the decision maker, and achieving the optimal combination of levels of each algorithm is determined using the Means of SN Ratio chart. In this diagram, the higher the signal-to-noise value, the higher the parameter level can help the AI algorithm achieve the optimal value of the objective function. Figure 13 shows the Means of the SN Ratio diagram for AI algorithms used in this paper.

After setting the algorithms’ parameters, the small numerical example was optimized. The optimal value of this numerical example was 19,253.86 dollars. Therefore, the algorithms’ convergence in 200 repetitions is obtained in Figure 14.

Based on the results, EPO has achieved the numerical optimal value of 19,253.86 dollars in 23.14 s. GA, PSO, and GWO algorithms have achieved numerical values of 19,403.42, 19,451.20, and 19,314.38 for 22.48, 25.64, and 24.18 s, respectively. These results show that the maximum percentage of the relative difference between the obtained results is less than 1%, and the time to solve the problem has decreased by about 70%. This problem shows the high efficiency of AI algorithms in solving the CCL problem.

4.3. Analysis of a Large Numerical Example

The high efficiency of the AI algorithm compared to the exact methods has led to an investigation of the efficiency of these methods in ample numerical examples. Therefore, 15 numerical examples have been considered according to

Table 4. Size of numerical examples in larger size.

Sample Problem	$\left(\left|\mathit{J}\right|\mathbf{\times }\left|\mathit{K}\right|\mathbf{\times }\left|\mathit{P}\right|\mathbf{\times }\left|\mathit{V}\right|\mathbf{\times }\left|\mathit{T}\right|\right)$	Sample Problem	$\left(\left|\mathit{J}\right|\mathbf{\times }\left|\mathit{K}\right|\mathbf{\times }\left|\mathit{P}\right|\mathbf{\times }\left|\mathit{V}\right|\mathbf{\times }\left|\mathit{T}\right|\right)$
1	$(4\times 8\times 3\times 3\times 3)$	9	$(10\times 24\times 6\times 8\times 6)$
2	$(4\times 10\times 3\times 3\times 3)$	10	$(10\times 26\times 6\times 8\times 6)$
3	$(5\times 12\times 3\times 4\times 4)$	11	$(12\times 28\times 6\times 8\times 6)$
4	$(5\times 14\times 4\times 4\times 4)$	12	$(12\times 30\times 7\times 10\times 7)$
5	$(6\times 16\times 4\times 4\times 5)$	13	$(15\times 32\times 7\times 10\times 7)$
6	$(6\times 18\times 4\times 6\times 5)$	14	$(15\times 35\times 8\times 10\times 8)$
7	$(8\times 20\times 5\times 6\times 6)$	15	$(18\times 40\times 8\times 12\times 8)$
8	$(8\times 22\times 5\times 6\times 6)$

, which increases as the number of numerical examples increases. The sizes presented in Table 4 are designed to increase the number of decision variables in each numerical example. Also, the value of the parameters of each problem is random and based on the uniform distribution function, according to Table 1.

To reduce the calculation error, each numerical example is executed three times by each AI algorithm, and the lowest value of the objective function among the three executions is reported in

Table 5. The total cost of CCL is based on the AI algorithm.

Sample Problem	GA	PSO	GWO	EPO
1	22,578.66	22,752.02	22,568.40	22,743.71
2	24,637.01	24,994.96	24,830.12	24,773.48
3	28,700.88	28,898.05	28,639.51	28,463.25
4	32,025.15	31,977.58	31,916.65	31,996.74
5	33,226.66	32,963.75	33,069.36	32,967.86
6	36,671.18	36,641.42	36,401.62	36,640.89
7	38,277.41	37,720.64	37,997.56	38,007.52
8	38,621.28	38,664.54	38,414.08	38,731.60
9	41,903.64	41,687.78	41,738.45	41,891.86
10	43,395.43	43,195.34	43,093.24	42,717.62
11	45,804.59	46,092.97	45,637.99	45,237.60
12	48,557.79	49,132.25	48,662.82	48,424.79
13	50,480.66	50,930.18	50,440.43	49,949.86
14	55,246.67	54,422.19	54,935.01	54,619.23
15	58,269.60	58,710.85	58,686.21	58,872.91

. The time it takes for AI algorithms to solve numerical examples is also presented in Figure 15.

Table 5 shows that with the increase in the size of the problem, the number of customers in the logistics network has increased, and this problem has led to an increase in the amount of traffic, location of facilities, transportation costs, operational costs, and of course, total costs. This table shows that the average total costs among 15 numerical examples for the EPO algorithm are lower than other algorithms based on AI. The average RPD has been calculated to more accurately check the algorithms’ efficiency. Studies show that the average RPD of the EPO algorithm is 0.38%, the GWO algorithm is 0.5%, the PSO algorithm is 0.83%, and the GA algorithm is 0.73%. Therefore, the convergence of the EPO algorithm in solving the CCL problem based on the IoT is higher than that of other AI algorithms.

Figure 15. Time to solve the CCL based on the AI algorithm.

Figure 15. Time to solve the CCL based on the AI algorithm.

Figure 15 shows that the PSO algorithm has a high speed in achieving the solution close to the optimum. Thus, the average calculation time in the GA algorithm is equal to 127.32 s, in the PSO algorithm equal to 110.89 s, in the GWO algorithm equal to 137.35 s, and in the EPO algorithm equal to 118.57 s. The very close difference between the average computing time of EPO and PSO and the low RPD value of the EPO algorithm show that this AI algorithm has a higher efficiency in terms of computing time and is close to the optimal solution.

5. Discussion

Cold chain logistics ensures the integrity of perishable goods through temperature-controlled networks. With growing investments and a market expected to exceed $410 billion by 2028, research focuses on optimizing costs using mathematical models and IoT-based tools, highlighting the necessity of integrating advanced technologies to enhance efficiency and sustainability in supply chain operations.

This paper models a CCL problem by considering IoT tools and using artificial intelligence algorithms to solve it. The developed model combines two important problems: the location of high-capacity facilities and the routing of multi-storage vehicles. Since IoT tools are considered in location and routing, the resulting savings effect has been seen in the results. This position is consistent with previous research in the field of conceptual models of IoT applications, such as Tadejko [40]. The results also show that parameters such as demand affect total costs and change with increasing demand, location, routing, and costs. These changes lead to an increase in total costs and make managers’ decisions difficult. These results are consistent with the findings of Ghaderi et al. [41].

Cold chain logistics (CCL) systems ensure the efficient distribution of temperature-sensitive products while maintaining quality. This study’s integration of the Artificial Intelligence of Things (AIoT) into CCL optimization represents a significant step forward in addressing operational and cost-efficiency challenges. By combining IoT-enabled monitoring with advanced artificial intelligence (AI) algorithms, this research offers a robust framework for reducing costs, enhancing efficiency, and guiding managerial strategies.

One of this study’s key contributions is its focus on incorporating IoT tools in distribution centers and transportation vehicles to monitor and control operations dynamically. While IoT implementation initially increases costs by 15%, the findings reveal substantial long-term benefits, including a 26% reduction in operational costs and a 60% reduction in transportation costs. These savings ultimately lead to a net 2.78% reduction in total costs. This highlights the transformative potential of IoT in optimizing logistics systems and offsetting initial capital investments.

The deployment of advanced AI algorithms is another critical innovation in this study. Among the four algorithms applied—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Gray Wolf Optimizer (GWO), and Emperor Penguin Optimizer (EPO)—EPO emerged as the most effective. It achieved an optimal balance between computational speed and accuracy, reducing solution time by 70% while maintaining high performance in key indicators such as the objective function value and relative performance deviation (RPD) error. This demonstrates the capability of modern AI methods to address the computational complexity of logistics problems.

The research also underscores the importance of considering the holistic impact of IoT integration on the logistics network, moving beyond the narrow focus of traditional studies that concentrate solely on routing optimization. By evaluating the entire system, this study provides actionable insights into cost distribution and the potential for energy savings, which are critical for managers seeking to implement technology-driven strategies in CCL operations. The results reinforce the need for investment in IoT infrastructure to enhance overall efficiency and reduce long-term costs.

From a managerial perspective, the findings emphasize balancing initial investments with long-term benefits. The observed cost savings in operations and transportation validate the importance of adopting IoT tools, even for small and medium-sized enterprises. Managers are encouraged to view IoT not merely as a technological upgrade but as a strategic enabler of efficiency and competitiveness. Furthermore, the demonstrated efficiency of AI algorithms provides a reliable decision-support tool for optimizing resource allocation, routing, and system performance.

This study also highlights key areas for improvement and potential limitations. The initial cost increase associated with IoT deployment may deter organizations with limited budgets. While the long-term savings offset this investment, the need for financial and infrastructural readiness remains challenging. Additionally, while the study prioritizes cost and operational metrics, it underexplored environmental impacts. Considering the growing emphasis on sustainability, incorporating green metrics such as energy consumption, carbon emissions, and waste reduction into future analyses could broaden the applicability of the proposed framework.

Another limitation is the study’s scope, which focuses on general CCL systems without delving into specific contexts such as urban logistics. Urban environments present unique challenges, including congestion, delivery time constraints, and diverse customer demands. Adapting the proposed IoT-enabled framework to address these challenges could enhance its practical relevance and scalability. Moreover, exploring the implications of IoT deployment in areas such as inventory management, demand forecasting, and real-time decision-making offers promising directions for future research.

Integrating IoT and AI in this study provides a foundation for addressing the multifaceted challenges of CCL systems. The results demonstrate that technological innovation can significantly improve cost efficiency while maintaining quality standards. Managers can leverage these findings to make informed decisions about technology investments and strategic planning. At the same time, the study serves as a call for further exploration into IoT’s environmental and contextual implications in logistics.

Despite the operational benefits demonstrated in this study, integrating these strategies with IoT-enabled solutions could provide a more comprehensive framework for sustainable logistics. For example, IoT sensors can monitor and optimize energy usage in refrigeration systems, contributing to cost efficiency and reduced environmental impact. Future work should include lifecycle assessments of IoT devices and their contribution to overall sustainability goals. Moreover, expanding the scope of analysis to include emissions metrics and waste management would align with the broader objectives of green supply chain management.

Sensitivity analysis in cold chain logistics (CCL) helps optimize vehicle capacity and packaging strategies, reducing costs and extending product shelf life. IoT-enabled data recording enhances demand prediction, cutting expenses and improving efficiency. Mobile distribution centers offer flexibility, reducing fixed depot construction costs. However, IoT integration remains challenging, with limited exploration of multi-vehicle coordination and perishable product harvesting, both critical for quality and sustainability. These gaps highlight the need for further research to refine CCL optimization models, ensuring cost efficiency, environmental sustainability, and robust network performance. Addressing these challenges will advance future logistics systems.

In conclusion, this research showcases the potential of AIoT-driven optimization to transform cold chain logistics. Addressing operational costs, computational efficiency, and system-wide impacts provides a comprehensive framework for enhancing performance and sustainability. Future studies can build on this foundation by integrating environmental considerations, adapting to specific logistical contexts, and exploring additional IoT and AI technology applications. As CCL systems become increasingly complex, incorporating advanced tools and methods will remain vital for achieving cost-effective and sustainable solutions.

6. Conclusions

This paper discussed the modeling of a CCL problem based on the IoT and its solution with algorithms based on the AIoT. Specifically, the topic studied in this research was CCL based on AIoT. In the presented model, which was a combination of two problems of the location of capacity facilities and heterogeneous vehicle routing, strategic decisions (locating distribution centers and equipping them with IoT tools) and tactical decisions (routing trucks and equipping them with IoT tools) simultaneously are adopted. Making simultaneous choices for CCL is aimed at reducing the entire network’s costs. In the presented model, according to the type of cold chain products, the minimum quality of the network should be guaranteed, which was considered by using a decreasing exponential function in the model.

The results of solving various numerical examples showed that using the IoT and equipping distribution centers and trucks with it has increased the total costs of CCL by 15%. While it has reduced operational costs in distribution centers by 26% and transportation costs by 60%. Also, the studies showed that using different IoT tools in combination with each other can reduce the total transportation costs even more. On the other hand, by examining the model results, it was observed that the total costs have increased with the increase in the minimum quality of the products distributed in the network. This analysis also shows the rise in demand for the CCL network. By analyzing a numerical example with AI algorithms such as GA, PSO, GWO, and EPO, it was observed that algorithms have improved the calculation time by 70%. In comparison, the maximum relative error is reported to be less than 1%. In the small numerical example, EPO achieved the optimal value of the objective function of the problem in a much shorter time than CPLEX.

By solving different numerical examples, it was observed that EPO has the lowest average RPD error and PSO has the lowest average calculation time among the AI algorithms. The comparison of two measurement indices between algorithms introduces EPO as a more efficient algorithm than other algorithms. The results of this paper show that managers should use IoT tools in their businesses, especially when distributing cold items. The profit from implementing IoT tools is far more than the creation of the infrastructure and the costs of equipping the IoT. These tools help route vehicles so that distributed product quality does not decrease too much. On the other hand, AI algorithms provide results that are very close to actual results. Although there is a possibility of a minor error, the speed of achieving it is much higher. Therefore, managers can use AIoT to implement CCL.

After reviewing the results and analyzing different numerical examples, it is suggested that environmental and social examples be considered in the objective function of the presented model. Also, developing a mathematical model and considering manufacturers can bring CCL closer to the real world. Considering uncertainty in demand is suggested as a future proposal to reduce cost fluctuations. In this paper, the mathematical model does not consider delivery time and time window. The importance of this issue in the transportation of cold goods can be raised as a field of future research.