1. Introduction
In recent years, competitive markets, challenging customer demands, and increased awareness of logistics and transportation activities have increased the importance of technology for Thailand’s poultry industry. In order to develop new technology for the marketplace, companies “can and should use external ideas and internal ideas, as well as internal and external paths to market,” according to the open innovation paradigm [
1]. In addition to logistics management being influenced by innovations, new technologies are evolving in response to businesses’ goals and competitiveness conditions, increasing their complexity [
2]. Currently, logistics, also known as logistics 4.0, is receiving the most attention in the fourth industrial revolution trend. Artificial intelligence, real-time tracking, data-driven network logistics, the internet of things, optimization software, and so on are examples of technologies [
3,
4,
5]. These logistics 4.0 technologies will significantly impact Thailand’s poultry industry’s outbound logistics planning.
The outbound logistics of the poultry industry in Thailand are considered in this paper, as agricultural products comprise a significant part of Thailand’s development, impacting Thailand’s economic growth. Outbound logistics is the shipping of finished products to customers from a distribution center. At this stage, transportation is typically carried out by trucks. Distribution planning can be a challenging problem and adhering to distribution center best practices is also crucial for ensuring the efficient transportation of products. The importance of poultry distribution planning has increased, due to rising transportation costs and opportunities for decreasing costs in incorporating optimal distribution planning. A flow process of outbound logistics for the poultry industry in Thailand is depicted in
Figure 1. In short, the outbound logistics of the poultry industry in Thailand consists of three principal distributions: (1) The old hens are slaughtered and then sold as poultry meats to customers; (2) eggs are mainly sold directly to the end-consumers; and (3) broken eggs are sent to a processing plant [
6,
7]. Various egg products (e.g., egg powder) are produced, which are used in the food industry. Poultry distribution, regarding the design of the routing scheme for routing problems, is known as the multiple-depot vehicle-routing problem (MDVRP). One characteristic of this problem is that many customers need to be served by vehicles from many depots (e.g., egg distribution centers 1,2 and a slaughterhouse). Each vehicle must start at its depot, visit customers in order, and return to the same depot. Therefore, poultry distribution planning is intended to route the vehicle at each depot, with respect to the orders of customers.
The MDVRP has been the focus of many studies, as it is widely applicable to many real-world situations, including logistics distribution problems for optimizing total transportation costs. After all, an optimal route can minimize the total distance of each route, thereby leading to cost savings. Hence, it is essential to have an optimized plan for vehicle routing to complete poultry distribution.
In this paper, we focus on outbound logistics planning of the poultry industry in Thailand, with the objective being to minimize transportation costs. We developed a mixed-integer linear programming (MILP) model for small-sized instances. In terms of large-sized instances, we developed a new enhanced differential evolution (DE) algorithm, which should make the best decision to minimize the distance between each depot and the customers. The main contributions of this paper are twofold. First, we developed a new mutation formula for re-initializing solutions for the DE algorithm in the context of protecting movements to a local optimal. Secondly, we designed an algorithm to further enhance the DE algorithm. The local search techniques were used in the k-variable move to improve the ability to search for the best solutions to enhance the exploitation search capability, called the local vector. Hence, using the re-initialization solution formula on the DE algorithm is known as the novel re-initialization solution and local search function on the DE algorithm (RI-DE), which will be implemented in Thailand’s Poultry Industry.
This paper is organized as follows: In
Section 2, a review of the related literature is presented.
Section 3 introduces the problem statement and formulation of MDVRP.
Section 4 presents our proposed algorithm for solving the MDVRP. The computational results are discussed in
Section 5. Finally, our conclusion is detailed in
Section 6.
2. Literature Review
Developing an efficient production planning system for the poultry industry is challenging and interesting to manage, in terms of the supply chain and logistics; this is especially the case in the transportation planning for poultry, which is a process that covers activities involving both inbound, production, and outbound logistics. Optimizing operational and production planning results in lower operating costs and links to the outbound logistics system, where each customer receives the product according to their quantity demand. Therefore, this research aims to develop decision-making guidelines for solving poultry transportation planning problems based on obtaining globally optimal solutions, then developing a mathematical model for a mixed-integer linear program considering a single objective optimization problem to minimize the total cost of transportation, solving poultry transportation planning problems based on obtaining globally optimal solutions. By developing a mathematical model of a mixed-integer linear program considering a single objective optimization problem, the minimization of the total distance from each depot to all customers can be achieved.
The literature on open-innovation dynamics and multiple-depot vehicle-routing problems mainly considers three factors: MDVRP, metaheuristics in routing problems, and local search problems. In the following, we review the related papers in terms of these three directions.
Open innovation is intended for exploring and exploiting [
8] new opportunities to obtain and develop new knowledge and technology [
9], specifically in the poultry industry in Thailand, in which Small and Medium Enterprises (SMEs) assist in overcoming innovation obstacles [
8,
10,
11]. In addition, previous research on open innovation investigates the importance of management in SMEs [
12].
Given the novelty of open innovation dynamics in various research domains such as SMEs, as well as small and medium industries (SMIs), numerous studies have attempted to establish a precise description of this concept through research techniques by using qualitative methods such as system dynamics [
13,
14,
15,
16,
17,
18,
19], theory-building [
20,
21,
22] content analysis [
3,
23,
24] optimization [
12,
25] and etc. Open innovation dynamics vary across different ecosystems [
26], Moreover businesses’ attitudes toward open innovation result from a mix of the ecosystem’s various aspects [
27,
28].
Open innovation appears to be an ideal strategy for promoting a firm’s operations for knowledge exploration and exploitation to produce optimization software for routing problems in the context of Industry 4.0 technologies and their execution and integration [
2,
3]. Theeraviriga et al. [
29] presented a new optimization technique for the location-routing problem of agriculture in Thailand. They developed a mathematical model and variable neighborhood strategy adaptive search (VaNSAS). They compared the solution of the proposed algorithm with the probability of selecting a black box in four different equations. Theeraviriga et al. [
30] studied location decision making and transportation for the palm oil collection center. Firstly, they proposed a mixed-integer linear programming model (MILP) and adaptive large neighborhood search (ALNS). Then, the results were compared between the solution from the MILP by the LINGO program and ALNS. Supattananon and Akararungruangkul [
31] presented a combination of a web application and the modified differential evolution (MDE) algorithm for the vehicle dispatching problem (VDP). They modified the DE with the probability of accepting the solution in the four different equations. The results demonstrated that the MDE outperformed the traditional DE.
Reviewing of the open innovation dynamics literature demonstrates that a combined approach of metaheuristic techniques such as genetic algorithm (GA), particle swarm optimization (PSO), and differential evolution (DE) algorithm in the field, planning the distribution of SMEs/SMIs, has not been used yet.
In 2015, Montoya-Torres et al. [
32] provided a state-of-the-art survey on vehicle routing with multiple depots (MDVRP). Most of the initial papers on MDVRP considered transportation cost minimization. Moreover, due to the intricacy of transportation issues, there are numerous elements which should be as near to a real-world scenario as possible, including time windows, split delivery, heterogeneous fleets, periodic deliveries, and pickup and delivery.
Ho et al. (2008) [
33] considered the topic of reverse logistics for a company that wants to collect cores from dealers during campaign seasons. Moreover, they proposed the distribution of products from multiple warehouses to sample customers in the transportation industry. This study developed two hybrid genetic algorithms (HGAs) to deal with the challenge efficiently. The primary distinction between the HGAs was that, in HGA1, the initial solutions were produced at random. For the initialization technique, HGA2 used the Clarke and Wright savings approach and the closest neighbor heuristic. Computational modeling was carried out in order to compare the methods with different issue sizes. In terms of overall delivery time, HGA2 outperformed HGA1. Aras, Aksen, and Tekin (2011) [
34] presented two mixed-integer linear programming (MILP) models in MDVRP. They developed a Tabu search-based heuristic technique to modify medium- and large-sized cases, as the issue is NP-hard.
Sombuntham and Kachitvichyanukul (2010) [
35] developed a particle swarm optimization algorithm with multiple social-learning structures (GLNPSO) to solve MDVRP with simultaneous pickup and delivery time windows. They created a new decoding technique, and their preliminary findings suggested that the proposed method could effectively solve most of the test issues.
Subsequently, many studies have focused on local search algorithms in MDVRP. A heuristic approach can tackle issues that are computationally difficult to solve. A local search may be employed to address issues when moving from one solution to the next in the context of candidate solutions, by making local adjustments until a solution which is deemed optimal is discovered, or a time limit has passed. Kuo and Wang (2012) [
36] offered a variable neighborhood search (VNS) solution for the MDVRP with loading costs (LC). There were three phases in the proposed VNS: (1) Initial solution generation; (2) random neighborhood solutions; and (3) neighborhood solution acceptance by simulated annealing (SA). Their findings demonstrated that the proposed technique is both efficient and successful in addressing the related issues. In 2016, Alinaghian and Shokouhi [
37] presented a hybrid algorithm composed of an adaptive large neighborhood search (ALNS) and VNS for a multi-compartment MDVRP. In the same year, Bezerra et al. [
38] presented a modified randomized variable neighborhood descent (RVND) for solving MDVRP.
Sadati, Çatay, and Aksen (2021) [
39] have recently developed a hybrid Tabu search and variable neighborhood search to escape from local optima; the algorithm was called the variable tabu neighborhood search (VTNS). The VTNS was used to solve three problems: MDVRP, MDVRPTW, and multi-depot open vehicle routing problem (MDOVRP). The study found that VTNS was competitive, in terms of the speed of solution, compared to state-of-the-art solution approaches published in the literature. Sethanan and Pitakaso (2016) [
40] indicated a DE metaheuristic for the transportation of raw milk. In order to increase the quality of the solution, they developed five modified DE algorithms, including two new steps: reincarnation and survival processes. The modified DE algorithms offered higher efficiency in minimization of the total costs. Dechampai et al. (2015) [
41] used the Multifactor Based Evolving Self-Organizing Maps with Differential Evolution for the General Q-Delivery Vehicle Routing Problem (G-Q-DVRP) with considerations of flexibility in mixing pickup and delivery services and the maximum duration of a route constraint (MESOMDE_G-Q-DVRP-FD) algorithm for the egg industry. The algorithm was beneficial for minimizing overall costs, compared to real-world cases, and for the efficient handling of a poultry production system.
Therefore, in the field of work related to the DE algorithm [
40,
41] we developed, in contrast to the above-mentioned works, the new mutation formula for re-initialization and new operation of using the
k-valuable move algorithm in the DE algorithm.
Stodola (2018) [
42] developed the ant colony optimization (ACO) theory to minimize the length of the longest route of all vehicles in the standard MDVRP. Later, Stodola (2020) [
43] used a hybrid ant colony optimization algorithm. Mutual colony optimization was conducted twice. ACO applies the local optimization process, and updates pheromone trails according to selected solutions in a current generation, using the simulated annealing technique for decisions. The algorithm was found to minimize the total distance and the longest route for all vehicles. Zhang et al. (2020) [
44] presented a multi-depot green vehicle routing problem considering alternative fuel-powered vehicles with limited fuel tank capacity. They proposed a two-stage ant colony system (TSACS). The proposed TSACS is distinguished through the utilization of two types of ants for two different objectives: the first type of ant was used to assign customers to depots, while the second type of ant was assigned to find the routes. The overall goal was to reduce total carbon emissions as much as possible. This approach could effectively reduce the total carbon emissions. Shi, Hu, and Han (2020) [
45] considered waste collection problems from waste collection points to waste disposal plants formulated in terms of MDVRP. They presented the sector combination optimization (SCO) algorithm to generate initial solutions and used the merge-head and drop-tail (MHDT) strategy in the process of updating solutions to minimize the total transportation distance. This algorithm provided more effective solutions compared to the other algorithms presented, and used the lowest computational time in the tabu search to obtain near-optimal solutions. Zhen et al. [
46] investigated a multi-depot multi-trip vehicle routing problem with time windows and release dates. They developed a mixed integer programming model for small-sized instances, and a hybrid particle swarm optimization algorithm and a hybrid genetic algorithm for large-sized instances. A summary of the past work on MDVRP is shown in
Table 1.
5. Computational Experiment
In this section, the experiments were executed on a computer with the following parameters: Intel
® Core™ i7-8750H CPU @ 2.20 GHz, 2.21 GHz RAM, and 16.0 GB. We developed the mathematical model in LINGO software, based on the branch and bound method, and our proposed algorithms were coded in MATLAB (R2018a). The implementation of our proposed algorithm requires parameters, as provided in
Table 3 [
7,
51,
52,
53]. We divided the parameters into small- and large-sized instances, shown in the third and fourth columns, respectively. For each experimental set, we attempted 15 replicates. Comparisons based on several population-based algorithms were discovered as well, such as traditional differential evolution (DE) algorithm, genetic algorithm (GA) [
54,
55], and particle swarm optimization (PSO) [
55].
The results of our proposed algorithms were compared with LINGO for small-sized instances, as illustrated in
Table 4, which is organized as follows. The first column contains the number of the instance
ID. Column 2 contains the instance
ID. In addition, each instance comprises three parts: the number of depots, the number of customers, and the number of vehicles. In column three, we show the optimal solution obtained by LINGO. Columns 4–12 show the best, average, and worst solutions obtained by the genetic algorithm (GA), particle swarm optimization (PSO), traditional differential evolution (DE), and re-initialization differential evolution (RI-DE) algorithm. We tested a total of 25 instances with 5, 10, 15, 20, and 25 customers. The number of the depots was 2, 3, and 4 depots. The numbers of vehicles at each depot were 3, 4, 5, and 6 vehicles. We used the best solution obtained from the 15 replicates of our proposed algorithm to demonstrate the transportation cost. The computational time of our proposed algorithms is shown in
Table 5.
The case study (CS) on this research was motivated by the small and medium-sized enterprises (SMEs) in northeastern Thailand. Currently, the total number of distribution centers is 6 with customers numbering about 500. To deliver to the customers, the case-study company has a contract with a third-party delivery company, which provides about 250 vehicles.
In
Table 6, the heuristic performance (
HP) percentage is shown, which was calculated as
HP = (
SL/So) × 100. Here,
SL and
So are the solutions obtained by LINGO and the solution obtained by our proposed algorithm in
Table 4, respectively. The statistical test results in the solution obtained by our proposed algorithm using the Wilcoxon test are shown in
Table 7. We used the Wilcoxon test because it neither depends on the form of the parent distribution nor its parameters and does not depend on any assumptions about the shape of the distribution or on being normally distributed. The statistical test was performed based on the transportation cost of LINGO and our proposed algorithm, and the SPSS V14 software for Windows was used to carry out the statistical analysis.
Our proposed algorithm could also obtain the optimal solutions for instances 1 to 10 from
Table 4 (see bold numbers in
Table 4). However, for instances 11 to 25, our proposed algorithm found near-optimal solutions. The best solutions for our proposed algorithms were 12/15, 2/15, 1/15, and 0/15 times by RI-DE, DE, PSO, and GA, respectively, which implies the new formula of the re-initialization DE algorithm and the local search function can improve protection against trapping in local optima for small-sized instances. The average computational time of the mathematical model (LINGO) and our proposed algorithms were 9922.40, 2.98, 3.01, 3.16, and 4.95 s with LINGO, GA, PSO, DE, and RI-DE, respectively.
The statistical test results demonstrated that the RI-DE algorithm obtained solutions that differed in a statistically significant manner from the other algorithms (p-value ≤ 0.05). In addition, in our experiments, we found that the DE and PSO did not significantly differ. In terms of small-sized instances, RI-DE outperformed the other proposed algorithms.
In large-sized instances, where LINGO cannot obtain solutions, our proposed algorithm was evaluated on Cordeau’s benchmark instances. The best knowledge solutions were taken from NEO Web, with all instances available for download at
https://neo.lcc.uma.es/vrp/vrp-instances (23 September 2021).
Table 8 shows some properties of Cordeau’s benchmark instances for each instance; the numbers of nodes (
N) and depots (
M) are shown, as well as the results of the GA, PSO, traditional DE and RI-DE algorithms, in terms of the best and average solutions found. Our proposed algorithm ran 10 replicates on all instances. The best solutions, average solutions, and average computational time of our proposed algorithm are recorded. The numbers in bold in the best solutions columns record the best-known solutions (BKS) taken from our proposed algorithm.
The results for the 23 instances of Cordeau’s benchmark in
Table 9 report the deviation from the best-known solutions (Δ) for our proposed algorithms. The last column reports the percentage relative improvement (
RI%) between the traditional DE and RI-DE algorithm, calculated by
RI = (
SDE − SRI-DE/SDE) × 100. Here,
SDE and
SRI-DE are the solutions obtained by the traditional DE and RI-DE algorithms, respectively. The average deviation from the best-known solutions (Δ) for different GA, PSO, DE and RI-DE algorithms was 9.98%, 6.15%, 4.05% and 1.48%, respectively. In addition, the average percentage of relative improvement between the traditional DE and RI-DE algorithms was 2.53%. Also, when considering the large-sized instances from Cordeau’s benchmark, it was demonstrated that the RI-DE algorithm outperforms the traditional DE algorithm.
The discussion of metaheuristics and open innovation is applied to the features of outbound logistics for distribution in order to develop the new optimized technique. in our opinion, the metaheuristic can be applied to minimize the transportation of the poultry industry in Thailand. One of the complexities of multiple vehicle routing problems is the NP-hard problem [
47]. However, many researchers have considered the problem of open innovation [
29,
30,
31]. To develop the optimization software for finding the optimal solution for the vehicle routing problem, it is discussed how the open innovation concept can be applied to the metaheuristics technique, such as our proposed algorithm to industrial dynamics perspective. Moreover, this paper is virtually the first case in which the differential evolution algorithm has been enhanced using the re-initialization mutation formula and local search function, in terms of the theoretical implications of open innovation among the poultry industry SMEs in Thailand via the concept of open innovation [
1].
As a result, it is essential to remember that it extends beyond traditional logistical boundaries. A concept model of open innovation developed in [
26] aims to investigate current open innovation channels, which might motivate engineering research to increase open innovation and the creation of new open-business models from meta-heuristics.
6. Conclusions
This paper focused on the planning of outbound logistics for the poultry industry in Thailand. The problem involves the planning of distribution of poultry products where the distribution center has more than one depot, making the situation characteristic of the multi-depot vehicle routing problem (MDVRP), which aims to minimize transportation costs.
Considering the NP-Hardness of our proposed problem, a new enhanced DE algorithm composed of a re-initialization solution and a local search function was developed. In the computational results, our proposed algorithm reached the optimal solution in small-sized instances (numbers 1–10). The average transportation costs of our proposed algorithm for small-sized instances for LINGO (exact method), GA, PSO, DE, and RI-DE were equal to 10,245.64, 10,727.49, 10,518.37, 10,465.73, and 10,379.83, respectively. The average computational times for LINGO (exact method), GA, PSO, DE, and RI-DE were equal to 9922.40, 2.98, 3.01, 3.16, and 4.95 s, respectively. The statistical test showed that the RI-DE solution obtained based on transportation costs was significantly different from the solutions from the GA, PSO, and DE algorithms. Heuristic performance (HP) indicated that GA, PSO, DE, and RI-DE obtained near-optimal results, with an average of 96.48, 97.97, 98.33 and 99.03% respectively. The experimental results showed that the IR-DE algorithm obtained a near-optimal solution ranging from 96.62% to 100% of 15 replicated runs. When solving large-sized instances on Cordeau’s benchmark instances, the enhanced DE algorithm (RI-DE) returned 1.48% error on average, which was significantly lower than that of the traditional DE algorithm. Moreover, given that the relative improvement (RI) comparing the transportation cost obtained from the traditional DE to that of RI-DE was equal to 2.53% on average, the results show that the RI-DE algorithm provides better transportation cost that the DE algorithm, ranging from 0.00% to 9.68%.
The RI-DE algorithm demonstrated an ability to obtain effective solutions by using the re-initialization mutation formula and local search function. The re-initialization solution could protect against trapping in local optima when the solution did not improve and create new vectors to find the best solution. In addition, the local search function was used to enhance the exploitation searchability of the DE algorithm. This implies that the re-initialization mutation formula and the local search function significantly improved the DE algorithm.
Future work can be extended in the following directions: firstly, there is still much opportunity to extend our work in many aspects when there are multiple periods, multiple products, heterogeneous fleets, and time window constraints, which may also provide an interesting topic for minimizing the total cost, including transportation, holding, and hiring costs. Secondly, the performance of the algorithm will be assessed in other real-world environments involving difficult combinatorial optimization problems in logistics and supply management. Lastly, our proposed algorithm could be extended to solve problems in other industries, i.e., agriculture and food.