1. Introduction
As a necessity of daily life, a large amount of inventory for fresh products is required to meet the diverse needs of customers. In daily operations, however, it is challenging to reduce inventory costs due to the characteristics of perishability and fragility of fresh products. It is extremely necessary and sometimes difficult for enterprises to study how to make a reasonable arrangement for fresh products, including what quantity to order, when to order, the expired date of inventory, and balanced inventory cost. However, in the model of supply chain management, we should carry out overall optimization control for each inventory levels, based on a view of the whole supply chain. Because inventory controls are more complex and difficult, it is significant to study the control strategy for fresh products with multi-echelon inventory management.
The inventory control strategy of fresh products has been studied previously by many groups. Olsson et al. developed two models of a stepped continuous inventory system for perishable goods [
1]. Mo et al. developed a multi-item inventory model for perishable items, where the demand rate of items depends on inventory. The Lagrange approach was applied to discuss the existence and uniqueness of the optimal period, and line search algorithms were developed to solve the optimal solution of the model [
2]. Kaya et al. studied perishable products with random demand related to customer age and price in the regular inventory system, considering product inventory and pricing decisions, and using dynamic programming to model the system [
3]. Rijpkema et al. set up an ordering model with and without shelf life loss cost parameters. The shelf life loss during transportation and storage was predicted through the microbial growth model and evaluated using a mixed discrete event chain simulation model with continuous mass attenuation [
4]. Zheng et al. established a mathematical model of inventory and price decision-making in a two-echelon supply chain system, and illustrated that centralized decision-making performs more efficiently than decentralized decision-making [
5]. Janssen et al. proposed a micro-periodic inventory replenishment policy for fast and perishable goods by targeting customer service levels with fixed material life, deterministic lead time, fixed order period, shelf life, damage, and random demands [
6].
A number of studies have assessed the genetic algorithm and multi-echelon supply inventory. Clark and Scarf firstly performed theoretical studies about multi-echelon supply inventory, pointing out the concept of “multi-echelon supply inventory” based on an N-echelon serial system, in which the batch limit is not considered, while the stock-out penalty and inventory cost are considered, and formulating an optimal inventory control strategy [
7]. Duong et al. reached three factors that worsen management challenges: uncertain consumer demand, product lifetimes, and consumer substitution among the product range. This research understands the effects of these factors on inventory performance [
8]. Hill et al. upgraded the model and established a joint production-inventory model for the secondary supply chain with a single supplier and a single retailer [
9]. Weng presented models for determining optimal all-unit and incremental quantity discount policies and investigates the effect of quantity discounts on increasing demand and ensuring pareto-efficient transactions under general price-sensitive demand functions [
10]. Diks et al. determined a multi-echelon inventory system optimal replenishment strategy with the objective to minimize the expected holding and penalty costs per period [
11]. In order to obtain a rapid response to the service speed of supply chain inventory, Moinzadeh used the method of rapid information exchange to control multi-echelon inventory, and assessed the study of multi-echelon inventory control model for urgent ordering strategies (R, Q) [
12]. Giannoccaro et al. used the fuzzy set theory to solve the uncertain factors in the inventory control problem, and used the average total inventory cost method to solve the multi-echelon inventory system by establishing models [
13]. Chen et al. used decentralized and centralized decision-making methods to study the joint replenishment problem of the secondary supply chain inventory with a variety of products, and proved that the centralized joint replenishment strategy is better than the decentralized strategy. The optimal replenishment cycle and optimal replenishment quantity was also solved by algorithms [
14]. Considering a supply chain composed of multiple suppliers, a manufacturer, and multiple distributors, Wang et al. established a new model and solved it with an immune genetic algorithm by integrating the time cost of delayed transportation into previous research [
15]. Presbitero et al. proposed an immune system model based on genetic algorithm [
16]. Iida et al. identified the problem of dynamic multi-echelon inventory with unstable demand and found that the near-myopic policies from the multi-echelon inventory problem are close enough to the optimal cost [
17]. Mandel and Vilms introduced stationary strategies and developed a software package, where the algorithm was numerically modelled for two varieties of Gaussian-like and nearly uniform discrete demand distributions [
18]. Wang et al. established an inventory cost control model and an inventory time model to minimize inventory costs among manufacturers, distributors, and retailers [
19]. Ech-Cheikh et al. established a multi-echelon distribution inventory system composed of suppliers, distributors, and retailers. The main purpose of the simulation model is to analyze the multi-echelon distribution system based on the key performance indicators of each echelons, such as cost, replenishment, and customer service [
20]. Goswami et al. devise an analytical framework to converge upon product design concept(s) that would be associated with lesser supply chain risks, usually a function of both technical and commercialization considerations. The high-level and constituent lower-level supply chain risks are represented by parent and root nodes, respectively, within the devised Bayesian network-driven research framework [
21]. De et al. formulate the mathematical model in the form of mixed integer non-linear programming to minimize the total cost associated with transportation, inventory holding, and operational activities. A mathematical formulation-based heuristic approach, which comprises four algorithms, is proposed for solving purposes [
22]. Choudhary et al. presented a comprehensive set of KPIs for sustainable supply chain management using a mixed method approach including analysing data from the literature survey, content analysis of sustainability reports of manufacturing firms and expert interviews [
23]. Ray et al. present a comprehensive set of KPIs for sustainable supply chain management using a mixed method approach including analyzing data from the literature survey, content analysis of sustainability reports of manufacturing firms, and expert interviews. A three-level hierarchical model is developed [
24].
The simulation-based optimization method is widely used to study multi-echelon inventory control problems. In the fifth part of their review paper, Pourhejazy et al. delivered a detailed summary and elaboration on the optimization of supply chain system by simulation. Of the wide variety of S-O frameworks that have been developed under the large S-O family, the authors analyzed those distinctly based on the technical features frameworks such as simulation-based optimization, simulation optimization (optimization of simulation), and optimization-based simulation [
25]. Under the condition of uncertain demand, Schwartz et al. determined the method to reduce enterprise costs by balancing the relationship between safety stock echelon and customer satisfaction [
26]. Chu et al. studied the multi-echelon inventory control model under uncertain conditions and performed simulation solutions [
27]. The inventory system studied by Attar et al. has the characteristics of complex requirements, random order lead time, and high stock-out costs. It was solved using a complex hybrid simulation optimization method [
28]. Lee et al. established an inventory model of supply chain distribution system with multi-period and multi-product, and proposed the use of simulation technology to solve the manufacturing-allocation problem [
29]. Kochel et al. indicated that simulation optimization can be successfully applied to define optimal policies in very general multi-echelon inventory systems through a numerical example [
30]. Starting with the multi-period newsboy problem, Heidary et al. established a simulation model of customer demand behavior, and solved the dual-objective optimization problem with uncertain customer demand and supply interruption through simulation-based optimization methods [
31]. Zhao et al. applied the feedback control method to the three-echelon inventory system through control engineering. The simulation model was established by using the proportional integral algorithm to modify the model control strategy of the three-echelon inventory system [
32]. Focusing on the shelf premium problem in a multi-objective intensive supply chain, Avci et al. determined the demand forecast adjustment factors and safety stock parameters using the differential evolution algorithm and optimized the system objectives [
33]. Gueller et al. studied a multi-echelon production inventory system in a random environment and used a simulation-based optimization method to determine the best inventory control parameters [
34]. Thammatadatrakul et al. explored remanufacturing inventory problems with different priorities, and a simulation-based optimization method that combines mixed integer programming and simulation model was proposed [
35].
In the literature mentioned above, a number of experts and scholars have studied the inventory optimization model for perishable goods by single-level or two-levels, as well as the multi-echelon inventory control strategy for stable property goods and its simulating optimization. However, few studies regard the deterioration rate of fresh products as a decision-making factor when modeling in supply chains. Based on the perishable property of fresh products, this article developed the mathematical model for fresh product inventory decisions in supply chains by combining the deterioration rate and inventory control model, and obtained the optimal solution for the whole supply chain from the optimal fitness function of genetic algorithm.
The remainder of this paper is organized as follows.
Section 2 serves to analyze the cost of inventory system for fresh products, taking into account the loss of fresh perishable products, and target on control of minimum inventory cost to establish the mathematical model of multi-echelon inventory control for fresh products.
Section 3 discusses an example case of a supply chain with three-level inventory control, showing how our modeling approach would be applied. Firstly, we proceed to calculate and make decisions by independent inventory at each levels with a decentralized strategy, then the entire optimization of the supply chain is carried out with the genetic algorithm to find the optimal strategy of multi-echelon inventory, which is the centralized strategy. In
Section 4, we apply the simulation software Flexsim5.0 of the discrete system by simulating the operation running by these two options of inventory control strategies, to prove the feasibility and advantages of the centralized optimization model by verifying and comparing the mathematical model analysis.
Section 5 discusses the results of this paper and presents some future research opportunities.
4. Simulation Model Verification
We obtained an optimal inventory management solution by optimizing the mathematical model. However, we need to verify the effects of the two ordering strategies before and after optimization in practice by simulation. Flexsim is simulation software for discrete event systems. Its functions include the design of a simulation model, the implementation of simulation logic, model validation, and result output and simulation analysis. Many researchers have used Flexsim to solve many practical problems [
36,
37,
38,
39,
40]. Based on the characteristics of Flexsim, it is very suitable for simulating the logistic process between the warehouse systems at all levels of the supply chain, so we chose Flexsim to simulate the operation effect under both strategies.
4.1. Simulation Model Establish
A simulation model layout for multi-echelon inventory is established, and every 100 units as one day is selected on the simulation time clock. The warm-up period is defined as 700, which equivalent to one week in reality.
In the Flexsim environment, we use the “Queue” as the warehouse of each node in the system to store the “Item” which represents fresh goods.
The “Source” is used to simulate the product supply and the initial inventory of each enterprise node. The customer’s arrival is simulated by the “Source”, while the departure is simulated by the “Sink”. The spoiled product enters the “Sink” directly. "Flexsim Experiment Control" is used to record the inventory amount of each node for 20 simulations. The specific layout is shown in
Figure 6.
4.2. Simulation Results Analysis
In order to verify the feasibility of strategies using genetic algorithms in the mathematical model, the simulation model was performed 20 times for the two strategies.
The inventory of each enterprise node was selected as the performance index. The average value of inventory at each node of the two strategies by running 20 simulations was recorded with a confidence of 90, as shown in
Figure 7 and
Figure 8.
The average inventory and the total inventory costs of supply chain were calculated as shown in
Table 6.
In the inventory comparison of the simulation results, the centralized strategy optimized by the algorithm performs better than the decentralized strategy of directly solving the lowest inventory cost at all levels, as shown in
Table 6:
(1) Due to the reduction in the order quantity, the average inventory of every node at all levels has declined, which not only reduces the inventory holding cost, but also reduces the loss of deterioration of the products;
(2) The ordering costs at retail level slightly increase due to frequent ordering times caused by lower ordering volume. With the gradual increase in demand fluctuations, the reduced inventory maintenance costs for upstream node enterprises are sufficient to compensate for the increased ordering costs of retailers.
(3) The inventory cost (RMB 39,658.5) from the simulation model of the centralized strategy is smaller than that of the decentralized strategy (RMB 39,663.2). It can be seen that the optimized solution from the mathematical model remains better in the simulation model, proving the effectiveness of the multi-echelon inventory model of fresh products established in this paper, and also the effective of the fitness function designed based on the genetic algorithm.
(4) In practice, it is common that the reduction in inventory costs for one node enterprise will lead to an increase in that cost for other node enterprises, but in general, if coordination does not work well, enterprises are not willing to sacrifice their interests for the optimization of the whole supply chain. Therefore, the best strategy is through contracts and other means, by a leading enterprise conducting the overall planning, to avoid each level of independent processing decisions and plans so as to minimize the total inventory cost of the whole supply chain.
In this study, some decision values solved by the mathematical model, such as the order quantity, order point, and demand of each enterprise node, were taken as the input conditions for a simulation. The simulation was carried out according to the supply process in the actual supply chain environment. After 20 simulations, the average inventory volume and inventory costs of each node were obtained. By comparing the simulation output values of the two inventory control strategies, we find that the total cost value of the centralized strategy model is still lower than that of decentralized strategy. It is proved that the optimized inventory control strategy is better for cost-saving in actual operation. An optimized inventory control strategy can provide reference and direction for the practical link of supply chain inventory management, and has practical management significance.