Journal Search Engine
Search Advanced Search Adode Reader(link)
Download PDF Export Citaion korean bibliography PMC previewer
ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.20 No.4 pp.548-554

A Vendor Inventory Management Policy to Optimize Sales of Thermal Energy Using Evolutionary Algorithms

Valentin Yakovlevich Afanasyev*, Vladimir Fyodorovich Ukolov, Ekaterina Alexandrovna Tregubova
Department in the Fuel and Energy Complex, State University of Management, Moscow, Russia
Department of Management of a Digital Enterprise in the Fuel and Energy Complex, Peoples’ Friendship University of Russia, Moscow, Russia
State University of Management, Moscow, Russian Federation, Department of Economics and Management in the Oil and Gas Comple, Moscow, Russia
*Corresponding Author, E-mail:
August 10, 2021 September 10, 2021 September 27, 2021


In recent years, supply chain management with the aim of making the supply chain more efficient and reducing overall costs, is one of the key issues addressed in every industry. In today's energy supply chain, determining the level of sales for manufactured goods in specific time periods and to specific customer groups is very important. This becomes even more important when we have to do this for sensitive marine products that have different customer categories. This article presents a model for determining the optimal level of sales of thermal energy in two levels and according to customer demand in different time periods to determine the optimal level of sales using accurate methods and some meta-innovative methods. For this purpose, two meta-heuristic methods of particle swarm optimization (PSO) and the evolutionary algorithm CPSO have been used.



    In a traditional supply chain, each member of the chain plans the level of inventory, as well as the number of orders and productions solely based on customer demand. This is mainly due to the fact that the information of each chain member is only related to its direct and immediate customers. Therefore, the productivity of the supply chain is not necessarily at the highest possible level (Chen et al., 2013;Choi et al., 2013). Accordingly, supply chain management (SCM) aiming at making the supply chain more productive and reducing overall costs has become a fundamental issue in the past few years and has been addressed in all industries, especially in the thermal energy industry and related technologies. The supply chain includes all activities from receiving raw materials to delivering the final product. In addition, these activities involve all construction stages, inventory control, distribution, warehousing and customer service. In general, SCM models all activities into one integrated process (Askarany et al., 2010).


    The supply chain is a set of factors that generate added value in the economy. In the current global competition, diverse products must be available to customers based on their desire. Since customer demand for high quality and rapid services has increased pressure on industries, companies can no longer do all the work alone. In the existing competitive market, economic and production enterprises have found themselves in need of the management and monitoring of resources and related elements outside the organization in addition to dealing with their domestic resources and organization. Therefore, SCM has been identified as one of the fundamental aspects of electronic business implementation. SCM enables customers to receive reliable and quick services, along with high-quality products at the minimum cost. As such, all activities such as supply and demand planning, material preparation, product planning and production, service, warehousing, inventory control, distribution and delivery to customers, which were formerly conducted at the company’s level, are now transferred to the supply chain level. A key issue in the supply chain is to manage and control all these activities coordinately (Ganeshan and Harrison, 1995;Janvier-James, 2012).

    2.1 Two Echelon Supply Chain with Vendormanaged Inventory Policy

    A two-echelon supply chain consists of two main components, namely the seller (vendor) and the buyer (consumer). In this system, which is known as the vendor- managed inventory (VMI) system, the seller of goods plays the role of service provider and supporter and delivers goods to the buyer (consumer) without intermediaries. This issue is specifically important for marine industry products. Similar to any other supply chain, the goal of a VMI-based supply chain is to reduce the overall costs at various levels of the chain and increase profit using the mentioned policy. The managerial components of the marine industry supply chain are exhibited in Figure 1:


    In a research, Diabat focused on the two-echelon supply chain using a VMI system. This scholar attempted to design a model in order to find an optimal sales amount. In the end, the model developed in the foregoing research was compared to the traditional method following defining the mixed solution technique (Diabat, 2014). Other studies have been conducted on a two-echelon supply chain, including a research by Nachiappan and Jawahar (2007). The model proposed by these scholars was a VMI-based two-echelon supply chain, and a heuristic algorithm was applied to solve the model. The VMI is one of the systems used for the two-echelon supply chain in various studies. Primarily, VMI is a process where the vendor creates orders for their customers based on the demand information that they receive from the customer. In other words, VMI is a model in which the vendor is responsible for meeting customer demand. Using this concept, Diabat showed that the vendor controls the inventory and makes the orders instead of the customer (Holmström, 1998). Meanwhile, the application of an inventory system that can help maintain, control and distribute goods is critical. In this regard, some of these systems include economic order quantity (EOQ) and economic production quantity (EPQ). In fact, these two inventory control systems support the main VMI system. Diabat (2014) as well as Nachiappan and Jawahar (2007) used the EOQ system in their two-echelon models. Nonetheless, the integration and coordination of supply chain components (e.g., taw material and semi-finished goods purchasing, production, distribution and sales of the product) have a significant effect on the decrease of supply chain costs, a decrease of delivery time, and delays in product delivery from distribution centers to markets and sales centers, and consequently, customer satisfaction. In this regard, the VMI system is an important aspect of the supply chain (Zahedi et al., 2021). During the 60s, experts were able to reduce their inventory by studying the internal relationships between warehousing and transportation and their integration, the result of which was identified as distribution management. In the evolution path, the logistics concept was formed by adding the management of construction, procurement and orders to management. The current status (i.e., supply chain) is the result is a combination of different operational loops, the beginning and end of which include vendors and customers, respectively. The main goal of port logistics and supply chain management is to reduce uncertainty and risks in the supply chain. Conventional logistics systems are based on a paradigm that seeks to determine the optimal quantities and location available with the aim of reducing costs and providing excellent services (9). Recent studies, including a research by Pérez- Rodríguez (2021), have considered new approaches for the design of a supply chain network, including considering the financial flow in the supply chain and using hybrid metaheuristic algorithms for their optimization.

    4. METHOD

    This paper designs and models a two-echelon supply chain, which is a type of supply chain formed of two main components, namely the seller (vendor) and the buyer (consumer). One of the fundamental issues in a two-echelon supply chain is VMI, where the vendor creates orders for their customers based on the demand information that they receive from the customer. In other words, the vendor is responsible for meeting customer demand in a VMI. In addition, the vendor controls the inventory and makes the order instead of the customer (Grammenos, 2013;Dong and Xu, 2002;Mastos et al., 2021). Moreover, the seller does all the work, including supplying the product and providing after-sales services, and delivers the product to the buyer (consumer) without intermediaries. In this research, we model and solve the problem of determining the optimal level of multi-period sales of marine products in a two-echelon supply chain, aiming at maximizing the total profit from sales. In addition to the general information, there is a need for maximum product shelf life.

    4.1 Model Premises

    Similar to other supply chain models, modeling of a two-echelon supply chain requires some premises. In the present research, the model premises include:

    • - Customers have different and definite demands in various periods.

    • - There are certain upper and lower bounds for the sales amount of each seller in each period.

    • - Each inventory unit can be stored for a maximum of a certain number of periods.

    In addition to the mentioned items, the model’s parameters include seller demand, seller capacity, inventory costs and order submission, cost of starting production in each period, and cost of delivery of products from the vendor to the seller.

    4.2 Modeling

    According to the mentioned premises, the modeling parameters are presented as follows:

    • Ijt : Level of inventory for the j-th buyer at the end of the t-th period

    • djt : The demand of the j-th buyer in the t-th period

    • ajt : The y-intercept of the price-demand curve for the j-th customer

    • bjt : The slope of the price-demand curve for the j-th customer

    • C : Seller capacity

    • Hbjt : Inventory cost for the j-th buyer independently in the t-th period

    • Hst : Inventory cost for the seller independently in the t-th period

    • Qjt : Economic order amount in the t-th period

    • Sbjt : Cost of establishment for the j-th buyer in each order in the t-th period independently

    • Sst : Cost of establishment for seller in each order in the t-th period independently

    • Wjt : Cost of the contract between the j-th buyer and seller in the t-th period

    • yjtmin : Minimum expected sales for the j-th buyer in t-th period

    • yitmax : Maximum expected sales for the j-th buyer in the t-th period

    • θjt : Flow cost per unit, from the seller to the j-th buyer in the t-th period

    • vjt : Cost of transportation resources per unit, from seller to the j-th buyer in the t-th period

    • δ : Manufacturing cost per unit

    • τmax : Maximum product storage time

    After solving the model, the amount of goods delivery from the vendor to each seller in each period must be determined, which is presented by yjt, which shows the amount of product delivery from the vendor to the j-th seller in the t-th period.

    4.3 Objective Function

    As mentioned earlier in the literature review section, the objective function of the problem is to maximize the profit from the sale of products to customers. Seller costs are based on costs related to production, distribution, orders, and inventory maintenance. The objective function of the problem is calculated from the difference between the net profit and the seller-related costs. The price in each period will be a function of the amount of demand in that period. If the j-th customer demand in the t-th period is assumed to be equal to yjt, the cost of the problem will be estimated using the equation below:

    P ( y j t ) = a j t b j t y j t

    where ajt and bjt show the price-demand y-intercept and curve slope for the j-th costumer, respectively. According to Equation (1), the selling price of goods to customers in different time periods can be different. Therefore, the gross profit from sales is equal to the product of the number of sales P(yjt) multiplied by the sale price yjt :

    a j t y j t b j t y j t 2

    - Production Costs

    The production costs are obtained by multiplying the cost of manufacturing each product by the sales amount (demand for goods), and this value is expressed in the form of δyit based on the parameters defined in the problem.

    - Distribution Costs

    The distribution costs are obtained by multiplying the flow cost θjt yjt by the cost of transportation resources vjtyjt. Accordingly, the distribution costs are estimated, as follows:

    D C = v j t θ j t y j t 2

    - Inventory Ordering and Maintenance Costs

    In this study, the EOQ is used to calculate the total inventory ordering and maintenance cost. In this system, the inventory ordering cost is obtained using the equation below:

    A C = D A Q

    By placing the related amounts in Equation (4) for ordering cost, we will have:

    T A C = y j t ( S s t + S b j t ) Q j t

    To calculate the maintenance cost in the same way:

    I C = H Q 2 = ( H s t + H b j t ) Q j t 2

    Finally, and based on Diabat’s model (6), the total cost of ordering and maintaining inventory can be calculated by the equation below after replacing Qjt with the optimal amount obtained from the economic order model E O Q = [ 2 ( S s t + S b j t ) y j t ( H s t + H b j t ) ] 1 2 .

    T I C = [ 2 ( H s t + H b j t ) ( S s t + S b j t ) y j t ] 1 2

    The objective function (8) minimizes profit from the sale of perishable items at different times. In addition, given the use of coefficients related to the flow cost and the use of the inventory system of the amount of economic order, the optimization problem is of non-linear type. It is notable that the vjt coefficient includes costs such as transportation costs, human march costs, and administrative costs in each unit. Ultimately, the mentioned coefficient is calculated at 0.5 following reviewing various articles (Dubey et al., 2021;Pahlevan et al., 2021).

    M a x   n j = 1 τ m a x t = 1 { a j t y j t b j t y j t 2 δ y j t 0.5 θ j t y j t 2 [ 2 ( H s t + H b j t ) ( S s t + S b j t ) y j t ] 1 2 }

    4.4 Constraints

    The problem of determining the optimal level of multi-period sales of marine products in a two-echelon supply chain encompasses various constraints, which are classified below:

    - Capacity Constraints

    In constraints (9), the sales amount related to different periods is considered lower or equal to the sales capacity, as shown below:

    n j = 1 y j t C

    - Sales Minimization and Maximization Constraints

    Given the diversity of items and different customer demands at various periods, a lower and upper bound is considered for selling different products in the present problem. This is clearly shown by constraints (10):

    y j t m i n y j t y j t m a x

    - Demand Balance Constraints

    Constraints (11) express that the total inventory of the previous period and sales of the current period must be equal to the amount of demand and inventory in the present period:

    I j , t 1 + n j = 1 y j t = d j t + I j , t

    - Symbol Constraints

    Constraints (12) show that the values related to sales, inventory and demand must be positive in each period:

    y j t , d j t , I j , t 0

    5. RESULTS

    According to the objective function and constraints of the proposed model, the problem is of constrained optimization type, which is solved by two methods: A) using classic techniques and B) using smart or evolutionary methods. In this paper, PSO meta-heuristic methods and CPSO evolutionary method are used to solve the proposed model and finally, the solutions are compared with the method solved by GAMS software. The problems are assumed to have five customers and five periods, and the demand of customers in the five different periods is predetermined. The final solution of the problem for sales amount in 20 problems is presented in Table 2 based on the problem’s parameters. In addition, the results of the comparison of different methods are shown in Table 1.

    According to Figure 2, all methods are between the lower and upper bound. In addition, GAMS has the lowest difference with the lower bound in all problems since GAMS accurately solves mathematical models and the lowest amount of objective function is obtained by using this method. Among the meta-heuristic methods, the CPSO has the lowest amount in different problems. In addition, the PSO algorithm has very little difference with the upper bound, which shows the weakness of the algorithm. In order to more accurately examine the solution methods, a problem is presented in more detail. The complete solution to the data set of problem 2 is shown in Table 2:


    The critical role of SCM in society is perhaps overlooked and less emphasized. In general, SCM can help people survive by improving the healthcare conditions and protecting people against overindulgence and weather conditions. People trust supply chains to provide necessities such as food and water as well as medicines and health care. The supply chain is also critical to supplying electricity to homes and businesses and provides the energy needed for light, heat, air conditioning and refrigeration. In addition, SCM improves the quality of life by improving employment, thereby laying the foundation for economic growth and improvement of living standards. This leads to many employment opportunities since supply chain experts design and control all supply chains of a community. Moreover, they manage the inventory, warehousing, packaging and logistics. Furthermore, a common feature of most poor nations is the lack of a developed supply chain. Communities with strong and welldeveloped supply chain infrastructures, such as large rail networks, interurban highway systems and a range of airports and ports, can trade goods at lower costs, allowing consumers to buy more products, thus providing economic growth. The present study evaluated a VMI-based two-echelon model for optimal sales management in a supply chain, which encompassed two seller and buyer sections and its objective function related to the sales amount was optimized. In addition, the solution obtained from the accurate method was compared to the solutions achieved from meta-heuristic techniques. As observed, the accurate techniques yielded more optimal solutions. However, meta-heuristic algorithms could generate a near-optimal solution in a much shorter period. It is recommended that hybrid algorithms (e.g., simulated annealing and genetics algorithms) be used to evaluate and compare the mentioned solutions.


    This work was supported by the Russian Foundation for Basic Research (RFBR) in the framework of research project No. 20-010-00137. The work was pre-pared at the State University of Management (GUU), together with the Peoples' Friendship University of Russia (RUDN).



    Managerial components of thermal energy supply chain.


    Comparison of different solution methods


    Optimization results of the mathematical model with different techniques

    Results of the model for problem 2


    1. Askarany, D. , Yazdifar, H. , and Askary, S. (2010), Supply chain management, activity-based costing and organizational factors, International Journal of Production Economics, 127(2), 238-248.
    2. Chen, Y. C. , Fang, S.-C. , and Wen, U.-P. (2013), Pricing policies for substitutable products in a supply chain with Internet and traditional channels, European Journal of Operational Research, 224(3), 542-551.
    3. Choi, T.-M. , Li, Y. , and Xu, L. (2013), Channel leadership, performance and coordination in closed loop supply chains, International Journal of Production Economics, 146(1), 371-380.
    4. Diabat, A. (2014), Hybrid algorithm for a vendor managed inventory system in a two-echelon supply chain, European Journal of Operational Research, 238(1), 114-121.
    5. Dong, Y. and Xu, K. (2002), A supply chain model of vendor managed inventory, Transportation Research Part E: Logistics and Transportation Review, 38(2), 75-95.
    6. Dubey, R. , Gunasekaran, A. , Childe, S. J. , Fosso Wamba, S. , Roubaud, D. , and Foropon, C. (2021), Empirical investigation of data analytics capability and organizational flexibility as complements to supply chain resilience, International Journal of Production Research, 59(1), 110-128.
    7. Ganeshan, R. and Harrison, T. P. (1995), An introduction to supply chain management, Department of Management Sciences and Information Systems, 303, 560-564.
    8. Grammenos, C. (2013), The Handbook of Maritime Economics and Business, Taylor & Francis.
    9. Holmström, J. (1998), Business process innovation in the supply chain: A case study of implementing vendor managed inventory, European journal of purchasing & Supply Management, 7(2-3), 127-131.
    10. Janvier-James, A. M. (2012), A new introduction to supply chains and supply chain management: Definitions and theories perspective, International Business Research, 5(1), 194-203.
    11. Mastos, T. D. , Nizamis, A. , Terzi, S. , Gkortzis, D. , Papadopoulos, A. , Tsagkalidis, N. , and Tzovaras, D. (2021), Introducing an application of an industry 4.0 solution for circular supply chain management, Journal of Cleaner Production, 300, 126886.
    12. Nachiappan, S. and Jawahar, N. (2007), A genetic algorithm for optimal operating parameters of VMI system in a two echelon supply chain, European Journal of Operational Research, 182(3), 1433-1452.
    13. Pahlevan, S. M. , Hosseini, S. M. S. , and Goli, A. (2021), Sustainable supply chain network design using products’ life cycle in the aluminum industry, Environmental Science and Pollution Research, 8, 1-25.
    14. Pérez-Rodríguez, R. (2021), A radial hybrid estimation of distribution algorithm for the vehicle routing problem with time windows, Industrial Engineering & Management Systems, 20(2), 172-183.
    15. Zahedi, A. , Salehi-Amiri, A. , Hajiaghaei-Keshteli, M. , and Diabat, A. (2021), Designing a closed-loop supply chain network considering multi-task sales agencies and multi-mode transportation, Soft Computing, 25(8), 6203-6235.
    Do not open for a day Close