Providing a Robust Dynamic Pricing Model and Comparing It with Static Pricing in Multi-level Supply Chains Using a Game Theory Approach

Objective
Designing a multi-level supply chain network with efficient product flow management is an important issue in supply chain management. Determining the price of products, which can be affected by different factors such as environmental uncertainty, will have a significant impact on the strategic decision of designing the supply chain network. In recent research on dynamic pricing, the majority focused on two-level supply chains, exploring the impact of advertising on the supply chain. In this study, the levels of the supply chain are upgraded to three levels, and the advertising and inventory variables as well as the pricing issue in the supply chain are investigated. Hence, the overarching objective is to scrutinize the coordination of a supply chain involving three variables: advertising, warehouse inventory, and a comparison between static and dynamic pricing. Given the accelerated expansion of e-commerce, dynamic pricing emerges as a potent strategy for profit augmentation within the supply chain, an aspect that has received comparatively less attention. The supply chain in this research includes three levels: producer, supplier, and retailer. In addition, many sources, including Chen et al, 2018, have indicated that dynamic pricing is being used in many innovative businesses, that 60% of market development managers around the world are familiar with dynamic pricing methods, and that 35% of CEOs and business managers plan to base all their pricing models on dynamic pricing methods in the next three years. This research initially aims to provide a stable model for dynamic pricing and compare it with static pricing in multi-level supply chains using a game theory approach. Secondly, it examines the theoretical foundations, thirdly, the research methodology is presented, and fourthly, the discussion and conclusions are discussed.
 
Methods
The present research falls under the category of applied research. It considers discount-oriented models to examine the planning horizon, the use of dynamic pricing in some actors at one level of the chain from the concept of dynamic pricing, and the use of static pricing by others at the same level and considering the demand in a non-deterministic (stable) manner. Finally, the use of Stackelberg’s game is presented to examine the core of the game and the Nash equilibrium point. The robust optimization model is presented by Malloy et al. Initially, the model introduces symbols: x as the vector of design variables, and y as the vector of control variables. Parameters A, B, and C are coefficient parameters, while b and e are parameter vectors. Values for A and B are predetermined, and B, C, and e involve uncertainty. A particular understanding of the parameter is called scenario uncertainty, which is assigned the symbol s, and its probability is specified by ps. K retailers operate in the supply chain, and each retailer supplies the desired product from only one manufacturer. In general, the outcome for each retailer is the disparity between their income and expenses. In such a situation, the retailer faces ordering, holding, and marketing costs for each product. The profit margin of each retailer is the difference between the price paid to the manufacturer for the bulk purchase and the selling price to the customer. It is worth noting that considering that the final product of each manufacturer is sent to only one retailer, the number of manufacturers and retailers is equal. For data analysis, a genetic algorithm, particle accumulation optimization, and MATLAB software were employed. Initially, the model underwent analysis in static mode, followed by dynamic mode analysis using Games software. Ultimately, the outcomes of the two pricing methods were compared.
 
Results
This article introduces the development of a stochastic demand function utilizing genetic algorithms and particle optimization. It presents two distinct single-period models designed for a competitive environment. In the first model, retailers have only an intermediary role and do not decide on pricing or optimal order quantity. In the mentioned model, it is assumed that retailers transfer the demand exactly and to the same extent as it is from the customers to the suppliers. Based on the amount of their production, suppliers face shortages and excess supply. The purpose of this model is to determine the optimal and desirable amount of production as well as the price for each supplier. In addition, routing costs are approximated. The results indicate that the presented approximation is very accurate and evaluates the equilibrium point in much less time than the original model. In the second model, retailers are assumed to incur shortage or maintenance costs according to the number of orders they send. Here, the suppliers determine the final price, and the goal of the retailers is to determine the optimal amount of the order. In this model, it is assumed that suppliers’ production is customized, and inventory costs are considered only for retailers. A noteworthy aspect of this model is the emphasis on dynamic pricing—an inherently crucial and intricate element within the domain of supply chain dynamics theory
 
Conclusion
The results underscore the substantial efficacy of the proposed combination in addressing the multi-level supply chain network design model with both dynamic and static pricing. The sensitivity analysis of the manufacturer’s profit showed that the changes indicating an increase in the market base of a manufacturer will lead to an increase in profit for both manufacturers. The graph of the change in the producer’s profit compared to the change in the costs showed that a decrease in the production cost leads to an increase in the profit for the producer, while the profit of the next producer decreases in these conditions. Like the producer’s profit, the distributor’s profit also increases with the market base. Expanding the market base not only leads to an increase in the distributor's profit through collaboration with producers but also occurs through two distinct mechanisms. Firstly, there's a profit increase due to raising retailer prices. Although wholesale prices increase with the expanded market base and heightened demand, the distributor, to maintain balance, can elevate retail prices at a higher ratio. Consequently, the value of the pi-wi term increases. Secondly, there's a profit increase resulting from boosting sales volume. The distributor's profit is positively influenced by the increase in sales volume, thereby reinforcing the overall financial outcome.