Solving bilevel programs based on lower-level Mond-Weir duality

This paper focuses on developing effective algorithms for solving bilevel program. The most popular approach is to replace the lower-level problem by its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity constraints (MPCC). However, MPCC does not satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. In this paper, inspired by a recent work using the lower-level Wolfe duality (WDP), we apply the lower-level Mond-Weir duality to present a new reformulation, called MDP, for bilevel program. It is shown that, under mild assumptions, they are equivalent in globally or locally optimal sense. An example is given to show that, different from MPCC, MDP may satisfy the MFCQ at its feasible points. Relations among MDP, WDP, and MPCC are investigated. Furthermore, in order to compare the new MDP approach with the MPCC and WDP approaches, we design a procedure to generate 150 tested problems randomly and comprehensive numerical experiments showed that MDP has evident advantages over MPCC and WDP in terms of feasibility to the original bilevel programs, success efficiency, and average CPU time.Comment: arXiv admin note: text overlap with arXiv:2302.0683

A novel approach for bilevel programs based on Wolfe duality

This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most popular approach is to replace the lower-level program by its KKT conditions and then the bilevel program can be reformulated as a mathematical program with equilibrium constraints (MPEC for short). However, since the MPEC does not satisfy the Mangasarian-Fromovitz constraint qualification at any feasible point, the well-developed nonlinear programming theory cannot be applied to MPECs directly. In this paper, we apply the Wolfe duality to show that, under very mild conditions, the bilevel program is equivalent to a new single-level reformulation (WDP for short) in the globally and locally optimal sense. We give an example to show that, unlike the MPEC reformulation, WDP may satisfy the Mangasarian-Fromovitz constraint qualification at its feasible points. We give some properties of the WDP reformulation and the relations between the WDP and MPEC reformulations. We further propose a relaxation method for solving WDP and investigate its limiting behavior. Comprehensive numerical experiments indicate that, although solving WDP directly does not perform very well in our tests, the relaxation method based on the WDP reformulation is quite efficient

Service selection strategic analysis for selfoperated e-commerce platforms under settlement

In order to study whether e-commerce platforms carry out service cooperation after settlement in-depth, this paper focuses on service selection strategic analysis for agent channels on some self-operated e-commerce platforms settled in hybrid e-commerce platforms. We present multi-leader-follower models in two different scenarios with the platforms as leaders and the manufacturers as followers and give some numerical experiments to analyze the impacts of service selection strategies for self-operated platforms on all supply chain members. Our finding shows that if the service cost efficiency is moderate or low, the self-operated platform prefers to provide its service for the agent; otherwise, its selection mainly depends on the unit product service fee. In addition, fierce service competition and high unit service fee are unfavorable to all members, while high service cost efficiency may hurt both the platform and the manufacturer

Sales Mode Selection Strategic Analysis for Manufacturers on E-Commerce Platforms under Multi-Channel Competition

This paper considers a sales mode selection problem between resale and agency modes on e-commerce platforms for a manufacturer with traditional retail channel, direct selling channel, and e-commerce platform channel. By considering the factors price competition, market shares, and commission rate, we construct two leader-follower models with the manufacturer as a leader and traditional retailer and e-commerce platform as followers. To obtain optimal solutions, we discuss the conditions under which the upper and lower models are convex and then give optimal strategies for all members in the network. Through numerical experiments, we analyze the impact of price competition intensity, market shares, and commission rate on mode selection strategies and the changing trend of each member’s optimal pricing and profit under different sales modes. The numerical results reveal the following revelations: If the market share of the traditional retail channel is lower than the direct selling channel, the manufacturer should choose the agency mode when the market share of the direct selling channel and price competition are lower or when the market share of the direct selling channel together with the price competition and the commission rate is higher; otherwise, the manufacturer should choose the resale mode. If the market share of the direct selling channel is lower than the traditional retail channel, the manufacturer should choose the agency mode when the price competition is weak and choose the resale mode when the price competition is strong. Under certain conditions, a win–win situation can be achieved no matter how the manufacturer chooses

Bundling Strategies for Ride-Hailing Platforms Based on Price and Service Level

The increasing popularity of ride-hailing applications has given rise to a new channel in which ride-hailing platforms are bundled into aggregation platforms to earn additional orders by charging commissions and slotting fees. Such bundled channels, unlike traditional reseller electronic ones, may flutter prices, service levels, market demands, and then further affect their profits. These divergent attitudes raise an interesting and key question about whether and under what conditions bundled channels should be introduced to ride-hailing platforms. In this paper, we provide an analytical framework for ride-hailing and aggregation platforms in unbundled and bundled scenarios, respectively. We build a Stackelberg game model in which ride-hailing and aggregation platforms as leaders obtain prices by constructing Nash equilibria, while drivers as followers determine service levels given to two platforms. Drivers’ best responses in terms of service levels for two platforms, as well as platforms’ optimal pricing strategies and profits are achieved. To capture access conditions of the ride-hailing platform and the profit contention between two platforms, we further conduct sensitivity analysis on cost coefficients of service levels, price and cross-price substitutions, service level and cross-service level substitutions, revenue-sharing ratio, cost, as well as commission and slotting fee. Based on numerical examples and analysis of the results, some interesting managerial insights about bundling strategies are gained for ride-hailing platforms

Pricing Decisions and Coordination in E-Commerce Supply Chain with Wholesale Price Contract Considering Focus Preferences

Decision makers’ behavioral preferences have always been important in coordinating the supply chain. Decision makers need to choose a partner wisely to increase the profitability of the entire supply chain, especially in the competitive e-commerce environment. In this paper, we examine a two-echelon e-commerce supply chain with one retailer and one supplier using the most popular wholesale price contract to facilitate collaboration. Traditional research has shown that the classical expectation model cannot coordinate the supply chain. We apply the focus theory of choice to describe the retailer’s behavior as a follower, and we examine the impact of the retailer’s pricing decisions on the supplier under different focus preferences and the coordination for the entire supply chain. The lower the parameter φ, which represents the degree of positivity, and the higher the parameter κ, which represents the level of confidence, the closer the profit of the whole supply chain is to the coordination result—both are visualized through numerical experiments and images. In the case of φ determination, the lower the κ, the better the supply chain coordination. The finding implies that the retailer may be able to coordinate the supply chain and produce better results than the expectation model when he or she makes choices using a positive evaluation system that includes both higher levels of optimism and lower levels of confidence. The findings of the FTC model can simultaneously offer a theoretical foundation for expanding collaboration among supply chain participants and management insights for decision makers to choose cooperation partners

Return Policy Selection Analysis for Brands Considering MCN Click Farming and Customer Disappointment Aversion

In order to solve the problem of separation between consumer purchase and product experience in online sales, live streaming e-commerce came into being. However, the interaction of streamers is easy to cause consumers’ impulse consumption, which leads to the soaring return rate. In this context, how to make reasonable return policies to avoid the loss is an important issue for brands. This paper studies return policy selection for brands. We mainly focus on MCN (multi-channel network) click farming and customer disappointment aversion in the situations that the return-freight insurances are paid by brands or consumers or brands and MCN jointly. Three leader-follower models with brands as leaders and platforms and MCN as followers are established. To solve the above bilevel models, we discuss the conditions under which the upper and lower models are both convex and, based on these theoretical results, we give the optimal strategies for all members. Then, through numerical experiments, we analyze the impacts of customer disappointment aversion level, MCN’s ability, commission rate, brand’s return-freight insurance purchasing ratio, and other factors on each member’s optimal decision. The results show that the return policy in the situation of return-freight insurance paid by brand is suitable for a market with the high level of customer disappointment aversion; the return policy in the situation of return-freight insurance paid by consumers is applicable to the case of low customer disappointment aversion and high commission rate; the return policy in the situation of return-freight insurance paid by brand and MCN jointly is suitable for the case of low MCN capability and can effectively restrain the click farming from MCN

Strategy Analysis for Retailer-Leading Supply Chain under Buyback Contract with Focus Theory of Choice

This paper investigates a retailer-leading two-tier supply chain with a buyback contract under market demand uncertainty, where the retailer first announces a potential maximal order quantity and the supplier then provides a unit wholesale price to influence the retailer’s order quantity. In recent years, an increasing number of experimental studies have reported that even in repeated multi-turn games, the decisions of suppliers viewed as newsvendors deviate significantly from the expectation-maximizing options. In light of this observation, we employ the focus theory of choice to characterize suppliers’ behavioral tendencies and theoretically derive optimal unit wholesale prices based on suppliers’ focus preferences. With these results, we further explore how suppliers’ foci may influence the interactions between the retailer and the supplier. We find that when the supplier takes the positive evaluation system as the decision criterion, optimism degree and confidence level have a negative effect on the wholesale price and a positive effect on the final order quantity, and the final order quantity must be located between the most possible market demand and the upper limit of the market demand. This paper provides a behavioral perspective to analyze suppliers’ optimal responses and their influences on retailers’ decision-making. Theoretical and numerical analyses gain managerial insights for retailers to make decisions when faced with suppliers with different focus preferences