Equilibrium analysis of distribution channel structures under power imbalance and asymmetric information

This paper investigates the problem of channel choice game in two power-imbalanced supply chains consisting of the leader supply chain and the follower supply chain. We assume that there exists symmetric and asymmetric cost information between the two supply chains, and that the two chains as well as the two members in each chain follow the Stackelberg game setting. We analyse four competition scenarios: both chains are decentralised, where individual members of both supply chains maximise their own profits by independently selecting their price policies; both chains are integrated, where manufacturers and retailers coordinate their decisions to maximise supply chain profits; the leader chain is decentralised and the follower integrated; the leader is integrated and the follower decentralised. The primary objective of this paper is to investigate the influence of power imbalance, information asymmetries, and the degree of product substitutability under channel choice equilibrium. We find that, in contrast to earlier literature where all manufacturers share equal or balanced decision-making power, an integrated distribution channel is the dominant strategy for the leader under symmetric and asymmetric information Stackelberg game. As the degree of product substitutability increases, the follower will gradually switch from integrated distribution channel to decentralised distribution channel; the follower can gain from constructing a decentralised distribution channel as the prediction accuracy of the leader increases.     

A Stackelberg-Nash model for new product design

Existing conjoint approaches to optimal new product design have focused on the Nash equilibrium concept to model competitive reactions. Whereas these approaches have treated all competing firms equally as Nash players, one firm may have an advantage over its rivals, e.g., more pre-experience on competitors’ behavior and/or a first-mover advantage. This paper proposes a Stackelberg-Nash (leader-followers) model which can accomodate such information for decision making. The optimal product design problem is formulated from the perspective of a profit-maximizing new entrant (the leader) who wants to launch a brand onto an existing product market and acts with foresight by anticipating price-design reactions of the incumbent firms (the Nash followers). In the absence of closed-form solutions, we use a sequential iterative procedure to compute a Stackelberg-Nash equilibrium and to establish its uniqueness. The new conjoint model is illustrated under several competitive scenarios and price, design and profit implications are compared to a simple Nash equilibrium model. We find that a Stackelberg leader strategy may not only yield a much higher profit for the new entrant than a Nash strategy, but may also lead to strong profit asymmetries between competitors with still higher profits for the incumbent firms. In other words, the incumbent firms may also benefit strongly from a new entrant choosing a Stackelberg leader strategy.     

On the impact of spatial pattern,aggregation, and model parameters in planar Huff-type competitive location and design problems

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximize the profit obtained for the chain. Several types of constraints and costs are considered. Applying an interval analysis based global optimization method on several spatial patterns in a quasi-real-world environment, the behaviour of optimal solutions is investigated when changes are made in the basic model parameters. The study yields valuable insight for modellers into the impact of spatial pattern and various model parameters of the model on the resulting location and design decision. Spatial patterns differ in distribution of demand, of own and/or competing facilities, and of facility qualities. Studied model parameters include push force effects, investment restrictions and aggregation of demand. An extended version of this paper including additional studies on model parameters and the exact data used in the computational experiments is available at Optimization Online (see Tóth et al. (2008)). This work has been supported by grants from the Ministry of Science and Innovation of Spain (TIN2008-01117, SEJ2005-06273/ECON and ECO2008-00667/ECON), Junta de Andalucía (P08-TIC-3518), and in part by the European Regional Development Fund (ERDF).     

A bilevel game theoretic approach to optimum design of flywheels

Multiobjective optimization problems arise frequently in mechanical design. One approach to solving these types of problems is to use a game theoretic formulation. This article illustrates the application of a bilevel, leader–follower model for solving an optimum design problem. In particular, the optimization problem is modelled as a Stackelberg game. The partitioning of variables between the leader and follower problem is discussed and a variable partitioning metric is introduced to compare various variable partitions. A computational procedure based on variable updating using sensitivity information is developed for exchanging information between the follower and leader problems. The proposed approach is illustrated through the design of a flywheel. The two objective functions used for the design problem include maximizing the kinetic energy stored in the flywheel while simultaneously minimizing the manufacturing cost.     

汽车制造商的零售与租赁混合渠道管理策略

在两周期设置下,将制造商占主导的零售与租赁混合渠道结构区分为独立式、冲突式和回购式三类,然后分析了租赁渠道对零售渠道的影响以及制造商相应的渠道管理策略。结果表明:对于制造商而言,回购式结构是较为稳定的渠道结构,其可以平衡零售商和租赁商的利益。     

Impact of demand price elasticity on advantages of cooperative advertising in a two-tier supply chain

This paper focuses on pricing and vertical cooperative advertising decisions in a two-tier supply chain. Using a Stackelberg game model where the manufacturer acts as the game leader and the retailer acts as the game follower, we obtain closed-form equilibrium solution and explicitly show how pricing and advertising decisions are made. When market demand decreases exponentially with respect to the retail price and increases with respect to national and local advertising expenditures in an additive way, the manufacturer benefits from providing percentage reimbursement for the retailer’s local advertising expenditure when demand price elasticity is large enough. Whether the manufacturer benefits from cooperative advertising is also closely related to supply chain member’s relative advertising efficiency. In the decision for adopting coop advertising strategy, it is critical for the manufacturer to identify how market demand depends on national and local advertisements. The findings from this research can enhance our understanding of cooperative advertising decisions in a two-tier supply chain with price-dependent demand.     

Designing a model for service facility protection with a time horizon based on tri-level programming

ABSTRACT

This study investigates the tri-level location problem of defence facilities with a time horizon. This research focuses on the r-interdiction median model over a finite time horizon. This research aims to protect the service facilities using the defence facilities against the most severe attack scenario of the attacker, so that the system is able to use its maximum power to serve the customers after being damaged. This problem is established on the basis of leader–follower games in the form of defender–attacker–defender. Moreover, attempts are made to make the model more realistic by considering a time horizon. To solve the problem, a combination of a genetic algorithm, simulated annealing and an exact method is used. Comparison of the solution method of the applied metaheuristic algorithm and the exact solution method in a number of small samples indicates the desirable performance of this algorithm in a reasonable time.     

零售商主导下考虑增值物流服务的供应链期权契约协调

在零售商为主导者,生产商为跟随者且承担物流服务的模式下,考虑物流服务价值增值,建立了物流服务水平影响市场需求情形下的两级Stackelberg博弈模型。研究表明,分散决策下生产商的生产量和物流服务水平均低于集中决策下的结果,引入期权契约和物流服务成本共担契约可同时协调生产量和物流服务水平。最后,通过算例验证了上述契约组合的可行性,改变物流服务成本分担比例的取值,分析了零售商期权价格、期望利润以及第一次订购产品量的变化情况。     

基于风险规避的绿色供应链定价研究

为了解决风险规避型厂商在不同市场结构下的绿色供应链定价问题,首先以由一个风险规避的制造商和一个风险规避的零售商组成的二级绿色供应链为背景,考虑了消费者偏好、产品绿色度、厂商风险规避度等因素,构建厂商的期望效用函数,然后运用博弈论的方法建立了集中决策模型和三种分散决策模型。比较分析了这四种模型下的批发价格、产品绿色度和零售价格,并进一步分析了四种模型在制造商与零售商风险态度不同时的情况。最后通过MATLAB软件数值仿真研究了集中决策模型下的风险规避度对批发价格、产品绿色度、零售价格和供应链效用的影响以及产品绿色度对供应链效用的影响。仿真结果表明：在一定市场条件下,制造商风险规避对批发价格的影响程度要大于零售商,而对于产品绿色度、零售价格和供应链效用的影响程度是相同的且负向相关;同时,在固定制造商和零售商的风险规避度为0.5时,最优产品绿色度在3.3~3.4之间,最大产品绿色度为7.8。     

Path synthesis of four-bar mechanisms using synergy of polynomial neural network and Stackelberg game theory

In this article, a novel approach based on game theory is presented for multi-objective optimal synthesis of four-bar mechanisms. The multi-objective optimization problem is modelled as a Stackelberg game. The more important objective function, tracking error, is considered as the leader, and the other objective function, deviation of the transmission angle from 90° (TA), is considered as the follower. In a new approach, a group method of data handling (GMDH)-type neural network is also utilized to construct an approximate model for the rational reaction set (RRS) of the follower. Using the proposed game-theoretic approach, the multi-objective optimal synthesis of a four-bar mechanism is then cast into a single-objective optimal synthesis using the leader variables and the obtained RRS of the follower. The superiority of using the synergy game-theoretic method of Stackelberg with a GMDH-type neural network is demonstrated for two case studies on the synthesis of four-bar mechanisms.     

Supply chain network design with unreliable suppliers: a Lagrangian relaxation-based approach

This paper deals with the integrated facility location and supplier selection decisions for the design of supply chain network with reliable and unreliable suppliers. Two problems are addressed: (1) facility location/supplier selection; and (2) facility location/supplier reliability. We first consider the facility location and supplier selections problem where all the suppliers are reliable. The decisions concern the selection of suppliers, the location of distribution centres (DCs), the allocation of suppliers to DCs and the allocation of retailers to DCs. The objective is to minimise fixed DCs location costs, inventory and safety stock costs at the DCs and ordering costs and transportation costs across the network. The introduction of inventory costs and safety stock costs leads to a non-linear NP-hard optimisation problem. To solve this problem, a Lagrangian relaxation-based approach is developed. For the second problem, a two-period decision model is proposed in which selected suppliers are reliable in the first period and can fail in the second period. The corresponding facility location/supplier reliability problem is formulated as a non-linear stochastic programming problem. A Monte Carlo optimisation approach combining the sample average approximation scheme and the Lagrangian relaxation-based approach is proposed. Computational results are presented to evaluate the efficiency of the proposed approaches.     

Bilevel joint optimisation for product family architecting considering make-or-buy decisions

Product family architecting (PFA) aims at identification of common modules and selective modules to enable product family configuration for mass customisation. Due to nowadays manufacturers moving more towards assembly-to-order production throughout a distributed supply chain, the common practice of outsourcing of certain modules entails make-or-buy (MOB) decisions that must be taken into account in PFA. While the PFA and MOB decisions are enacted for different concerns of the manufacturer and the suppliers, it is important to deal with joint optimisation of the PFA and MOB problems. The prevailing decision models for joint optimisation are mainly originated from an ‘all-in-one’ approach that assumes both PFA and MOB decisions can be integrated into one single-level optimisation problem. Such an assumption neglects the complex trade-offs underlying two different decision-making problems and fails to reveal the inherent coupling of PFA and MOB decisions. This paper proposes to formulate joint optimisation of the PFA and MOB problems as a Stackelberg game, in which a bilevel decision mechanism model is deployed to reveal the inherent coupling and hierarchical relationships between PFA and MOB decisions. A nonlinear bilevel optimisation model is developed with the PFA problem acting as the leader and each MOB problem performing as a follower. A nested genetic algorithm is developed to solve the bilevel optimisation model. A case study of power transformer PFA subject to MOB considerations is presented to illustrate the feasibility and effectiveness of bilevel joint optimisation.     

引入补偿、惩罚策略的配送中心选址问题研究

根据配送中心与零售商在市场中的相对地位,针对保持市场份额或降低物流成本不同目标,配送中心对远距离零售商可制定补偿或惩罚两种策略。在LMRPVCC问题优化模型基础上,在目标函数与约束条件中引入运输补偿、惩罚成本项及服务半径Dr,可将模型扩展为引入补偿、惩罚策略的LMRPVCC选址-库存问题的非线性整数规划模型。利用所设计的粒子群算法对Hakimi文章中10节点算例和Daskin和Shen的文章中的49节点求解,对惩罚、补偿系数W、服务半径Dr进行敏感性分析的结果表明,不同配送策略对配送中心物流总成本、各分项成本以及配送中心满意区位有重要影响。     

Pricing and location decisions in multi-objective facility location problem with M/M/m/k queuing systems

This article presents a new multi-objective model for a facility location problem with congestion and pricing policies. This model considers situations in which immobile service facilities are congested by a stochastic demand following M/M/m/k queues. The presented model belongs to the class of mixed-integer nonlinear programming models and NP-hard problems. To solve such a hard model, a new multi-objective optimization algorithm based on a vibration theory, namely multi-objective vibration damping optimization (MOVDO), is developed. In order to tune the algorithms parameters, the Taguchi approach using a response metric is implemented. The computational results are compared with those of the non-dominated ranking genetic algorithm and non-dominated sorting genetic algorithm. The outputs demonstrate the robustness of the proposed MOVDO in large-sized problems.     

不同市场结构下绿色闭环供应链决策分析

为了分析不同市场结构对绿色闭环供应链成员决策以及绩效的影响,引入环保参数,采用Stackelberg博弈法,比较了三种市场结构下渠道成员的决策、利润和渠道总利润。研究结果表明：制造商主导市场时批发价、零售价和制造商利润最高;零售商领导市场时回收水平、单位利润和零售商利润最高;环保水平和渠道总利润在垂直纳什市场结构下最高。理论上无领导者的垂直纳什结构最理想,但考虑实际情况,零售商控制市场时较好。     

On bilevel machine scheduling problems

Bilevel scheduling problems constitute a hardly studied area of scheduling theory. In this paper, we summarise the basic concepts of bilevel optimisation, and discuss two problem classes for which we establish various complexity and algorithmic results. The first one is the bilevel total weighted completion time problem in which the leader assigns the jobs to parallel machines and the follower sequences the jobs assigned to each machine. Both the leader and the follower aims to minimise the total weighted completion time objective, but with different job weights. When the leader’s weights are arbitrary, the problem is NP-hard. However, when all the jobs are of unit weight for the leader, we provide a heuristic algorithm based on iterative LP-rounding along with computational results, and provide a sufficient condition when the LP-solution is integral. In addition, if the follower weights induce a monotone (increasing or decreasing) processing time order in any optimal solution, the problem becomes polynomially solvable. As a by-product, we characterise a new polynomially solvable special case of the MAX m-CUT problem, and provide a new linear programming formulation for the P||?_j C_j{P||\sum_j C_j} problem. Finally, we present some results on the bilevel order acceptance problem, where the leader decides on the acceptance of orders and the follower sequences the jobs. Each job has a deadline and if a job is accepted, it cannot be late. The leader’s objective is to maximise the total weight of accepted jobs, whereas the follower aims at minimising the total weighted job completion times. For this problem, we generalise some known single-level machine scheduling algorithms.     

Optimal replenishment cycle for perishable items facing demand uncertainty in a two-echelon inventory system

We consider a two-echelon supply chain with an upstream manufacturer and a downstream retailer for a single perishable product. The manufacturer processes raw materials into finished products, which are purchased by the retailer in each replenishment cycle. The raw materials of the manufacturer are highly perishable (i.e. perishing within hours or days), and the finished goods at the retailer face demand uncertainty and obsolescence. We model the manufacturer–retailer relationship as a Stackelberg game where the retailer is the leader and decides the replenishment cycle that minimises its mismatch cost between supply and uncertain demand. The manufacturer is the follower and decides its processing rate to minimise its unit cost for finished goods. Our results show that the raw material and finished goods lifetimes, which are interrelated through the duration of the replenishment cycle, have a significant impact on supply chain costs. Although raw material spoilage cost by itself is low, we show that short raw material lifetimes have a significant impact on the costs of both parties. Additionally, we find that while high manufacturer markups increase retailer costs, they reduce the manufacturer's costs due to large production batches.     

Multi-commodity warehouse location and distribution planning with inventory consideration

We consider the problem of designing a distribution network for a logistics provider that acquires products from multiple facilities and then delivers those products to many retail outlets. Potential locations for consolidation facilities that combine shipments for cost reduction and service improvements are considered. The problem is formulated with direct shipment and consolidation opportunities. A novel mathematical model is derived to solve a complex facility location problem determining: (i) the location and capacity level of warehouses to open; (ii) the distribution route from each production facility to each retailer outlet; and (iii) the quantity of products stocked at each warehouse and retailer. A genetic algorithm and a specific problem heuristic are designed, tested and compared on several realistic scenarios.     

Applying genetic algorithm to a new location and routing model of hazardous materials

Nowadays – particularly in systems dealing with hazardous materials (HAZMAT) – in addition to minimising the cost of operations in facility location and routing problems, the risk of these operations is considered an important objective. In this paper, a new mathematical model for the location and routing in facilities and disposal sites is proposed. Also, the risk and cost of transporting goods from facilities to customers is considered. The model minimises weighted sum of the cost and risk by answering these questions: (1) where to open the facilities which produce HAZMAT; (2) where to open disposal sites; (3) to which facilities every customer should be assigned; (4) to which disposal site each facility should be assigned; (5) which route a facility should choose to serve the customers; and (6) which route a facility should choose to reach a disposal site. A novel GA is applied to solve the mathematical model. The results show the robustness of GA in terms of finding high-quality non-dominated solutions and running time.     

Facility location and scale optimisation in closed-loop supply chain

This paper solves a strategic-level decision problem on determining the optimal location of (re)manufacturers and logistics centres with the consideration of facility scales in an integrated closed-loop supply chain network. A two-stage stochastic mixed-integer non-linear programming model is established to minimise the fixed cost and the expected operation costs under uncertain demand and return. We develop an improved tabu search heuristic algorithm to solve the model. We also design a distance-based decision rule to validate the effectiveness of the proposed model. Numerical experiments are conducted to test the performance of the proposed model and the solution method. In addition, sensitivity analysis is provided to investigate the influences of varying inspection locations and recovery rates on the final performance.