Fouad El Ouardighi

A DYNAMIC GAME OF OPERATIONS AND MARKETING MANAGEMENT IN A SUPPLY CHAIN

The aim of the paper is to study some important differences between (classical) non-cooperative and (modern) cooperative supply chain management. For this purpose, the paper develops a differential game model involving operations and marketing activities that are performed by a manufacturer and a retailer in a simple two-member supply chain. We consider a particular single brand of the manufacturer. The manufacturer decides on production volume, production process improvement and national advertising efforts, while the retailer decides her purchase volume by the manufacturer and her pricing policy toward the final consumers. A revenue sharing contract is employed in the non-cooperative setting. Among the issues addressed on the manufacturer side are the trade-off between production and process improvement activities, the path of inventory over time, and the trade-off between attracting new customers and improving the loyalty of current customers. For the retailer we study the inventory and price evolution over time.

Quality improvement and goodwill accumulation in a dynamic duopoly

Abstract This paper analyzes optimal advertising and quality improvement decisions by duopolist firms competing in a dynamic setting. An extended version of the Lanchester model is formulated where conformance quality and goodwill are both involved in competition for market share. Each competitor’s new customer attraction rate depends on its own goodwill, while the disloyalty rate for current customers is influenced by the proportion of defective items. The search for a non-cooperative solution by qualitative as well as numerical means leads to definition of the optimal path for advertising and improvement efforts for each competitor, examined under a wide range of configurations.

Dynamic conformance and design quality in a supply chain: an assessment of contracts’ coordinating power

We consider a two-echelon supply chain involving one manufacturer and one supplier who collaborate on improving both design and conformance quality. Design quality is supposed to increase product desirability, and therefore market demand, while conformance quality should reduce the proportion of defective items, and therefore increase the manufacturer’s sales revenue. We investigate how the supply chain parties allocate effort between design and conformance quality under both cooperative and non-cooperative settings in an intertemporal framework. Furthermore, we evaluate wholesale price contracts and revenue-sharing contracts in terms of their performance and coordination power. We show that although a revenue-sharing contract enables the manufacturer to effectively involve the supplier in quality improvement, neither contract type allows for perfect coordination resulting in the quality that can be achieved by a cooperative supply chain. We thus suggest a reward-based extension to the revenue-sharing contract, to ensure system-wide optimal quality performance. Importantly, we find that the supplier would be better off adopting a reward-based revenue sharing contract and refusing a standard revenue-sharing contract, while the opposite would be true for the manufacturer.

Pollution accumulation and abatement policy in a supply chain

This paper seeks to determine how the double marginalization phenomenon affects the tradeoff between polluting emissions and abatement activities related to pollution accumulation in a supply chain composed of one manufacturer and one retailer. The environmental consequence of this inefficiency, which emerges in a non-cooperative vertical setting governed by a single-parameter contract, is overlooked in the literature on pollution control. In the setup of a two-stage game, we investigate the impact of double marginalization for non-cooperative equilibrium. To check whether there are differences between dynamic and strategic effects of double marginalization on pollution accumulation, both the open-loop and feedback Nash equilibria are derived over a finite time horizon, with the cooperative solution as a benchmark.

The impact of partial information sharing in a two-echelon supply chain

Abstract We consider a simple two-echelon supply chain composed of a manufacturer and a retailer in which the demand process of the retailer is an AR(1) where the random component is a function of both sides’ information. We focus on partial information sharing under which each side informs the other of an interval in which the exact value of its own component of demand lies. These various levels of information sharing can reduce the supply chain costs.

Controlling pollution and environmental absorption capacity

This pollution accumulation model shows that the environmental absorption capacity is impacted by economic activity. The resulting optimal control problem has two inter-related state variables: the stock of pollution and the absorption capacity of the environment. The stock of pollution decreases with environmental absorption capacity and increases with the rate of current emissions, which is controlled by a production level as well as an emissions reduction effort. However, the environmental absorption capacity is positively affected by an absorption development effort, and negatively impacted by the stock of pollution. Under specific conditions, it is shown that an optimal path, which can be either monotonic or following transient oscillations, leads to a (nontrivial) saddle-point characterized by a positive environmental absorption capacity.

A dynamic game with monopolist manufacturer and price-competing duopolist retailers

The paper considers a dynamic game with a single manufacturer who supplies two retailers. The manufacturer determines his production rate of a specific product, the rate of quality improvement efforts as well as the rate of advertising for the product. Each retailer controls her purchasing rate and the consumer sales price. Payments from a retailer to the manufacturer are determined by a wholesale price or a revenue-sharing scheme. The retailers operate in the same consumer market in which they compete in prices for the consumer demand. Nash equilibrium conditions are derived and numerical methods are employed to characterize equilibrium behavior of the players in a differential game of fixed and finite duration.

Quality and the diffusion of innovations

In this paper, we solve the problem of optimal control of products diffusion by quality in a context of monopolistic competition. To do so, we introduce a dynamic demand function leaning on two hypotheses: first, price acts a signal of quality; second, demand is more sensitive to quality than to price. Using the maximum principle of Pontryagin, we then characterize the optimal dynamic trajectory of quality and its qualitative properties.

Autonomous and advertising-dependent ‘word of mouth’ under costly dynamic pricing

Autonomous ‘word of mouth’, as a channel of social influence that is out of firms’ direct control, has acquired particular importance with the development of the Internet. Depending on whether a given product or service is a good or a bad deal, this can significantly contribute to commercial success or failure. Yet the existing dynamic models of sales in marketing still assume that the influence of word of mouth on sales is at best advertising-dependent. This omission can produce ineffective management and therefore misleading marketing policies. This paper seeks to bridge the gap by introducing a contagion sales model of a monopolist firms product where sales are affected by advertising-dependent as well as autonomous word of mouth. We assume that the firms attraction rate of new customers is determined by the degree at which the current sales price is advantageous or not compared with the current customers’ reservation price. A primary goal of the paper is to determine the optimal sales price and advertising effort. We show that, despite costly price adjustments, the interactions between sales price, advertising-dependent and autonomous word of mouth can result in complex dynamic pricing policies involving history-dependence or limit cycling consisting of alternating attraction of new customers and attrition of current customers.

The Dynamics Of Cooperation

In this paper, the problem of cooperation is formulated in a dynamic framework. The proposed model interrelates the process of a joint production activity involving two partners and the dynamics of a common monitoring activity of their respective contributions. Analysis of the existence of a stationary equilibrium leads to a set of predictions on the long run issue of cooperation from given initial conditions.