Sourour ELLOUMI- CEDRIC / CNAM Paris, France

May 19th 2014

Facility location and network design: the p-median problem and the notion of good formulation in discrete mathematical optimization

Abstract: We consider the p-median problem where one has to open a given number p of facilities, and assign customers to their closest open facilities in such a way that the total distance between customers and facilities is as small as possible. We show some applications of this fundamental problem in discrete location theory. We then present several formulations of the p-median problem by mixed integer linear programming. We compare these formulations from different aspects. Our objective will be to illustrate how the choice of a formulation may have an important influence on the running time needed to compute an optimal solution.

Virginie GABREL - LAMSADE / Université de Paris-Dauphine, France

May 5th 2014

Designing Incentive Systems for Truthful Information Sharing in Supply Chains

Abstract: We consider the problem of portfolio optimization with uncertainty on asset returns. In the context of a scenario-based approach, we want to determine a robust portfolio performing an acceptable compromise between the expected returns and the risk of making losses. Many approaches have been suggested, all based on the formulation of two criteria : one for expected return and the other for measuring the risk. Some approaches propose to determine the set of Pareto-optimal solutions, other approaches consists in optimizing one criterion and transforming the second criterion into a constraint. In this latter approach, we propose a new criterion (inducing a new optimization model), called the pw-robustness criterion : the parameter w allows to manage the risk while the parameter p handles the maximization of expected return. This criterion generalizes the classical risk measure Value-at-Risk and can be compared to the Conditional Value-at-Risk measure regarding the worst cases. Joint work with Cécile Murat.

Ulrich THONEMANN- University of Cologne, Germany

March 31st 2014

Designing Incentive Systems for Truthful Information Sharing in Supply Chains

Abstract: We consider a firm where sales is responsible for demand forecasting and operations is responsible for ordering. Sales has better information about the demand than operations and sends a non-binding demand forecast to operations. Based on the demand forecast, operations determines the order quantity. To incentivize truthful demand information sharing, we include a penalty for forecast errors in the incentive system of sales. In the utility function of sales, we also include the behavioral factors lying aversion and loss aversion. We model the setting as a signaling game and derive equilibria of the game. In a laboratory experiment, we observe human behavior that is in-line with the model predictions, but deviates substantially from expected payoff maximizing behavior. Finally, we use the behavioral model to design incentive systems for truthful information sharing and conduct an experiment to validate the approach with out-of-sample treatments and out-of-sample subjects.

Victor MARTINEZ DE ALBENIZ - IESE Business School, Spain

February 17th 2014

A Closed-Loop Approach to Dynamic Assortment Planning

Abstract: Firms are constantly trying to keep the customers interested by refreshing their assortments. In industries such as fashion retailing, products are becoming short-lived and, without product introductions or in-store novelties, category sales quickly decrease. We model these dynamics by assuming that products lose their attractiveness over time and we let the firm enhance the assortment at a cost, for single or multiple categories. We characterize the optimal closed-loop policy that maximizes firm profits. When adjustment costs are linear in the attractiveness, we find that an assort-up-to policy is best: it is optimal to increase category attractiveness to a target level, which is independent of the current attractiveness. Furthermore, we develop heuristics to quickly determine good assort-up-to levels. Finally, we show that a closed-loop approach is valuable compared to open-loop strategies, especially when there is significant uncertainty about the decay rate of products. Joint work with Esra Çinar.

Fouad EL OUARDIGHI - ESSEC Business School, France

February 10th 2014

Operations and Marketings Strategies under Wholesale Price and Revenue Sharing Contracts in a Dynamic Supply Chain

Abstract: The objective of the paper is to study how wholesale price and revenue sharing contracts affect operations and marketing strategies in a supply chain under different dynamic informational structures. We suggest a differential game model of a stylized supply chain consisting of a manufacturer and a single retailer.The focus is on the production and sales of a single product. The model includes key operational and marketing activities in the supply chain. The manufacturer decides a production rate and the rate of national advertising efforts while the retailer chooses a purchase rate and the consumer price. Depending on whether the information on the current state of key operational and marketing variables of the supply chain is available or not, firms may either make decisions contingent on information on the current state of the game (feedback Nash equilibrium strategy), or commit to a predetermined plan of action during the whole game (open-loop Nash equilibrium strategy). The state of the game is summarized in the firms’ backlogs and the manufacturer’s advertising goodwill. A main result suggests that the double marginalization can be better mitigated if the supply chain members adopt a feedback Nash equilibrium strategy under wholesale price contract and open-loop Nash equilibrium strategy under revenue-sharing contract. Joint work with Gary Erickson, Dieter Grass, and Steffen Jorgensen.

Konstantin KOGAN - Bar-Ilan University, Israel

December 2nd 2013

A generalized Two-Agent Location Problem: Asymmetric Dynamics and Coordination

Abstract:We generalize a static two-agent location problem into dynamic, asymmetric settings. The dynamics is due to the ability of the agents to move at limited speeds. Since each agent has its own objective (demand) function and these functions are interdependent, decisions made by each agent may affect the performance of the other agent and thus affect the overall performance of the system. We show that under a broad range of system's parameters, centralized (system-wide optimal) and non-cooperative (Nash) behavior of the agents are characterized by a similar structure. The timing of these trajectories and the intermediate speeds are however different. Moreover, non-cooperative agents travel more and may never rest and thus the system performance deteriorates under decentralized decision-making. We show that a static linear reward approach recently developed in Golany and Rothblum (2006) can be generalized to provide coordination of the moving agents and suggest its dynamic modification. When the reward scheme is applied, the agents are induced to choose the system-wide optimal solution even though they operate in a decentralized decision-making mode.

Gustav FEICHTINGER - Vienna University of Technology, Austria

November 4th 2013

Dynamics and Control of Deviant Behavior

Abstract: Two essential aspects of deviant behavior are the time aspect and social interactions. The consumption of illicit drugs, the spread of corruption and the incidence of violence exhibit epidemic structure. Thus, mathematical models describing deviant behavior are intertemporal and non-linear. We illustrate how the efficient control of such behavior can be analysed by using dynamic optimisation models. Typically, one gets multiple equilibria and tipping behavior (history-dependence) of optimal solutions. In particular, it is shown how the optimal mix of various control instruments evolve over time. Homogenous socio-economic agents are often unrealistic simplifications. A first step to include heterogeneity is the distinction of light and heavy deaviance. It is the escalation from light to heavy which has to be controled efficiently. Finally, we discuss age-specific extensions as well as dynamic game issues in the economics of crime.

Yael PERLMAN - Bar-Ilan University, Israel

September 9th 2013

Reducing shoplifting by investment in security

Abstract: We consider a single retailer with a number of potential customers, who sells a product that is subject to shoplifting. In order to decrease losses due to shoplifting and to maximize his profit, the retailer can invest in security measures. In particular, we assume that the retailer hires the security services of a single security supplier. While the retailer decides how many security services to buy, the security supplier decides which price to charge the retailer for these services, with the purpose of maximizing his own profit. We address this problem using a game theoretic approach, where the retailer competes with the supplier—the leader—who specifies first the service price. The retailer responds by deciding how much to invest in security. We study the conditions under which both players are profitable and the extent to which the double marginalization affects the supply chain performance.