Federgruen outline

Econometric Institute and Princeton University Press organize the intensive PhD-course:

"Modeling Competition and Coordination in Supply Chains and Service Network"

Prof. Awi Federgruen (Graduate School of Business, Columbia University)

June 8-10, 2005
Erasmus University Rotterdam

Course outline

Lecture I: Competition and Coordination in Supply Chains with Price and Service Level Competition

In this lecture, we develop a stochastic general equilibrium inventory model for an oligopoly, in which all inventory constraint parameters are endogenously determined. We propose several systems of demand processes whose distributions are functions of all retailers' prices and all retailers' service levels. We proceed with the investigation of the equilibrium behavior of infinite horizon models for industries facing this type of generalized competition, under demand uncertainty. We systematically consider the following three competition scenarios. (I) price- competition only: here, we assume that the firms' service levels are exogenously chosen but characterize how the price and inventory strategy equilibrium varies with the chosen service levels. (II) simultaneous price- and service level- competition: here, each of the firms simultaneously chooses a service level and a combined price- and inventory strategy. (III) two-stage competition: the firms make their competitive choices sequentially; in a first stage all firms simultaneously choose a service level; in a second stage, the firms simultaneously choose a combined pricing- and inventory strategy with full knowledge of the service levels selected by all competitors. We show that in all of the above settings a Nash equilibrium of infinite horizon stationary strategies exists and that it is of a simple structure, provided a Nash equilibrium exists in a so-called reduced game. We pay particular attention to the question of whether a firm can choose its service level on the basis of its own (input) characteristics (i.e., its cost parameters and demand function) only. We also investigate under which of the demand models a firm, under simultaneous competition, responds to a change in the exogenously specified characteristics of the various competitors by either: (i) adjusting its service level and price in the same direction, thereby compensating for price increases (decreases) by offering improved (inferior) service, or (ii) adjusting them in opposite directions, thereby simultaneously offering better or worse prices and service. Next, we discuss how wholesale and retail prices should be specified, in an attempt to maximize supply-chain wide profits? We show what types of coordination mechanisms allow the decentralized supply chain to generate aggregate expected profits equal to the optimal profits in a centralized system, and how the parameters of these (perfect) coordination schemes can be determined. We systematically compare the coordination mechanisms when retailers compete only in terms of their prices, and when they engage in simultaneous price and service competition.

Lecture II: Competition in Service Industries

In many service industries, companies compete with each other on the basis of the waiting time their customers’ experience, along with the price they charge for their service. A firm's waiting time standard may either be defined in terms of the expected value or a given, for instance 95%, percentile of the steady state waiting time distribution. We investigate how a service industry's competitive behavior depends on the characteristics of the service providers' queuing systems. We provide a unifying approach to investigate various standard single stage systems covering the spectrum from M/M/1 to general G/GI/s systems, along with open Jackson networks to represent multi-stage service systems. Assuming that the capacity cost is proportional with the service rates we refer to its dependence on (i) the firm's demand rate and (ii) the waiting time standard as the capacity cost function. We show that across the above broad spectrum of queuing models, the capacity cost function belongs to a specific four-parameter class of function, either exactly or as a close approximation. We then characterize how this capacity cost function impacts on the equilibrium behavior in the industry. We give separate treatments to the case where the firms compete in terms of (i) prices (only) (ii) their service level or waiting time standard (only), (iii) simultaneously in terms of both prices and service levels. The firms' demand rates are given by a general system of equations of the prices and waiting time standards in the industry.

Lecture III: Competition in Service industries with Segmented Markets

We analyze the equilibrium behavior of service industries where firms cater to multiple customer classes or market segments with the help of shared service facilities or processes, so as to exploit pooling benefits. Different customer classes typically have rather disparate sensitivities to the price of service as well as the delays encountered. In such settings firms need to determine: (i) the prices charged to all customer classes, (ii) the waiting time standards, i.e. expected steady-state waiting time promised to all classes, (iii) the capacity level and (iv) a priority discipline enabling to meet the promised waiting time standards under the chosen capacity level, all on an integrated planning model which accounts for the impact of the strategic choices of all competing firms. To this end, we represent the demand rate faced by a given firm for a given market segment (customer class) as a separable function of all prices and waiting time standards offered to this segment in the industry, which in addition is linear in the price vector. This class of demand models allows us to represent general tradeoffs between (i) the prices, (ii) the waiting time standards, and (iii) all other attributes. We model each service provider as an M/M/1 queuing facility. Each customer class generates an independent Poisson stream of customers to this service provider at the rate determined by the above mentioned demand functions. Its service times are i.i.d. with a firm and class dependent service rate proportional to the firm’s capacity level.  Each firm incurs a given class dependent cost per customer as well as a cost per unit of time proportional to the adopted capacity level.  We distinguish between three types of competition: (I) Price competition: here all waiting time standards are exogenously given and the firms compete on the basis of their prices only, (II) Waiting time competition: here all prices are exogenously given and the competition is in terms of waiting time standards, and (III) Simultaneous competition: all prices and waiting time standards are selected simultaneously by the various service providers. We establish in each of the three competition models that a Nash equilibrium exists under minor conditions regarding the demand volumes. We also systematically compare the equilibria with those achieved when the firms service each market segment with a dedicated service process.

References

  • Allon, G., A. Federgruen (2004), Competition in Service Industries, Working paper .
  • Allon, G., A. Federgruen (2004), Competition in Service in Service Industries with Segmented Markets, Working paper .
  • Allon, G., A. Federgruen (2004), Service Competition with General Queueing Facilities, Working paper .

Presentations

Lecture Wilco van den Heuvel

Abstract

We consider a number of retailers that face a deterministic demand for the same item in a finite discrete time horizon. The retailers order the items at the same manufacturer. We assume a fixed ordering cost for each order placed and linear holding costs to carry inventory from one period to the next period. This means that every retailer has to solve an economic lot-sizing (ELS) problem to minimize his/her total costs. If the retailers cooperate, a cost saving can be obtained by placing joint orders instead of individual orders and a cooperative game arises (the ELS game). We address the question of how to allocate the cost savings among the retailers. To answer this question a (cooperative) game theoretical approach is used. We will show that for every ELS game there exists a cost allocation among the retailers in which no coalition of retailers has a direct incentive to end the cooperation. (paper , presentation )

Lecture Albert Wagelmans

Abstract

In this talk we consider the uncapacitated economic lot-size model, where demand is a deterministic function of price. In the model a single price need to be set for all periods. The objective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage  proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Moreover, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time. (paper , presentation )