In this paper, we investigate the equilibrium behavior of decentralized supply chains with competing retailers under demand uncertainty. We also design contractual arrangements between the parties that allow the decentralized chain to perform as well as a centralized one. We address these questions in the context of two-echelon supply chains with a single supplier servicing a network of (competing) retailers, considering the following general model: Retailers face random demands, the distribution of which may depend only on its own retail price (noncompeting retailers) or on its own price as well as those of the other retailers (competing retailers), according to general stochastic demand functions.decentralized supply chains, coordination mechanisms, uncertain demands, inventory strategies
This paper develops 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. (1) Price competition only: Here, we assume that the firms' service levels are exogenously chosen, but characterize how the price and inventory strategy equilibrium vary with the chosen service levels. (2) Simultaneous price and service-level competition: Here, each of the firms simultaneously chooses a service level and a combined price and inventory strategy. (3) 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.
We consider a two-echelon distribution system in which a supplier distributes a product to N competing retailers. The demand rate of each retailer depends on all of the retailers' prices, or alternatively, the price each retailer can charge for its product depends on the sales volumes targeted by all of the retailers. The supplier replenishes his inventory through orders (purchases, production runs) from an outside source with ample supply. From there, the goods are transferred to the retailers. Carrying costs are incurred for all inventories, while all supplier orders and transfers to the retailers incur fixed and variable costs. We first characterize the solution to the centralized system in which all retailer prices, sales quantities and the complete chain-wide replenishment strategy are determined by a single decision maker, e.g., the supplier. We then proceed with the decentralized system. Here, the supplier chooses a wholesale pricing scheme; the retailers respond to this scheme by each choosing all of his policy variables. We distinguish systematically between the case of Bertrand and Cournot competition. In the former, each retailer independently chooses his retail price as well as a replenishment strategy; in the latter, each of the retailers selects a sales target, again in combination with a replenishment strategy. Finally, the supplier responds to the retailers' choices by implementing his own cost-minimizing replenishment strategy. We construct a perfect coordination mechanism. In the case of Cournot competition, the mechanism applies a discount from a basic wholesale price, based on the sum of three discount components, which are a function of (1) annual sales volume, (2) order quantity, and (3) order frequency, respectively.
We characterize supply chain settings in which perfect coordination can be achieved with simple wholesale pricing schemes: either retailer-specific constant unit wholesale prices or retailer-specific volume discount schemes. We confine ourselves to two-echelon supply chains with a single supplier servicing a network of retailers who compete with each other by selecting sales quantities. We identify a key sufficient condition, in terms of interdependencies between chain members' operational decisions, under which perfect coordination via simple schemes is feasible, under general cost and demand functions. This condition, which we refer to as echelon operational autonomy (EOA), states that the costs incurred by the supplier for a given vector of sales volumes depends only on operational decisions she controls herself. At the same time, the costs incurred by the retailers may depend on operational decisions controlled by the supplier, in which case, the supplier's operational decisions are made to minimize chainwide costs. We show how vendor-managed inventory (VMI) partnerships create EOA and compare the resulting coordinating pricing schemes with those required in a traditional decentralized setting (without EOA). We also discuss compliance issues with the coordinating schemes in view of the Robinson-Patman act and provide remedies to overcome these issues.supply chain coordination, pricing, vendor-managed inventory, echelon operational autonomy
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