Fernando Bernstein

Bricks-and-mortar vs. "clicks-and-mortar": An equilibrium analysis

Abstract The Internet has provided traditional retailers a new means with which to serve customers. Consequently, many “bricks-and-mortar” retailers have transformed to “clicks-and-mortar” by incorporating Internet sales. Examples of companies making such a transition include Best Buy, Wal-Mart, Barnes & Noble, etc. Despite the increasing prevalence of this practice, several fundamental questions remain: (1) Does it pay off to go online? (2) Which is the equilibrium industry structure? (3) What is the implication of this business model for consumers? We study these issues in an oligopoly setting and show that clicks-and-mortar arises as the equilibrium channel structure. However, we find that this equilibrium does not necessarily imply higher profits for the firms: in some cases, rather, it emerges as a strategic necessity. Consumers are generally better off with clicks-and-mortar retailers. If firms align with pure e-tailers to reach the online market, we show that a prisoner’s dilemma-type equilibrium may arise.

Decentralized Pricing and Capacity Decisions in a Multitier System with Modular Assembly

We model a modular assembly system in which a final assembler outsources some of the assembly task to first-tier suppliers (subassemblers), who produce modules made up of multiple components. The assembler sets module prices it will pay to the subassemblers, the subassemblers set component prices they will pay to suppliers, and then all players choose how much capacity to install, with the minimum capacity choice determining system capacity. Finally, stochastic end-product demand is observed and all players produce (and are paid for) the same number of units-the minimum of demand and system capacity. We characterize equilibrium price and capacity choices, and then use that characterization to derive results regarding higher-level structural choices by the assembler-such as how to group components into modules and which suppliers to choose as subassemblers. We also compare performance of the system to a traditional assembly system with an assembler and suppliers but without subassemblers.

Inventory Policies in a Decentralized Assembly System

We consider a system in which a single finished good is assembled from two components. Demand for the finished product is stochastic and stationary, and procurement and assembly lead times are constant. Unsatisfied demand is backordered. The inventory of each component or assembly is controlled by a separate firm using a base-stock policy. Each firm is charged holding costs on its own inventory, plus a share of the shortage cost due to backorders of the finished product. We investigate the equilibrium base-stock levels that arise in this system under both echelon and local base-stock policies. In both cases, the component firms base-stock levels are economic complements. We then examine the effect on system performance when one firm uses information about other firms pipeline inventory. We find that, under echelon base-stock policies, all firms benefit with the use of pipeline information. In contrast, under local policies, using pipeline information may actually increase costs for some firms (including the firm that makes direct use of the information). Also, we compare the behavior of the decentralized system with that of the assembly system under centralized control. Finally, we describe a payment scheme between the final assembler and the suppliers that allows the decentralized system to achieve the centralized solution.

Comparative statics, strategic complements and substitutes in oligopolies

Abstract Many fundamental questions in oligopoly models reduce to the analysis of the monotonicity properties of various performance measures under the model’s Nash equilibrium, with respect to specific exogenously specified parameters. These strategic parameters may have an impact on the demand functions of the various competitors, their cost structures or both. In this paper, we establish first- and second-order monotonicity properties of the equilibrium prices, quantities and profits for oligopoly models with general non-linear cost functions and general dependencies of the cost and demand functions on the strategic input parameters under consideration.

Dynamic Assortment Customization with Limited Inventories

We consider a retailer with limited inventory of identically priced, substitutable products. The retailer faces a market with multiple segments of customers that are heterogeneous with respect to their product preferences. Customers arrive sequentially, and the firm decides which subset of products to offer to each arriving customer depending on the customer’s preferences, the inventory levels, and the remaining time in the season. We show that it is optimal to limit the choice set of some customers (even when the products are in stock), reserving products with low inventory levels for future customers who may have a stronger preference for those products. In certain settings, we prove that it is optimal to follow a threshold policy under which a product is offered to a customer segment if its inventory level is higher than a threshold value. The thresholds are decreasing in time and increasing in the inventory levels of other products. We introduce two heuristics derived by approximating the future marginal expected revenue by the marginal value of a newsvendor function that captures the substitution dynamics between products. We test the impact of assortment customization using data from a fashion retailer. We find that the potential revenue impact of assortment customization can be significant, especially when customer heterogeneity is high and when the products’ inventory-to-demand ratios are asymmetric. Our findings suggest that assortment customization can be used as another lever for revenue maximization in addition to pricing.

The Impact of Demand Aggregation Through Delayed Component Allocation in an Assemble-to-Order System

We consider an assemble-to-order system in which multiple products are assembled from a common component and a set of product-dedicated components. Component capacities are chosen prior to a finite-horizon selling season, and the common component is allocated to the products based on observed demands. We propose a collection of allocation mechanisms involving varying degrees of demand aggregation, ranging from a scheme under which all demands are observed prior to making the allocation decision to allocations made for each arriving demand. In this context, we explore the impact of the allocation scheme on sales, profits, and capacity decisions, including the degree of capacity imbalance. We find that the benefit from increased demand aggregation is closely linked to the degree of capacity imbalance: profit gains from delayed allocation tend to be higher in systems in which the optimal capacity portfolio is highly unbalanced when the allocation decision is made after observing all demands. We develop insights into what detailed system parameters lead to the largest gains from demand aggregation and also explore the trade-offs associated with the choice of an allocation scheme when customers exhibit impatience if the allocation scheme forces them to wait to be served. This paper was accepted by Ananth Iyer, operations and supply chain management.

The Role of Component Commonality in Product Assortment Decisions

We consider a firm that produces multiple variants of a product. Products are assembled using a combination of common and dedicated components. We characterize the optimal assortment and derive the optimal inventory levels for the common and dedicated components under various bill-of-material configurations. We investigate the effect of commonality on product variety and compare its benefits under different demand characteristics. Commonality always leads to increased profits, but its effect on the level of product variety depends on the type of commonality. If all common components are used for the production of the entire set of products, then the optimal variety level increases relative to the system with no commonality. However, if the common components are used by a subset of the final products, then the optimal variety level may decrease with commonality. We find that the effects of commonality on profit and variety level are stronger under a demand model in which product demands are more variable and exhibit pairwise negative correlation relative to a model with independent demands.

Cooperation in assembly systems: The role of knowledge sharing networks

Process improvement plays a significant role in reducing production costs over the life cycle of a product. We consider the role of process improvement in a decentralized assembly system in which a buyer purchases components from several first-tier suppliers. These components are assembled into a finished product, which is sold to the downstream market. The assembler faces a deterministic demand/production rate and the suppliers incur variable inventory costs and fixed setup production costs. In the first stage of the game, which is modeled as a non-cooperative game among suppliers, suppliers make investments in process improvement activities to reduce the fixed production costs. Upon establishing a relationship with the suppliers, the assembler establishes a knowledge sharing network – this network is implemented as a series of meetings among suppliers and also mutual visits to their factories. These meetings facilitate the exchange of best practices among suppliers with the expectation that suppliers will achieve reductions in their production costs from the experiences learned through knowledge sharing. We model this knowledge exchange as a cooperative game among suppliers in which, as a result of cooperation, all suppliers achieve reductions in their fixed costs. In the non-cooperative game, the suppliers anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of knowledge sharing in their cost functions. Based on this model, we investigate the benefits and challenges associated with establishing a knowledge sharing network. We identify and compare various cost allocation mechanisms that are feasible in the cooperative game and show that the system optimal investment levels can be achieved only when the most efficient supplier receives the incremental benefits of the cost reduction achieved by other suppliers due to the knowledge transfer.

A Simple Heuristic for Joint Inventory and Pricing Models with Lead Time and Backorders

We study a joint inventory and pricing problem in a single-stage system with a positive lead time. We consider both additive and multiplicative demand forms. This problem is, in general, intractable due to its computational complexity. We develop a simple heuristic that resolves this issue. The heuristic involves a myopic pricing policy that generates each period’s price as a function of the initial inventory level and a base-stock policy for inventory replenishment. In each period, the firm monitors its so-called price-deflated inventory position and places an order to reach a target base-stock level. The price-deflated inventory position weights the on-hand and pipeline inventory according to a factor that reflects the sensitivity of price to the net inventory level. To assess the effectiveness of our heuristic, we construct an upper bound to the exact system. The upper bound is based on an information-relaxation approach and involves a penalty function derived from the proposed heuristic. A numerical study suggests that the heuristic is near-optimal. The heuristic approach can be applied to a wide variety of inventory systems, such as systems with fixed ordering costs or fixed batch sizes. The heuristic enables us to explore the use of price as a lever to balance supply and demand. Our findings indicate that a responsive strategy (that effectively reduces the replenishment lead time) leads to a more stable pricing policy and that the value of dynamic pricing increases with lead time. This paper was accepted by Martin Lariviere, operations management .

Advance Demand Information in a Multiproduct System

In this paper we examine the impact of different types of advance demand information on firm profit and on the benefits of resource flexibility. Specifically, we consider a firm that must choose capacities of resources that will be used to satisfy stochastic demand for multiple products, where demands follow a multivariate normal distribution. Prior to the capacity decision, the firm receives information revealing either the total volume of demand across products or the mix of demand between products. We examine two different scenarios: a dedicated resource setting with product-specific resources and a common resource scenario with one flexible resource. For both scenarios we derive the distribution of the (possibly imperfect) volume or mix demand signal, as well as the conditional distributions of demand given the particular signal. We explore the impact of either type of information on optimal capacities and profit. We find that commonality and volume information are strategic complements—so that it is more valuable to obtain volume information in settings with a common resource. On the other hand, commonality and mix information are strategic substitutes. Moreover, we find that mix and volume information themselves are complements in systems with dedicated resources. Having either type of information is valuable in reducing uncertainty for each individual product demand, but having both of them together provides information on two different dimensions, allowing for a much greater reduction in demand uncertainty. In systems with a common resource, however, the two types of information are substitutes. Because volume information is well aligned with commonality (both focus on total demand), such information already provides much of the value that can be obtained—having mix information adds limited additional value.