Competing on Time: An Integrated Framework to Optimize Dynamic Time‐to‐Market and Production Decisions

This study develops a comprehensive framework to optimize new product introduction timing and subsequent production decisions faced by a component supplier. Prior to market entry, the supplier performs process design activities, which improve manufacturing yield and the chances of getting qualified for the customer's product. However, a long delay in market entry allows competitors to enter the market and pass the customer's qualification process before the supplier, reducing the supplier's share of the customer's business. After entering the market and if qualified, the supplier also needs to decide how much to produce for a finite planning horizon by considering several factors such as manufacturing yield and stochastic demand, both of which depend on the earlier time‐to‐market decision. To capture this dependency, we develop a sequential, nested, two‐stage decision framework to optimize the time‐to‐market and production decisions in relation to each other. We show that the supplier's optimal market entry and qualification timing decision need to be revised in real time based on the number of qualified competitors at the time of market‐entry decision. We establish the optimality of a threshold policy. Following this policy, at the beginning of each decision epoch, the supplier should optimally stop preparing for qualification and decide whether to enter the market if her order among qualified competitors exceeds a predetermined threshold. We also prove that the supplier's optimal production policy is a state‐dependent, base‐stock policy, which depends on the time‐to‐market and qualification decisions. The proposed framework also enables a firm to quantify how market conditions (such as price and competitor entry behavior) and operating conditions (such as the rate of learning and inventory/production‐related costs) affect time‐to‐market strategy and post‐entry production decisions.     

Demand Fluctuations in the Ready‐Mix Concrete Industry

I investigate the role of demand shocks in the ready‐mix concrete industry. Using Census data on more than 15,000 plants, I estimate a model of investment and entry in oligopolistic markets. These estimates are used to simulate the effect of eliminating short‐term local demand changes. A policy of smoothing the volatility of demand has a market expansion effect: The model predicts a 39% increase in the number of plants in the industry. Since bigger markets have both more plants and larger plants, a demand‐smoothing fiscal policy would increase the share of large plants by 20%. Finally, the policy of smoothing demand reduces entry and exit by 25%, but has no effect on the rate at which firms change their size.     

Dynamic Matching,Two‐Sided Incomplete Information,and Participation Costs: Existence and Convergence to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length δ, and, each unit of time, continuums of new buyers and sellers consider entry. Traders whose expected utility is negative choose not to enter. Within a period each buyer is matched anonymously with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and the winning buyer exit the market with their realized utility. Traders who fail to trade continue in the market to be rematched. We characterize the steady‐state equilibria that are perfect Bayesian. We show that, as δ converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation. We also show the existence of equilibria for δ sufficiently small, provided the discount rate is small relative to the participation costs.     

A Dynamic Reinterpretation of Nash Bargaining With Endogenous Threats

This paper concerns the two‐stage game introduced in Nash (1953). It formalizes a suggestion made (but not pursued) by Nash regarding equilibrium selection in that game, and hence offers an arguably more solid foundation for the “Nash bargaining with endogenous threats” solution. Analogous reasoning is then applied to an infinite horizon game to provide equilibrium selection in two‐person repeated games with contracts. In this setting, issues about enforcement of threats are much less problematic than in Nash's static setting. The analysis can be extended to stochastic games with contracts.     

Life‐Cycle Channel Coordination Issues in Launching an Innovative Durable Product

We analyze the dynamic strategic interactions between a manufacturer and a retailer in a decentralized distribution channel used to launch an innovative durable product (IDP). The underlying retail demand for the IDP is influenced by word‐of‐mouth from past adopters and follows a Bass‐type diffusion process. The word‐of‐mouth influence creates a trade‐off between immediate and future sales and profits, resulting in a multi‐period dynamic supply chain coordination problem. Our analysis shows that while in some environments, the manufacturer is better off with a far‐sighted retailer, there are also environments in which the manufacturer is better off with a myopic retailer. We characterize equilibrium dynamic pricing strategies and the resulting sales and profit trajectories. We demonstrate that revenue‐sharing contracts can coordinate the IDP's supply chain with both far‐sighted and myopic retailers throughout the entire planning horizon and arbitrarily allocate the channel profit.     

Cash‐Flow Based Dynamic Inventory Management

Small‐to‐medium‐sized enterprises (SMEs), including many startup firms, need to manage interrelated flows of cash and inventories of goods. In this study, we model a firm that can finance its inventory (ordered or manufactured) with loans in order to meet random demand which in general may not be time stationary. The firm earns interest on its cash on hand and pays interest on its debt. The objective is to maximize the expected value of the firm's capital at the end of a finite planning horizon. The firm's state at the beginning of each period is characterized by the inventory level and the capital level measured in units of the product, whose sum represents the “net worth” of the firm. Our study shows that the optimal ordering policy is characterized by a pair of threshold parameters as follows. (i) If the net worth is less than the lower threshold, then the firm employs a base stock order up to the lower threshold. (ii) If the net worth is between the two thresholds, then the firm orders exactly as many units as it can afford, without borrowing. (iii) If the net worth is above the upper threshold, then the firm employs a base stock order up to the upper threshold. Further, upper and lower bounds for the threshold values are developed using two simple‐to‐compute myopic ordering policies which yield lower bounds for the value function. We also derive an upper bound for the value function by considering a sell‐back policy. Subsequently, it is shown that policies of similar structure are optimal when the loan and deposit interest rates are piecewise linear functions, when there is a maximal loan limit and when unsatisfied demand is backordered. Finally, further managerial insights are provided with extensive numerical studies.     

Looking Upstream: Optimal Policies for a Class of Capacitated Multi‐Stage Inventory Systems

We consider a multi‐stage inventory system with stochastic demand and processing capacity constraints at each stage, for both finite‐horizon and infinite‐horizon, discounted‐cost settings. For a class of such systems characterized by having the smallest capacity at the most downstream stage and system utilization above a certain threshold, we identify the structure of the optimal policy, which represents a novel variation of the order‐up‐to policy. We find the explicit functional form of the optimal order‐up‐to levels, and show that they depend (only) on upstream echelon inventories. We establish that, above the threshold utilization, this optimal policy achieves the decomposition of the multidimensional objective cost function for the system into a sum of single‐dimensional convex functions. This decomposition eliminates the curse of dimensionality and allows us to numerically solve the problem. We provide a fast algorithm to determine a (tight) upper bound on this threshold utilization for capacity‐constrained inventory problems with an arbitrary number of stages. We make use of this algorithm to quantify upper bounds on the threshold utilization for three‐, four‐, and five‐stage capacitated systems over a range of model parameters, and discuss insights that emerge.     

Entry Deterrence of Capacitated Competition Using Price and Non‐Price Strategies

We analyze the role of pricing and branding in an incumbent firm's decision when facing competition from an entrant firm with limited capacity. We do so by studying two price competition models (Stackelberg and Nash), where we consider the incumbent's entry‐deterrence pricing strategy based on a potential entrant's capacity size. In an extension, we also study a branding model, where the incumbent firm, in addition to pricing, can also invest in influencing market preference for its product. With these models, we study conditions under which the incumbent firm may block the entrant (i.e., prevent entry without any market actions), deter the entrant (i.e., stop entry with suitable market actions) or accommodate the entrant (i.e., allow entry and compete), and how the entrant will allocate its limited capacity across its own and the new market, if entry occurs. We also study the timing difference between the two different dynamics of the price competition models and find that the incumbent's first‐mover advantage benefits both the incumbent and the entrant. Interestingly, the entrant firm's profits are not monotonically increasing in its capacity even when it is costless to build capacity. In the branding model, we show that in some cases, the incumbent may even increase its price and successfully deter entry by investing in consumer's preference for its product. Finally, we incorporate demand uncertainty into our model and show that the incumbent benefits from demand uncertainty while the entrant may be worse off depending on the magnitude of demand uncertainty and its capacity.     

Self‐Control and the Theory of Consumption

To study the behavior of agents who are susceptible to temptation in infinite horizon consumption problems under uncertainty, we define and characterize dynamic self‐control (DSC) preferences. DSC preferences are recursive and separable. In economies with DSC agents, equilibria exist but may be inefficient; in such equilibria, steady state consumption is independent of initial endowments and increases in self‐control. Increasing the preference for commitment while keeping self‐control constant increases the equity premium. Removing nonbinding constraints changes equilibrium allocations and prices. Debt contracts can be sustained even if the only feasible punishment for default is the termination of the contract.     

Entry and Exit in OTC Derivatives Markets

We develop a parsimonious model to study the equilibrium and socially optimal decisions of banks to enter, trade in, and possibly exit, an OTC market. Although we endow all banks with the same trading technology, banks' optimal entry and trading decisions endogenously lead to a realistic market structure composed of dealers and customers with distinct trading patterns. We decompose banks' entry incentives into incentives to hedge risk and incentives to make intermediation profits. We show that dealer banks enter more than is socially optimal. In the face of large negative shocks, they may also exit more than is socially optimal when markets are not perfectly resilient.     

Pre‐Orders for New To‐be‐Released Products Considering Consumer Loss Aversion

Advance selling through pre‐orders is a strategy to transfer inventory risk from a retailer to consumers. A newsvendor retailer can have three strategies to choose from: no advance selling allowed (NAS), moderate advance selling with a moderate discount for pre‐orders (MAS), and deep advance selling with a deep discount for pre‐orders (DAS). This research studies how a retailer could design an advance selling strategy to maximize her own profits. We find some interesting results. For example, there exist two thresholds for the selling season profit margin and two thresholds for consumer's expected valuation. For products with higher profit margin than the high threshold on profit margin, a retailer should always use DAS. For products with medium profit margin within the two thresholds, a retailer should adopt MAS if consumer's expected valuation is lower than the high threshold and use DAS otherwise. For products with lower profit margin than the low threshold, a retailer should use NAS, DAS, or MAS, respectively, if consumer's expected valuation is lower than the low threshold, higher than the high threshold, or between the two thresholds, respectively. Through sensitivity analyses, we also show the effects of multiple consumer characteristics on a retailer's optimal advance selling strategy.     

Benchmark Schedules for Subcontracted Operations: Decentralization Inefficiencies that Arise from Competition and First‐Come‐First‐Served Processing*

Subcontracting has become a prominent business practice across many industries. Subcontracting of industrial production is generally based on short‐term need for additional processing capacity, and is frequently employed by manufacturers to process customer orders more quickly than using only in‐house production. In this article, we study a popular business model where multiple manufacturers, each capable of processing his entire workload in‐house, have the option to subcontract some of their operations to a single third party with a flexible resource. Each manufacturer can deliver customer orders only after his entire batch of jobs, processed in‐house and at the third party, is completed. The third party facility is available to several manufacturers who compete for its use. Current business practice of First‐Come‐First‐Served (FCFS) processing of the subcontracted workloads as well as the competitive Nash equilibrium schedules developed in earlier studies result in two types of inefficiencies; the third party capacity is not maximally utilized, and the manufacturers incur decentralization cost. In this article, we develop models to assess the value created by coordinating the manufacturers' subcontracting decisions by comparing two types of centralized control against FCFS and Nash equilibrium schedules. We present optimal and/or approximate algorithms to quantify the third party underutilization and the manufacturers' decentralization cost. We find that both inefficiencies are more severe with competition than they are when the third party allocates capacity in an FCFS manner. However, in a decentralized setting, a larger percentage of the players prefer Nash equilibrium schedules to FCFS schedules. We extend our analysis to incomplete information scenarios where manufacturers reveal limited demand information, and find that more information dramatically benefits the third party and the manufacturers, however, the marginal benefit of additional information is decreasing. Finally, we discuss an extension wherein each manufacturer's objective takes into account asymmetries in subcontracting, in‐house processing, and delay costs.     

Vertical Integration with Price‐Setting Competitive Newsvendors*

This article addresses the problem of distribution channel design under demand uncertainty. We consider two manufacturers, each producing a substitutable product and selling it through either a decentralized or an integrated retail store, which is modeled as a price‐setting newsvendor. A multiplicative demand function incorporating a random shock term is assumed. Of primary interest is how demand uncertainty and production cost affect the equilibrium distribution channel structure. Results indicate the following: On the one hand, if the random shock term is uniformly distributed on [0, x], then the equilibrium design does not depend on the variance of the shock. On the other hand, if the random shock term is uniformly distributed on [1 −r, 1 +r], then the equilibrium design does depend on the variance of the shock. In particular, an increase in r favors the integrated structure where both channels are integrated and hurts the decentralized configuration where both channels are decentralized. Additionally, we explain the qualitative similarities and differences between the structural properties of the equilibrium distribution channel structure when demand is, and is not, uncertain. We also establish that production cost always favors the decentralized structure, while it hurts the integrated one. One important managerial implication of our study is that, by reducing the number of decisions made in supply chains, the impact of demand uncertainty can be controlled to a certain extent.     

Experimental Results Indicating Lattice‐Dependent Policies May Be Optimal for General Assemble‐To‐Order Systems

We consider an assemble‐to‐order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite‐horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be produced, and whether an arriving demand for each product should be satisfied. Previous work has shown that a lattice‐dependent base‐stock and lattice‐dependent rationing (LBLR) policy is an optimal stationary policy for a special case of the ATO model presented here (the generalized M‐system). In this study, we conduct numerical experiments to evaluate the use of an LBLR policy for our general ATO model as a heuristic, comparing it to two other heuristics from the literature: a state‐dependent base‐stock and state‐dependent rationing (SBSR) policy, and a fixed base‐stock and fixed rationing (FBFR) policy. Remarkably, LBLR yields the globally optimal cost in each of more than 22,500 instances of the general problem, outperforming SBSR and FBFR with respect to both objective value (by up to 2.6% and 4.8%, respectively) and computation time (by up to three orders and one order of magnitude, respectively) in 350 of these instances (those on which we compare the heuristics). LBLR and SBSR perform significantly better than FBFR when replenishment batch sizes imperfectly match the component requirements of the most valuable or most highly demanded product. In addition, LBLR substantially outperforms SBSR if it is crucial to hold a significant amount of inventory that must be rationed.     

FROM FLEXIBILITY TO INSECURITY: HOW VERTICAL SEPARATION AMPLIFIES FIRM‐LEVEL UNCERTAINTY

This article presents a model where firms may endogenously externalize part of their production process. We start from the premise that adaptation to uncertainty cannot be contracted upon in the worker/employer relationship. Vertical separation then balances flexibility gains against hold‐up costs of opportunistic behavior by outside contractors. In equilibrium, the degree of separation is shown to depend on the degree of product market competition, contractor's bargaining power, and the volatility of demand shocks. Our main result is that an increase in the degree of vertical separation amplifies the elasticity to demand shocks of firms' sales and employment. It does not, however, amplify aggregate uncertainty. Evidence from firm‐level data is shown to be largely consistent with the main implications of our theory. (JEL: L16, L23, L24)     

Technical Note—Demand Uncertainty Reduction in Decentralized Supply Chains

This note analyzes the effects associated with reducing demand uncertainty in a decentralized supply chain comprising one manufacturer, one retailer, and a wholesale price contract that governs the transactions between them. The demand uncertainty level is parameterized through a mean‐preserving spread, and the manufacturer's and the retailer's equilibrium decisions are solved accordingly. We consider the case of an exogenous retail price as well as the case of an endogenous retail price, and we find in both cases that the manufacturer's and the retailer's expected profits in equilibrium are not necessarily monotone decreasing in the uncertainty level. Thus, we find that, even if the cost of reducing demand uncertainty is zero, uncertainty reduction can hurt rather than benefit either or both members of the supply chain.     

Managing Retail Shelf and Backroom Inventories When Demand Depends on the Shelf‐Stock Level

Inventory displayed on the retail sales floor not only performs the classical supply function but also plays a role in affecting consumers’ buying behavior and hence the total demand. Empirical evidence from the retail industry shows that for some types of products, higher levels of on‐shelf inventory have a demand‐increasing effect (“billboard effect”) while for some other types of products, higher levels of on‐shelf inventory have a demand‐decreasing effect (“scarcity effect”). This suggests that retailers may use the amount of shelf stock on display as a tool to influence demand and operate a store backroom to hold the inventory of items not displayed on the shelves, introducing the need for efficient management of the backroom and on‐shelf inventories. The purpose of this study is to address such an issue by considering a periodic‐review inventory system in which demand in each period is stochastic and depends on the amount of inventory displayed on the shelf. We first analyze the problem in a finite‐horizon setting and show under a general demand model that the system inventory is optimally replenished by a base‐stock policy and the shelf stock is controlled by two critical points representing the target levels to raise up/drop down the on‐shelf inventory level. In the infinite‐horizon setting, we find that the optimal policies simplify to stationary base‐stock type policies. Under the billboard effect, we further show that the optimal policy is monotone in the system states. Numerical experiments illustrate the value of smart backroom management strategy and show that significant profit gains can be obtained by jointly managing the backroom and on‐shelf inventories.     

Inefficient Job Destructions and Training with Hold‐up

This paper develops an equilibrium search model with endogenous job destructions and where firms decide at the time of job entry how much to invest in match‐specific human capital. We first show that job destruction and training investment decisions are strongly complementary. It is possible that there are no firings at equilibrium. Further, training investments are confronted to a hold‐up problem making the decentralized equilibrium always inefficient. We show therefore that both training subsidies and firing taxes must be implemented to bring back efficiency.     

Safety Stock,Excess Capacity or Diversification: Trade‐Offs under Supply and Demand Uncertainty

Firms mitigate uncertainty in demand and supply by carrying safety stock, planning for excess capacity and diversifying supply sources. In this study, we provide a framework to jointly optimize these three levers in a periodic review infinite horizon setting, and in particular we examine how one can reduce inventory and capacity investments through proper diversification strategies. Observing that a modified base‐stock inventory policy is optimal, we find that the capacity‐diversification problem is well behaved and characterize the optimal mix of safety stock, excess capacity and extra number of supply sources. We find that higher supply uncertainty results in higher safety stock, more excess capacity, and higher diversification. But safety stock and diversification are non‐monotonic in demand uncertainty. Our results can be extended to situations in which suppliers are heterogeneous, and can be used to develop effective heuristics.