The impact of operational decisions on the design of salesforce incentives

When facing high levels of overstock inventories, firms often push their salesforce to work harder than usual to attract more demand, and one way to achieve that is to offer attractive incentives. However, most research on the optimal design of salesforce incentives ignores this dependency and assumes that operational decisions of production/inventory management are separable from design of salesforce incentives. We investigate this dependency in the problem of joint salesforce incentive design and inventory/production control. We develop a dynamic Principal‐Agent model with both Moral Hazard and Adverse Selection in which the principal is strategic and risk‐neutral but the agent is myopic and risk‐averse. We find the optimal joint incentive design and inventory control strategy, and demonstrate the impact of operational decisions on the design of a compensation package. The optimal strategy is characterized by a menu of inventory‐dependent salesforce compensation contracts. We show that the optimal compensation package depends highly on the operational decisions; when inventory levels are high, (a) the firm offers a more attractive contract and (b) the contract is effective in inducing the salesforce to work harder than usual. In contrast, when inventory levels are low, the firm can offer a less attractive compensation package, but still expect the salesforce to work hard enough. In addition, we show that although the inventory/production management and the design of salesforce compensation package are highly correlated, information acquisition through contract design allows the firm to implement traditional inventory control policies: a market‐based state‐dependent policy (with a constant base‐stock level when the inventory is low) that makes use of the extracted market condition from the agent is optimal. This work appears to be the first article on operations that addresses the important interplay between inventory/production control and salesforce compensation decisions in a dynamic setting. Our findings shed light on the effective integration of these two significant aspects for the successful operation of a firm. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 320–340, 2014     

To wait or not to wait: Optimal ordering under lead time uncertainty and forecast updating

There has been a dramatic increase over the past decade in the number of firms that source finished product from overseas. Although this has reduced procurement costs, it has increased supply risk; procurement lead times are longer and are often unreliable. In deciding when and how much to order, firms must consider the lead time risk and the demand risk, i.e., the accuracy of their demand forecast. To improve the accuracy of its demand forecast, a firm may update its forecast as the selling season approaches. In this article we consider both forecast updating and lead time uncertainty. We characterize the firm's optimal procurement policy, and we prove that, with multiplicative forecast revisions, the firm's optimal procurement time is independent of the demand forecast evolution but that the optimal procurement quantity is not. This leads to a number of important managerial insights into the firm's planning process. We show that the firm becomes less sensitive to lead time variability as the forecast updating process becomes more efficient. Interestingly, a forecast‐updating firm might procure earlier than a firm with no forecast updating. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Inventory financing under Risk-Adjusted-Return-On-Capital criterion

Risk-Adjusted-Return-On-Capital (RAROC) is a loan-pricing criterion under which a bank sets the loan term such that a certain rate of return is achieved on the regulatory capital required by the Basel regulation. Some banks calculate the amount of regulatory capital for each loan under the standardized approach (“standardized banks,” the regulatory capital is proportional to the loan amount), and others under the internal rating-based (IRB) approach (“IRB banks,” the regulatory capital is related to the Value-at-Risk of the loan). This article examines the impact of the RAROC criterion on the bank's loan-pricing decision and the retailer's inventory decision. We find that among the loan terms that satisfy the bank's RAROC criterion, the one that benefits the retailer the most requires the bank to specify an inventory advance rate in addition to the interest rate. Under this loan term, the retailer's inventory level is more sensitive to his asset level when facing an IRB bank compared to a standardized bank. An IRB (standardized) loan leads to higher profit and inventory level for retailers with high (low) asset. For retailers with medium asset, an IRB loan results in a higher retailer profit but a lower consumer welfare. Calibrated numerical study reveals that the benefit of choosing standardized banks (relative to IRB banks) can be as high as 30% for industries with severe capital constraints, volatile demands, and low profit margins, highlighting the importance for retailers to carefully choose the type of banks to borrow from. When the interest rate is capped by regulation, retailers borrowing from a standardized bank are more likely to be influenced by the interest rate cap than those borrowing from an IRB bank. Under strong empire-building incentives (the bank will offer loan terms to maximize the size of the loan), retailers with medium initial asset level shift their preference from IRB banks to standardized banks.     

Selling to strategic and loss‐averse consumers: Stocking,procurement, and product design policies

Motivated by the presence of loss‐averse decision making behavior in practice, this article considers a supply chain consisting of a firm and strategic consumers who possess an S‐shaped loss‐averse utility function. In the model, consumers decide the purchase timing and the firm chooses the inventory level. We find that the loss‐averse consumers' strategic purchasing behavior is determined by their perceived gain and loss from strategic purchase delay, and the given rationing risk. Thus, the firm that is cognizant of this property tailors its inventory stocking policy based on the consumers' loss‐averse behavior such as their perceived values of gain and loss, and their sensitivity to them. We also demonstrate that the firm's equilibrium inventory stocking policy reflects both the economic logic of the traditional newsvendor inventory model, and the loss‐averse behavior of consumers. The equilibrium order quantity is significantly different from those derived from models that assume that the consumers are risk neutral and homogeneous in their valuations. We show that the firm that ignores strategic consumer's loss‐aversion behavior tends to keep an unnecessarily high inventory level that leads to excessive leftovers. Our numerical experiments further reveal that in some extreme cases the firm that ignores strategic consumer's loss‐aversion behavior generates almost 92% more leftovers than the firm that possesses consumers’ loss‐aversion information and takes it into account when making managerial decisions. To mitigate the consumer's forward‐looking behavior, we propose the adoption of the practice of agile supply chain management, which possesses the following attributes: (i) procuring inventory after observing real‐time demand information, (ii) enhanced design (which maintains the current production mix but improves the product performance to a higher level), and (iii) customized design (which maintains the current performance level but increases the variety of the current production line to meet consumers’ specific demands). We show that such a practice can induce the consumer to make early purchases by increasing their rationing risk, increasing the product value, or diversifying the product line. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 435–453, 2015     

Dynamic inventory management with cash flow constraints

In this article, we consider a classic dynamic inventory control problem of a self‐financing retailer who periodically replenishes its stock from a supplier and sells it to the market. The replenishment decisions of the retailer are constrained by cash flow, which is updated periodically following purchasing and sales in each period. Excess demand in each period is lost when insufficient inventory is in stock. The retailer's objective is to maximize its expected terminal wealth at the end of the planning horizon. We characterize the optimal inventory control policy and present a simple algorithm for computing the optimal policies for each period. Conditions are identified under which the optimal control policies are identical across periods. We also present comparative statics results on the optimal control policy. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008     

Should competing firms reveal their capacity?

In this article, we explore when firms have an incentive to hide (or reveal) their capacity information. We consider two firms that aim to maximize profits over time and face limited capacity. One or both of the firms have private information on their own capacity levels, and they update their beliefs about their rival's capacity based on their observation of the other firm's output. We focus on credible revelation mechanisms—a firm may signal its capacity through overproduction, compared to its myopic production levels. We characterize conditions when high‐capacity firms may have the incentive and capability to signal their capacity levels by overproduction. We show that prior beliefs about capacity play a crucial, and surprisingly complex, role on whether the firm would prefer to reveal its capacity or not. A surprising result is that, despite the fact that it may be best for the high‐capacity firm to overproduce to reveal its capacity when capacity information is private, it may end up with more profits than if all capacity information were public knowledge in the first place. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Should firms conceal information when dealing with common suppliers?

A firm making quantity decision under uncertainty loses profit if its private information is leaked to competitors. Outsourcing increases this risk as a third party supplier may leak information for its own benefit. The firm may choose to conceal information from the competitors by entering in a confidentiality agreement with the supplier. This, however, diminishes the firm's ability to dampen competition by signaling a higher quantity commitment. We examine this trade‐off in a stylized supply chain in which two firms, endowed with private demand information, order sequentially from a common supplier, and engage in differentiated quantity competition. In our model, the supplier can set different wholesale prices for firms, and the second‐mover firm could be better informed. Contrary to what is expected, information concealment is not always beneficial to the first mover. We characterize conditions under which the first mover firm will not prefer concealing information. We show that this depends on the relative informativeness of the second mover and is moderated by competition intensity. We examine the supplier's incentive in participating in information concealment, and develop a contract that enables it for wider set of parameter values. We extend our analysis to examine firms' incentive to improve information. © 2014 Wiley Periodicals, Inc. 62:1–15, 2015     

Capacity games for partially complementary products under multivariate random demands

In this study, we consider n firms, each of which produces and sells a different product. The n firms face a common demand stream which requests all their products as a complete set. In addition to the common demand stream, each firm also faces a dedicated demand stream which requires only its own product. The common and dedicated demands are uncertain and follow a general, joint, continuous distribution. Before the demands are realized, each firm needs to determine its capacity or production quantity to maximize its own expected profit. We formulate the problem as a noncooperative game. The sales price per unit for the common demand could be higher or lower than the unit price for the dedicated demand, which affects the firm's inventory rationing policy. Hence, the outcome of the game varies. All of the prices are first assumed to be exogenous. We characterize Nash equilibrium(s) of the game. At the end of the article, we also provide some results for the endogenous pricing. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 59: 146–159, 2012     

Collaboration in contingent capacities with information asymmetry

We study the optimal contracting problem between two firms collaborating on capacity investment with information asymmetry. Without a contract, system efficiency is lost due to the profit‐margin differentials among the firms, demand uncertainty, and information asymmetry. With information asymmetry, we demonstrate that the optimal capacity level is characterized by a newsvendor formula with an upward‐adjusted capacity investment cost, and no first‐best solution can be achieved. Our analysis shows that system efficiency can always be improved by the optimal contract and the improvement in system efficience is due to two factors. While the optimal contract may bring the system's capacity level closer to the first‐best capacity level, it prevents the higher‐margin firm from overinvesting and aligns the capacity‐investment decisions of the two firms. Our analysis of a special case demonstrates that, under some circumstances, both firms can benefit from the principal having better information about the agent's costs. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 54:, 2007     

Dynamic regulation on innovation and adoption of green technology with information asymmetry

This study investigates a regulator's dynamic policy to motivate firms' research on and adoption of green technology. In the proposed model, a firm makes unobservable efforts and can hide the technology's arrival from the regulator to avoid adoption costs. We find that the optimal policy follows a simple structure and induces part-time efforts, rather than the maximal effort reported in previous studies. In particular, the regulator should offer no subsidy before the arrival of a technology report, provide a one-time subsidy contingent upon that report, and always set a termination deadline. At the deadline, the firm is forced to select an external option that is associated with social costs. The optimal report-based subsidy decreases with time. Under the optimal policy, the firm works until an effort deadline, makes no effort thereafter, and reports the technology as soon as it arrives. This study also characterizes the necessary and sufficient conditions under which the optimal policy reduces to one that leads, in terms of throughout time, to effort that is maximal or minimal. Our results indicate that policymakers should implement a policy that compensates firms more in the present and less in the future.     

Capacity allocation with traditional and Internet channels

In this paper we study a capacity allocation problem for two firms, each of which has a local store and an online store. Customers may shift among the stores upon encountering a stockout. One question facing each firm is how to allocate its finite capacity (i.e., inventory) between its local and online stores. One firm's allocation affects the decision of the rival, thereby creating a strategic interaction. We consider two scenarios of a single‐product single‐period model and derive corresponding existence and stability conditions for a Nash equilibrium. We then conduct sensitivity analysis of the equilibrium solution with respect to price and cost parameters. We also prove the existence of a Nash equilibrium for a generalized model in which each firm has multiple local stores and a single online store. Finally, we extend the results to a multi‐period model in which each firm decides its total capacity and allocates this capacity between its local and online stores. A myopic solution is derived and shown to be a Nash equilibrium solution of a corresponding “sequential game.” © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Competition under time‐varying demands and dynamic lot sizing costs

We develop a competitive pricing model which combines the complexity of time‐varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. Each firm adopts, at the beginning of the planning horizon, a (single) price to be employed throughout the horizon. On the basis of each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan. We establish the existence of a price equilibrium and associated optimal dynamic lotsizing plans, under mild conditions. We also design efficient procedures to compute the equilibrium prices and dynamic lotsizing plans.© 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

The value of losing control: Competition in markets for complements

When selling complementary products, manufacturers can often benefit from considering the resulting cross‐market interdependencies. Although using independent retailers makes it difficult to internalize these positive externalities, the ensuing double marginalization can mitigate within‐market competition. We use standard game theoretic analysis to determine optimal distribution channel strategies (through independent retailers or integrated) for competing manufacturers who participate in markets for complements. Our results suggest that a firm's optimal channel choice is highly dependent on its competitive positioning. A firm with a competitive advantage in terms of product characteristics (customer preferences) or production capabilities (cost) might benefit from selling through company‐controlled stores, allowing coordinated pricing across the two markets, whereas a less competitive firm might be better off using independent channel intermediaries to mitigate price competition. We consider two scenarios depending on whether the two firms make their distribution channel decisions sequentially or simultaneously. Although firms are unlikely to make such decisions at exactly the same instant, the simultaneous model also serves as a proxy for the scenario where firms decide sequentially, but where they cannot observe each other's strategic channel choices. For the sequential case, we find that the sequence of entry can have tremendous impact on the two firms'profits; whereas in some cases, the first mover can achieve substantially higher profits, we find that when the two markets are of sufficiently different size and only loosely related, a firm with a competitive advantage might be better off as a follower. Interestingly, our results suggest that, when the markets are of rather similar size, both firms are better off if they enter the industry sequentially. In those cases, the first entrant has incentive to reveal its planned channel strategies, and the follower has incentive to seek out and consider this information. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A game theoretic approach to a two firm bidding problem

In this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view.     

Optimal control of a capacitated inventory system with multiple demand classes

This article studies the optimal control of a periodic‐review make‐to‐stock system with limited production capacity and multiple demand classes. In this system, a single product is produced to fulfill several classes of demands. The manager has to make the production and inventory allocation decisions. His objective is to minimize the expected total discounted cost. The production decision is made at the beginning of each period and determines the amount of products to be produced. The inventory allocation decision is made after receiving the random demands and determines the amount of demands to be satisfied. A modified base stock policy is shown to be optimal for production, and a multi‐level rationing policy is shown to be optimal for inventory allocation. Then a heuristic algorithm is proposed to approximate the optimal policy. The numerical studies show that the heuristic algorithm is very effective. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 43–58, 2011     

Evergreening and operational risk under price competition

“Evergreening” is a strategy wherein an innovative pharmaceutical firm introduces an upgrade of its current product when the patent on this product expires. The upgrade is introduced with a new patent and is designed to counter competition from generic manufacturers that seek to imitate the firm's existing product. However, this process is fraught with uncertainty because the upgrade is subject to stringent guidelines and faces approval risk. Thus, an incumbent firm has to make an upfront production capacity investment without clarity on whether the upgrade will reach the market. This uncertainty may also affect the capacity investment of a competing manufacturer who introduces a generic version of the incumbent's existing product but whose market demand depends on the success or failure of the upgrade. We analyze a game where capacity investment occurs before uncertainty resolution and firms compete on prices thereafter. Capacity considerations that arise due to demand uncertainty introduce new factors into the evergreening decision. Equilibrium analysis reveals that the upgrade's estimated approval probability needs to exceed a threshold for the incumbent to invest in evergreening. This threshold for evergreening increases as the intensity of competition in the generic market increases. If evergreening is optimal, the incumbent's capacity investment is either decreasing or nonmonotonic with respect to low end market competition depending on whether the level of product improvement in the upgrade is low or high. If the entrant faces a capacity constraint, then the probability threshold for evergreening is higher than the case where the entrant is not capacity constrained. Finally, by incorporating the risk‐return trade‐off that the incumbent faces in terms of the level of product improvement versus the upgrade success probability, we can characterize policy for a regulator. We show that the introduction of capacity considerations may maximize market coverage and/or social surplus at incremental levels of product improvement in the upgrade. This is contrary to the prevalent view of regulators who seek to curtail evergreening involving incremental product improvement. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 71–89, 2016     

Optimal joint preventive maintenance and production policies

We study joint preventive maintenance (PM) and production policies for an unreliable production‐inventory system in which maintenance/repair times are non‐negligible and stochastic. A joint policy decides (a) whether or not to perform PM and (b) if PM is not performed, then how much to produce. We consider a discrete‐time system, formulating the problem as a Markov decision process (MDP) model. The focus of the work is on the structural properties of optimal joint policies, given the system state comprised of the system's age and the inventory level. Although our analysis indicates that the structure of optimal joint policies is very complex in general, we are able to characterize several properties regarding PM and production, including optimal production/maintenance actions under backlogging and high inventory levels, and conditions under which the PM portion of the joint policy has a control‐limit structure. In further special cases, such as when PM set‐up costs are negligible compared to PM times, we are able to establish some additional structural properties. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Inventory control and replenishment with flexible delivery‐time upgrade

We consider a capacitated inventory model with flexible delivery upgrades, in which the seller allocates its on‐hand inventory to price‐ and delivery‐time‐sensitive customers. The seller has two decisions: inventory commitment and replenishment. The former addresses how the on‐hand inventories are allocated between the two classes of customers within an inventory cycle. The latter addresses how the inventory is replenished between inventory cycles. We develop optimal inventory allocation, upgrade, and replenishment policies and demonstrate that the optimal policy can be characterized by a set of switching curves. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 418–426, 2014     

Pricing and inventory management during new product introduction when shortage creates hype

In this study, we analyze the joint pricing and inventory management during new product introduction when product shortage creates additional demand due to hype. We develop a two‐period model in which a firm launches its product at the beginning of the first period, before it observes sales in the two periods. The product is successful with an exogenous probability, or unsuccessful with the complementary probability. The hype in the second period is observed only when the product is successful. The firm learns the actual status of the product only after observing the first‐period demand. The firm must decide the stocking level and price of the product jointly at the beginning of each of the two periods. In this article, we derive some structural properties of the optimal prices and inventory levels, and show that (i) firms do not always exploit hype, (ii) firms do not always increase the price of a successful product in the second period, (iii) firms may price out an unsuccessful product in the first period if the success probability is above a threshold, and (iv) such a threshold probability is decreasing in the first‐period market potential of the successful product. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 304–320, 2015     

Supplier‐buyer contracting: Asymmetric cost information and cutoff level policy for buyer participation

We consider the problem of designing a contract to maximize the supplier's profit in a one‐supplier–one‐buyer relationship for a short‐life‐cycle product. Demand for the finished product is stochastic and price‐sensitive, and only its probability distribution is known when the supply contract is written. When the supplier has complete information on the marginal cost of the buyer, we show that several simple contracts can induce the buyer to choose order quantity that attains the single firm profit maximizing solution, resulting in the maximum possible profit for the supplier. When the marginal cost of the buyer is private information, we show that it is no longer possible to achieve the single firm solution. In this case, the optimal order quantity is always smaller while the optimal sale price of the finished product is higher than the single firm solution. The supplier's profit is lowered while that of the buyer is improved. Moreover, a buyer who has a lower marginal cost will extract more profit from the supplier. Under the optimal contract, the supplier employs a cutoff level policy on the buyer's marginal cost to determine whether the buyer should be induced to sign the contract. We characterize the optimal cutoff level and show how it depends on the parameters of the problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 41–64, 2001