Search

We argue that dynamic pricing motivated by the management of inventory holding and ordering costs leads to increased operational efficiencies that could benefit firms without hurting consumers. To demonstrate this point, we equip the traditional economic order quantity (EOQ) setting with a rich set of demand models and compare social outcomes under two alternatives, dynamic and static pricing. We show that dynamic pricing generates higher retailer profits, a lower average price per unit sold, and higher sales volumes than static pricing. The mechanism behind the result is that with dynamic pricing the retailer ties the price of each unit to its holding costs, which allows him to increase the order quantity compared with static pricing and thus save on fixed ordering costs. Some of these cost savings are passed to consumers. Moreover, we demonstrate that this mechanism is robust to the presence of price-anticipating (strategic) consumer behavior. This paper was accepted by Serguei Netessine, operations management.

We present a continuous-time stochastic formulation of the standard Economic Order Quantity (EOQ) model incorporating all major costs incurred in carrying a product, including the cost of restocking, the cost of auditing the shelf stock level, the opportunity cost of capital, the cost of loss process, and the costs caused by not serving demand. In this formulation, the loss process is an unobservable point process while the demand point process is observed only when the item is in stock. The retailer’s control problem is reduced to an optimal stopping problem (corresponding to the restocking time) during which the shelf stock level can be audited finite number of times. The solution to the Hamilton-Jacobi-Bellman (HJB) equation of this stopping problem is fully characterized and constructed by applying a differential operator finite number of times. In particular, a closed-form expression for the optimal value function is obtained when auditing is infeasible or suboptimal. It is proved that the optimal restocking policy is a threshold policy in a three-dimensional state space that defines the Bayesian belief dynamics of the shelf stock level. Complete comparative statics analysis of this probability threshold along with its corresponding stopping time equivalent in the time domain are provided. We show that the jointly optimal auditing policy is not a threshold-based policy, that is the state trajectory can enter and leave the optimal audit region, leading to a finite time window during which auditing is optimal. We present a numerical example to illustrate the functional form of the optimal solution and estimate the impacts of inventory record inaccuracy on increasing the net present value of the expected total cost of carrying a product. The performance of the optimal policy is also compared with the best performing threshold-based heuristic policies in both time and probability domains. We show in this example that when the distribution of the shelf stock level is dynamically tracked, auditing the shelf stock level has a negligible impact on reducing the net present value of the expected total cost of carrying a product.

Antimicrobial resistance is a significant public health threat. In the U.S. alone, 2 million people are infected and 23,000 die each year from antibiotic resistant bacterial infections. In many cases, infections are resistant to all but a few remaining drugs. We examine the case where a single drug remains and solve for the optimal treatment policy for an SIS infectious disease model incorporating the effects of drug resistance. The problem is formulated as an optimal control problem with two continuous state variables, the disease prevalence and drug’s “quality” (the fraction of infections that are drug-susceptible). The decision maker’s objective is to minimize the discounted cost of the disease to society over an infinite horizon. We provide a new generalizable solution approach that allows us to thoroughly characterize the optimal treatment policy analytically. We prove that the optimal treatment policy is a bang-bang policy with a single switching time. The action/inaction regions can be described by a single boundary that is strictly increasing when viewed as a function of drug quality, indicating that when the disease transmission rate is constant, the policy of withholding treatment to preserve the drug for a potentially more serious future outbreak is not optimal. We show that the optimal value function and/or its derivatives are neither C(1) nor Lipschitz continuous suggesting that numerical approaches to this family of dynamic infectious disease models may not be computationally stable. Furthermore, we demonstrate that relaxing the standard assumption of constant disease transmission rate can fundamentally change the shape of the action region, add a singular arc to the optimal control, and make preserving the drug for a serious outbreak optimal. In addition, we apply our framework to the case of antibiotic resistant gonorrhea.

We argue that dynamic pricing motivated by the management of inventory holding and ordering costs leads to increased operational efficiencies which could benefit firms without hurting consumers. To demonstrate this point, we equip the traditional economic order quantity (EOQ) setting with a rich set of demand models and compare social outcomes under two alternatives, dynamic and static pricing. We show that dynamic pricing generates higher retailer profits, a lower average price per unit sold, and higher sales volumes than static pricing. The mechanism behind the result is that with dynamic pricing the retailer ties the price of each unit to its holding costs, which allows him to increase the order quantity compared to static pricing and thus save on fixed ordering costs. Some of these cost savings are passed to consumers. Moreover, we demonstrate that this mechanism is robust to the presence of price-anticipating (strategic) consumer behavior.

Many decision problems exhibit structural properties in the sense that the objective function is a composition of different component functions that can be identified using empirical data. We consider the approximation of such objective functions, subject to general monotonicity constraints on the component functions. Using a constrained B-spline approximation, we provide a data-driven robust optimization method for environments that can be sample-sparse. The method, which simultaneously identifies and solves the decision problem, is illustrated for the problem of optimal debt settlement in the credit-card industry.

This paper introduces a dynamic model of the stochastic repayment behavior exhibited by delinquent credit-card accounts. Based on this model, we construct a dynamic collectability score (DCS) that estimates the account-specific probability of collecting a given portion of the outstanding debt over any given time horizon. The model integrates a variety of information sources, including historical repayment data, account-specific, and time-varying macroeconomic covariates, as well as scheduled account-treatment actions. Two model-identification methods are examined, based on maximum-likelihood estimation and the generalized method of moments. The latter allows for an operational-statistics approach, combining model estimation and performance optimization by tailoring the estimation error to business-relevant loss functions. The DCS framework is applied to a large set of account-level repayment data. The improvements in classification and prediction performance compared to standard bank-internal scoring methods are found to be significant. This paper was accepted by Noah Gans, stochastic models and simulation.

This paper discusses an adaptive modulation/coding (AMC) strategy based on frequency-domain channel statistical information for OFDM systems in a frequency-selective fading environment. The proposed approach is based on the fact that the statistical properties of a time-varying channel vary very slowly with time and thus it is possible to obtain reliable knowledge at the transmitter. A programmable Reed-Solomon RS (n,k) code used with an adaptive multi-level modulation scheme is proposed as an illustrative example. Derivations of the frequency-domain channel statistical properties and performance of the proposed technique are presented along with illustrative results.

Based on a dynamic model of the stochastic repayment behavior exhibited by delinquent credit-card accounts in the form of a self-exciting point process, a bank can control the arrival intensity of repayments using costly account-treatment actions. A semi-analytic solution to the corresponding stochastic optimal control problem is obtained using a recursive approach. For a linear cost of treatment effort, the optimal policy in the two-dimensional (intensity, balance) space is described by the frontier of a convex action region. The unique optimal policy significantly reduces a bank’s loss given default and concentrates the collection effort onto the best possible actions at the best possible times so as to minimize the sum of the expected discounted outstanding balance and the discounted cost of the collection effort, thus maximizing the net value of any given delinquent credit-card account. This paper was accepted by Noah Gans, stochastic models and simulation.