Knowledge that Transforms

This paper models a cash conversion system in a subsidiary of a parent company where there is an active internal capital market, but otherwise the subsidiary has no access to additional external funds. The cash conversion system consists of a treasury, a single-product make-to-stock inventory, and a receivables pool. It implements a perpetual flow cycle, where funds convert to product and back to funds. The system is stationary, and revenues and costs flow directly to the parent company. The parent company aims to maximize equilibrium (long-run) financial metrics in terms of net profit rate and rate of return. To this end, we model this system as a discrete-state continuous-time Markov process and compute its equilibrium state distribution using analytic and numerical methods. These are then used to derive statistics of the equilibrium cash conversion cycle and define equilibrium financial rate metrics and cumulative counterparts that incorporate the time value of money. We further optimize the financial and operational designs of the system and, specifically, the internal capital allocation and inventory base stock level. Finally, noting the potential for friction in the parent–subsidiary relationship, we study numerically the impact of moral hazard and internal capital market inefficiency on optimal designs. The online appendix is available at https://doi.org/10.1287/msom.2017.0625 .

The timing of forest stands harvesting is an important operational decision in forestry. Major goals of private nonindustrial forest owners are to achieve a steady flow of profits while reaching an overall satisfactory and reliable profit level. These goals are pursued under uncertainties in the growth of trees in different regions and in the prices of wood products. We propose an optimization framework that uses financial risk concepts to capture the above goals and uncertainties, and apply it to a real forestry problem in Finland. Our results demonstrate that the obtained harvesting schedules outperform those obtained without the explicit consideration of the stability and reliability requirements in harvest profits. More generally, our results indicate that the forest owner can improve the profit stability by (i) harvesting a greater number of forest stands early and (ii) harvesting in the first periods of the planning horizon stands that are predominantly composed of slow-growing forests. This research responds to the call for scenario-based approaches that represent well, and in a solvable way, multiple uncertainties in large forestry problems. This study fills in a gap in stochastic programming and can be a cornerstone for subsequent improvements in the solution of combinatorial chance-constrained problems with multirow random technology matrix. The online appendix is available at https://doi.org/10.1287/msom.2017.0626 .

We analyze how performance metrics that contain equivalent information affect actual decisions. We consider two such performance metrics from supply chain management, days of supply and inventory turn rate, where one is the inverse of the other. We argue that individuals’ assessment of performance is also affected by the metric as opposed to solely based on the inventory value that actually matters. We perform three laboratory studies and analyze how decisions are affected by the metric used to indicate inventory performance. The first study considers alternative inventory optimizations, out of which one must be selected. The second study analyzes a decision maker who must decide on the effort to invest in optimizing inventory of a specific product. The third study corresponds to the economic order quantity model. Our behavioral models suggest that decisions are affected by the metric that is used to indicate performance, and we find support for the predictions in laboratory experiments with human subjects: Under the inventory turn rate metric, individuals overvalue inventory reductions. Compared to decisions under the days of supply metric, they choose worse inventory optimization options, invest more effort optimizing inventory of specific products, and choose higher ordering cost. The e-companion is available at https://doi.org/10.1287/msom.2017.0620 .

We consider the problem of managing production in a production-inventory system where a firm is subject to an allowance (a limit) on either the amount of input it can use or the amount of output it can produce over a specified compliance period (in addition to being subject to a constraint on the production capacity). Examples of such settings are numerous and include those where limits are placed on the use of scarce natural resources as input or on the amount of waste or harmful pollution generated by production as output. We study the structure of the optimal production policy for such systems and show that it is determined by dynamic thresholds that depend only on the sum of the on-hand inventory level and the remaining allowance. We provide an effective approximate solution approach that can compute these thresholds efficiently while retaining their essential properties. We examine the differences between how an allowance constraint and a constraint on production capacity affect production decisions and show that they exhibit opposite effects over time. We also examine, in the context of an extended version of the problem where both the allowance amount and the production capacity are endogenous, optimal investments in allowance and production capacity and the impact of both on firm profit. We also consider the optimal demand fulfillment policy in settings where the firm can decide whether to back-order or to reject demand that cannot be satisfied from on-hand inventory. The online appendix is available at https://doi.org/10.1287/msom.2016.0603 .

We formulate and analyze a stylized dynamic model of a price-taking firm that manages production and capacity, uses only internal financing, and faces stochastic market environments. The firm has two operationally independent production facilities, each of which makes two products, and a cash reserve that finances all operations and dividend issuance. Each period the firm chooses the amount of dividend to issue, and at each facility it chooses production quantities and amounts of capacity to augment or divest. Relevant market data are exogenous and evolve stochastically. We completely characterize the optimal policy and the endogenous values of the capacities and cash reserve, and show that they invite a real-option interpretation. We find that internal financing creates a spillover between the endogenous values of the two operationally independent facilities, and we specify how this leads to interdependence of their optimal policies. We show that an “invest/stay put/divest” (ISD) policy remains optimal for partially irreversible investments, but internal financing changes the ISD thresholds. If the exogenous data are intertemporally independent, an internally financed firm is less likely to issue dividends or to expand capacity than if it were in a perfect capital market. As the market becomes more volatile, the endogenous values of capacities and cash increase, and the firm becomes more reluctant to issue dividends. The online appendix is available at https://doi.org/10.1287/msom.2017.0655 . This paper has been accepted for the Manufacturing & Service Operations Management Special Issue on Interface of Finance, Operations, and Risk Management.

We consider a practical dynamic pricing problem with two substitutable products involving a number of business rules commonly seen in practice. Demand substitution exists between the two products (interproduct substitution) and may also exist across different time periods (intertemporal substitution). However, there is limited demand information such that the underlying probability distributions of the demand cannot be characterized precisely. We use an interval to represent, respectively, the demand for each individual product in each period, the aggregate demand for the two products in each period, and the total aggregate demand for the two products across multiple time periods. We propose a robust optimization model for this problem to maximize the worst-case total revenue. For the problem with interproduct demand substitution only, we develop a dynamic programming algorithm and show that the search spaces in the DP can be reduced greatly, which enables the algorithm to generate optimal solutions in a reasonable amount of time. For the problem with both interproduct and intertemporal demand substitutions, we develop a more complex dynamic programming algorithm and design a fully polynomial time approximation scheme that guarantees a proven, near optimal solution in a manageable computation time for practically sized problems. Our computational results show that, compared to a risk-neutral approach, our robust optimization approach can decrease the variance of the revenue at a small expense of the average revenue. We also generate a number of managerial insights: (i) none of the key structural properties commonly studied in the pricing literature hold for our problem; (ii) the revenue impact of ignoring intertemporal demand substitution when such substitution exists can be quite significant; and (iii) under- or overestimating the bounds of the demand intervals or imposing moderate business rules leads to relatively small revenue loss, typically less than 3%. The online appendix is available at https://doi.org/10.1287/msom.2017.0639 .

Inspired by the U.S. influenza vaccine market, we formulate a Cournot competition model with asymmetric firms facing capacity constraints and yield uncertainty. We derive the equilibrium of this model by defining a score that ranks firms based on their capacity, unit production cost, random yield mean, and variance. In particular, we show a threshold structure. Firms that have scores above a threshold produce at full capacity, while other firms produce less than their capacities in the equilibrium. Finally, for the case of symmetric firms, we correct mistakes in the analysis of Deo and Corbett [Deo S, Corbett CJ (2009) Cournot competition under yield uncertainty: The case of the U.S. influenza vaccine market. Manufacturing Service Oper. Management 11(4):563–576], showing that society can benefit from supplier diversification under weaker conditions. The online appendices are available at https://doi.org/10.1287/msom.2016.0610 .

Adverse commodity prices can cause significant negative cash flows and expose firms that deal in commodities to financial distress. In this paper we consider the dynamic risk management problem for a commodity processor operating in a partially complete market, facing both price uncertainty and significant financial distress costs. The firm procures an input commodity, processes it to produce an output commodity, and trades the output commodity in each period over a multiperiod horizon. The firm’s objective is to dynamically and jointly plan operational and financial hedging decisions to maximize the market-based value of cash flows under a time-consistent risk measure. We show that the optimal operational policy has the same price and horizon dependent threshold structure that obtains when markets are complete. We also characterize conditions under which a myopic policy is optimal. We present numerical studies to illustrate that (i) compared to using a myopic policy or a policy that neglects to model financial distress costs, the advantage of using the optimal policy is significant for firms that face moderate financial distress costs and have excess procurement capacity; (ii) more acute financial distress costs reduce the firm’s market-based value and throughput; and (iii) financial hedging provides considerable benefit by reducing the incidence of large negative cash flows. The online appendix is available at https://doi.org/10.1287/msom.2017.0647 .

The posterior price-matching policy, whereby a firm promises to reimburse the price difference to a customer who purchases a product before the firm marks it down, has been used in practice. The extensive literature has offered the following explanations for why posterior price matching is adopted: to reduce inventory, to soften competition, to price discriminate consumers, and to eliminate consumer strategic waiting incentives. In this paper, we provide a novel explanation and investigate the role of consumer bounded rationality in the sense of anecdotal reasoning. We adopt a simple model that allows us to isolate the role of customer bounded rationality on using posterior price matching. We demonstrate that while it is never optimal to adopt posterior price matching when consumers have rational expectations, it can be optimal when they have boundedly rational expectations. We show when and how a seller can intentionally mark down with some probability and adopt price matching to make a profit. Ignoring customer bounded rationality can result in a significant profit loss. Then, we build a dynamic programming model to investigate how the firm should dynamically manage its markdowns over the long run. We show that a cyclic policy switching between a high and low markdown probability is typically optimal for exploiting customer bounded rationality. We characterize the nature of the cyclic policy and the range in which it is optimal. Our findings underscore the importance of consumer bounded rationality and provide managerial and practical guidelines on how to manage price matching when customers are boundedly rational. The online supplement is available at https://doi.org/10.1287/msom.2016.0612 .

Many industries operate technologies in which multiple outputs (coproducts) are jointly produced. In some settings (“vertical”) the coproducts differ along a performance dimension and are substitutable. In other settings (“horizontal”) the coproducts differ in their applications and are not substitutable. In both cases, three important attributes of a coproduct technology are its processing cost, overall yield, and coproduct split, i.e., the proportion of each output produced. For both vertical and horizontal settings with deterministic market sizes, we characterize the optimal pricing and production decisions of a monopoly firm with two technologies. We establish the necessary and sufficient conditions for dual activation (i.e., using both technologies) to be optimal. Dual activation is driven by differences in marginal costs across the two technologies. There is an additional motive for dual activation in the horizontal setting: the desire to generate a product mix that better resembles the market mix. Building on the optimal production analysis, we characterize the optimal adoption-and-usage strategy of a firm with one incumbent technology considering a new technology. We establish the conditions for which a new technology will displace the incumbent or be used with the incumbent, and highlight some important adoption and usage differences between vertical and horizontal settings. Results are extended to the setting with uncertain market size(s). The online appendix is available at https://doi.org/10.1287/msom.2017.0637 .