Knowledge that Transforms

We address a production/inventory problem for a single product and machine where demand is Poisson distributed, and the times for unit production and setup are constant. Demand not in stock is lost. We derive a solution for a produce‐up‐to policy that minimizes average cost per unit time, including costs of setup, inventory carrying, and lost sales. The machine is stopped periodically, possibly rendered idle, set up for a fixed period, and then restarted. The average cost function, which we derive explicitly, is quasi‐convex sparately in the produce‐up‐to level Q , the low‐level R that prompts a setup, and jointly in R equals Q . We start by finding the minimizing value of Q where R equals 0, and then extend the search over larger R values. The discrete search may end with R less than Q , or on the matrix diagonal where R equals Q , depending on the problem parameters. Idle time disappears in the cycle when R equals Q , and the two‐parameter system folds into one. This hybrid policy is novel in make‐to‐stock problems with a setup time. The number of arithmetic operations to calculate costs in the ( Q , R ) matrix depends on a vector search over Q . The computation of the algorithm is bounded by a quadratic function of the minimizing value of Q . The storage requirements and number of cells visited are proportional to it.

We study the design of crowdsourcing contests in settings where the outputs of the contestants are quantifiable, for example, a data science challenge. This setting is in contrast to those where the output is only qualitative and cannot be objectively quantified, for example, when the goal of the contest is to design a logo. The literature on crowdsourcing contests focuses largely on ordinal contests, where contestants' outputs are ranked by the designer and awards are based on relative ranks. Such contests are ideally suited for the latter setting, where output is qualitative. For our setting (quantitative output), it is possible to design cardinal contests, where awards could be based on the actual outputs and not on their ranking alone—thus, the family of cardinal contests includes the family of ordinal contests. We study the problem of designing an optimal cardinal contest. We use mechanism design theory to derive an optimal cardinal mechanism and provide a convenient implementation—a decreasing reward‐meter mechanism—of the optimal contest. We establish the practicality of our mechanism by showing that it is “Obviously Strategy‐Proof,” a recently introduced formal notion of simplicity in the literature. We also compare the optimal cardinal contest with the most popular ordinal contest—namely, the Winner‐Takes‐All (WTA) contest, along several metrics. In particular, the optimal cardinal mechanism delivers a superior expected best output, whereas the WTA contest yields a greater expected contestant welfare. Furthermore, under a sufficiently large budget, the contest designer's expected net‐benefit is higher under the optimal cardinal mechanism than that under the WTA contest, regardless of the number of contestants in the two mechanisms. Our numerical analysis suggests that, for the contest designer, the average improvement provided by the optimal cardinal mechanism over the WTA contest is about 23%. For a given number of contestants, the benefit of the optimal cardinal mechanism is especially appreciable for projects where the ratio of the designer's utility to agents' cost‐of‐effort falls within a wide practical range. For projects where this ratio is very high, the expected profit of the best WTA contest is reasonably close to that of the optimal cardinal mechanism.

Retailers may collaborate with key suppliers to manage some specified categories. This collaboration is often formalized as a “captainship arrangement” between the retailer and her leading supplier in the category. The designated “category captain” assists the retailer with category management decisions. We show that captainship arrangements have the potential to generate a valuable information effect for the retailer: nonprice decisions by the category captain can reveal information that allows the retailer to improve profit through better retail pricing decisions. We also show that captainship arrangements have the greatest potential to make the retailer better off in categories where the retailer is highly uncertain about the impact of category resources on brands' demand. Moreover, the more substitutable the brands in the category, the more valuable a captainship arrangement is to the retailer. The information effect of category captainship is robust to a variety of arrangements. It is present under delegation arrangements (where the retailer delegates the task of category resources deployment to the captain), as well as under advisory arrangements (where the retailer retains control over category decisions, relying on the captain for advice). Interestingly, we find that delegation has a “better” potential to transmit information than advisory. Furthermore, in case of an advisory arrangement, the retailer is better off keeping the captain's advice confidential rather than sharing it with the other suppliers.

Discrete games provide the means to analyze market dynamics with limited data. However, computing such games with many players—especially in a complete information setting—is computationally infeasible because the strategy space increases exponentially with the number of players. This study presents a novel and practical method to compute and estimate discrete games. To do so, the study introduces two methodological innovations. First, we develop an efficient simulator that requires fewer random draws to evaluate the likelihood of discrete games with multiple equilibria. The augmented simulator avoids random draws that are not compatible with the observed equilibrium outcome and, thus, efficiently uses all draws to evaluate the likelihood. Second, we utilize general‐purpose computing on graphics‐processing unit (GPGPU), using multiple processing cores in a graphics‐processing unit, to increase computational speed. The two features allow us to estimate the model significantly faster compared to traditional methods. The study's empirical application examines the effect of Apple's company‐owned stores on the retail market structure. The results show that agglomeration effects exist between Apple and upscale firms. The presence of an Apple store attracts high‐income customers, promoting the entry of upscale firms and the exit of discount firms.

Customers of two‐sided platforms may succumb to choice overload due to the frequently overwhelming assortment in such markets. We investigate the effect of assortment size on consumers' purchase probability using a unique click‐stream dataset from a large peer‐to‐peer meal delivery platform. To resolve the key endogeneity challenge that assortment size may be larger in areas where consumers experience greater utility from purchase, we introduce a novel causal inference strategy that exploits a common but imperfect geographic targeting tool employed by the platform: limiting kitchens to a set of fixed delivery radii. We argue and show through simulation exercises that true assortment size effects on purchase probability can be estimated when we employ clustering algorithms to recover and account for neighborhoods that may be targeted by suppliers. Applying our causal inference strategy to the home‐cooked delivery setting, we find that purchase rate effects of assortment size are rapidly diminishing. In fact, our findings suggest that up to 18% of active users experience choice overload. These effects persist despite accounting for potential pricing, assortment variety, and personalization confounds and are robust to nonparametric specifications and accounting for unobserved heterogeneity in assortment effects. We further document the novel moderating role of new‐to‐user and off‐platform options on assortment size effects.

We study the optimal selling scheme when a seller sells a product/service with a positive consumption externality, and customers are uncertain about the product's/service's value. Because early adopters learn this value, we consider the customers' intrinsic signaling incentives and positive feedback effects. Allowing the seller to choose the sequence of customers' decisions (as an endogenous hierarchy) implies that signaling takes place in multiple rounds. To tackle this hierarchical signaling problem, we develop a novel dynamic‐programming approach that yields analytical expressions of the equilibrium outcomes. The profit‐maximizing structure turns out to be a chain in which the seller sells to the customers one by one. The sequential selling scheme is not only profitable for the seller but also beneficial to the society. The profit‐maximizing pricing exhibits a cream‐skimming property–decreasing prices along the sequence. The lack of seller's commitment is detrimental to the social welfare; nonetheless, the sequential selling still boosts up the seller's profit. When customers are allowed to freely disclose their quantity decisions to others, they willingly comply with the seller's plan of information transmissions. Despite the inherent value uncertainty, the optimal usage of information transmissions requires deliberate restricted access to information among customers. Our result also suggests some congruence between the profit and welfare maximization.

Auto‐delivery is a subscription model widely employed in supply chains, whereby a supplier delivers products to a buyer (or multiple buyers) according to the buyer's choice of a constant shipping quantity to be delivered at prescheduled dates. The buyer enjoys a discount for the auto‐delivery orders and other benefits, including free subscription and cancellation. Because these benefits seem to all accrue to the buyer at the supplier's expense, the rationale for the supplier's decision to offer auto‐delivery and its impact on the profitability of both parties is an intriguing concern. We first develop a model that consists of a supplier and a single buyer, whereby the supplier offers a discount for the auto‐delivery orders and the buyer chooses the auto‐delivery quantity with the flexibility of cancelling the subscription. We derive the two parties' operating characteristics of their inventory systems and examine their optimal decisions. Our analysis shows that buyers benefit from the auto‐delivery discount; the supplier benefits from the demand‐expansion effect and the inventory‐reduction effect, a potential discount on the cost of the auto‐delivery units; and the supply chain benefits from reducing the bullwhip effect. We also find that channel coordination requires the supplier to pass the inventory‐related savings to the buyer through the auto‐delivery discount, which depends on the ratio of the two parties' holding cost rates. Moreover, we examine a model extension whereby the supplier announces a discount that is available for multiple buyers, we show that the supplier's optimal auto‐delivery discount under exponential demand can be determined based on the aggregate‐level demand information from all buyers. Finally, we discuss another model extension whereby the lead time of the supplier's recurring orders for auto‐delivery is longer than that of the regular orders and present a full analysis of the case when the lead time differential is one time period.

The aging population and increasing chronic disease load are rapidly changing the face of primary care delivery, with mid‐level (e.g., nurse) practitioners providing growing proportion of patient care. Potential differences in the quality of care offered by physicians and nurse practitioners may affect patient preferences, thus leading to patient choice behavior. This paper focuses on the problem of appointment scheduling for physician–nurse teams in the presence of patient choice and no‐shows. We propose a novel model that accounts for patient choices in a system with two provider types. Despite the increased structural complexity of the model, we derive sufficient conditions under which the problem is efficiently solvable. To counter the computational challenges arising in the general setting, we propose an easy‐to‐implement heuristic, which is proven to be optimal in the absence of patient no‐shows. Our numerical study shows how the ratio of qualities of care delivered by nurses and physicians affect the profitability of the medical practice, enabling the analysis of the trade‐offs involved in hiring a nurse practitioner. This paper introduces a patient‐controlled approach to incorporating nonphysician providers into physician‐led outpatient care delivery systems and compares it to widely used “ice breaker” and “standalone” modes of using nonphysician providers. Our findings reveal that clinical practices that employ mixed (physicians and nonphysicians) provider pools can significantly improve their financial and operational performance by moving away from the “ice breaker” and “standalone” use of nonphysician providers by delaying the selection of an appropriate care provider till the actual day of care delivery.

We study mechanisms that encourage manufacturers of health products to build production and distribution capacity. This is important for low‐ and middle‐income country (LMIC) markets where ability to pay is lower and demand risks are greater. Development finance institutions and philanthropies are beginning to utilize new instruments to incentivize manufacturers to build production/distribution capacity for LMIC markets. The goal of this paper is to understand the effectiveness of such mechanisms in different settings. We examine four instruments: (1) subsidy proportional to unit sales (sales subsidy), (2) subsidy proportional to unit capacity (variable‐capacity subsidy), (3) subsidy proportional to total capacity investment (total‐capacity subsidy), and (4) a minimum volume guarantee. We analyze incentivized capacity as a function of the social‐investor budget for each instrument. We show how our framework can be used to identify a social investor's preferred instrument given relevant parameter estimates, and we provide insight into the type of settings where a particular instrument dominates. A sales subsidy dominates when ability to pay is very low; a total‐capacity subsidy dominates when ability to pay is low. Outside of these settings, instrument preference is nuanced, though a sales subsidy is dominated by at least one other instrument. When ability to pay is moderate, a variable‐capacity subsidy tends to be preferred under high variable‐capacity cost and high budget, a volume guarantee tends to be preferred under low variable‐capacity cost and high budget, and a total‐capacity subsidy tends to be preferred under low budget.