Management Science

Abstract: This paper introduces the price-elastic knapsack problem (PEKP), an extension of the classic knapsack problem where instead of fixed item characteristics, the weight of each item and the profit from including an item in the knapsack are a function of a parameter, namely the price. PEKP is first formulated as a generic nonlinear optimization problem and three special cases are investigated. First, we show a polynomial-time solvable case. Next, we formulate the case where the item weights are affine-linear functions as a quadratic program. The computational results show that solving the quadratic program to optimality is computationally challenging, and thus, an approach that decomposes the problem into three mixed integer programs is proposed. Similarly, the case where the weights of the items are piecewise-linear functions is investigated and a quadratic formulation is proposed. A solution approach based on decomposing the problem into three mixed integer programs that are solved independently is also proposed. Using randomly generated instances of varying sizes, the computational results show that the proposed decomposition leads to significant computational advantages compared to solving the quadratic program in the cases of affine-linear and piecewise-linear functions.

Abstract: Frequently releasing a new product generation has become a common practice to sustain sales over time, thus accurately forecasting the sales trajectory of each product generation plays a vital role in the short-, medium-, and long-term planning of a firm. Classic multigeneration diffusion models do not incorporate within-generation repeat purchases, making them unusable for product lines with high rates of such purchases. Concentrating on technology products, we develop a multigeneration sales model to fill this void. We demonstrate that the new model can be used for predictive and prescriptive analytics. Our empirical results show that the new model estimates and forecasts sales more accurately than a state-of-the-art benchmark model that does not account for within-generation repeat purchases, underscoring the importance of incorporating repeat purchases. Furthermore, we use two different versions of our model to examine market entry timing under two main strategies, i.e., (i) a phase-out transition strategy in which firms continue to sell the old generation after the release of the new generation, and (ii) a total transition strategy in which firms discontinue the old generation after the introduction of the new generation. Our results indicate that the repeat purchases rate determines whether it is optimal to expedite or delay the new product launch, underscoring the importance of incorporating repeat purchases in market entry strategies.

Abstract: We review the evolution of virtual care (VC) in Ontario. Pre–COVID-19, the primary focus was on patients in remote and underserved areas who went to host sites for care. Ontario’s vision pre-pandemic was for a gradual increase in VC by physicians registered with the Ontario Telemedicine Network (OTN), using OTN-approved video technologies; some accommodated patients and doctors wherever they were. Less than 1% of care was virtual pre-pandemic. We discuss how policies that altered access to in-person care (pandemic lockdowns and guidelines to seek and provide care virtually), compensation policy changes (allowing any Ontario physician to be compensated for VC), and policies allowing common technologies not previously allowed (including, importantly, the telephone), drove and enabled a rapid shift to >50% of care being virtual at the start of the pandemic, leveling off to ∼30% over time. We review policy changes in late 2022 and predict these will result in a drop in VC compared with the policies during the pandemic, particularly for walk-in clinic patients, in a province where 2.2-4.6 million people do not have a primary care doctor and presumably use walk-in clinics. This is because, going forward, physicians will be compensated less for telephone care than for in-person or video care for rostered patients, and because compensation will be less still for telephone or video care provided to walk-in patients. Through this case study we develop a visual model of how these key policy and technology factors influence the provision of VC.