An important generalization of the classic 0-1 knapsack problem is the multi-demand multidimensional knapsack problem (MDMKP). In addition to being theoretically difficult to solve (it is NP-hard), it can be in practice difficult to solve because of its conflicting knapsack and demand constraints. Since there are significant large-scale applications of the MDMKP, approximate solution approaches are commonly used to solve these problems. However, using 1620 MDMKPs discussed in the literature, this article demonstrates which types of large MDMKPs can be solved efficiently by operations research practitioners using general purpose integer programming software on a standard personal computer within 0.1% of optimum. Statistical analyses are used to determine which problem parameters significantly impact solution time. Finally, based on these 1620 MDMKP instances, a classification tree is generated. This tree can be used to guide practitioners in solving MDMKPs that arise in business and industry.

In this paper, we develop a residential mortgage valuation tree model that incorporates housing price volatility, along with interest rates and interest rate volatility as determinants of mortgage yield spreads (above Treasury yields). When initial loan-to-value (LTV) ratios are low (e.g., 80%), the sensitivity of theoretical mortgage yield spreads to housing price volatility occurs for housing price volatility at annualized rates of 9%–11%. Annual price volatilities of 9%–11% are primarily observed in ‘hot’ residential markets. When initial LTV ratios are high (e.g., 95%), we find the sensitivity of theoretical mortgage yield spreads to housing price volatility begins at annualized rates of 3%–8%, levels consistent with normal real estate markets. These sensitivities are generally irrespective of interest rate levels and interest rate volatilities. Ignoring the sensitivity of mortgage values to housing price volatility can cause lenders to misprice mortgages, and can cause insurance companies to misprice mortgage insurance. This can cause perverse incentives and unintended consequences, with substantial public policy implications including unsafe lending practices, excessive real estate speculation, and systemic risk.

In 2024, four papers that presented four different solution approaches for the knapsack problem with forfeits (KPF) appeared in the OR literature. However, none of these four solution approaches compared their performance to the other three on a standard set of 120 KPF test instances. In this short paper, both empirically and statistically, these four KPF solution approaches are compared. Furthermore, by using the solutions from the best method (HESM) among the four to initialize Gurobi, bounded solutions are obtained. For the 120 KPF test instances, this simple hybrid approach resulted in solutions that, on average, were guaranteed to be within 7% of the optimums. This type of guarantee does not exist for other KPF solution methods in the literature. It is very important for operations research (OR) practitioners that need to ensure the value of their solutions to management to have some guarantee of the quality of these solutions.

Since its founding in 2013, the Kutztown University Association for Women in Mathematics student chapter has built a supportive community of women students and faculty on campus and beyond. This article aims to share our successful experiences with the broader community by presenting our pre- and mid-pandemic AWM activities including Mathematics Day for Girls, Women's Empowerment Day, Beyond Pink-Collar Jobs, and our Kutztown University AWM Virtual Lecture Series. Feedback from past and current participants of our AWM student chapter is also included.