Leo MacDonald

Location and Capacity Allocations Decisions to Mitigate the Impacts of Unexpected Disasters

This paper develops a stochastic modeling framework to determine the location and capacities of distribution centers for emergency stockpiles to improve preparedness in the event of a disaster for which there is little to no forewarning. The proposed framework is applicable to emergency planning that must incorporate multiple sources of uncertainty, including the timing and severity of a potential event, as well as the resulting impact, while taking into consideration both disaster and region specific characteristics. To demonstrate the modeling approach, we apply it to a region prone to earthquakes. The model incorporates various uncertainties such as facility damage and casualty losses, based upon their severity and remaining survivability time, as a function of the magnitude of the earthquake. Given the computational complexity of the problem of interest, we develop an evolutionary optimization heuristic aided by an innovative mixed integer programming model that generates time efficient high quality solutions. We demonstrate the effectiveness of the heuristic via a case study featuring the HAZUS-MH software from the Federal Emergency Management Agency (FEMA). Finally, given the uncertainty associated with the magnitude of the earthquake, we use a decision analysis approach to develop robust solutions while taking into account the geological characteristics of the region.

Determination of number of dedicated OR's and supporting pricing mechanisms for emergent surgeries

Inefficient management of emergent surgeries in hospitals can, in part, be attributed to a lack of rigorous analysis appropriate to capturing the underlying uncertainties inherent to this process and a pricing mechanism to ensure its financial viability. We develop a non-preemptive multi-priority queueing model that optimally manages emergent surgeries and supports the resource allocation decision-making process. Specifically, we utilize queueing and discrete event simulation to develop empirical models for determining the required number of emergent operating rooms for a hospital surgical department. We also present algorithms that estimate the appropriate pricing for patient surgeries differentiated by priority level given the patient demand and the resources reserved to meet this demand.

A Teaching Supplement on Sensitivity Analysis for Linear Programming in Undergraduate Business Programs

Sensitivity analysis, a key linear programming LP concept, is often explained in text books using complex problem scenarios to which students have difficulty relating. Consequently, many students do not fully comprehend or appreciate the significance of shadow prices or range of optimality for objective coefficients. This adds to the challenges instructors face in promoting critical thinking, a key goal in operations research and management science courses. Limited student-faculty interactions further exacerbate the problem in online learning environments. These issues can be effectively addressed through use of simple real world examples for instruction, followed by discussion of insights and intuition behind results from these mathematical models. This is the motivation of this study, with a special focus on sensitivity analysis concepts and LP formulations. We then demonstrate its effectiveness by comparing student performance before and after exposure to this innovative teaching supplement and as well as results from a student feedback survey.

Pricing and inventory policies under price-tracking behaviour

We develop a demand rate model for the optimisation of retail sales of perishable assets when consumers track prices over the sales horizon. We model this behaviour within an aggregate demand framework, solving the initial joint inventory and pricing problem when the demand is deterministic as well as stochastic. We solve the problem numerically and discuss the specific results as well as the characteristics of the optimal price and inventory levels. We illustrate when firms are likely to choose a penetration vs. skimming pricing policy and describe solution updating procedure as actual sales occur.