Applying Scenario Reduction Heuristics in Stochastic Programming for Phlebotomist Scheduling

Laboratory services in healthcare play a vital role in inpatient care. Studies have indicated laboratory data affect approximately 65% of the most critical decisions on admission, discharge, and medication. This research focuses on improving phlebotomist performance in laboratory facilities of large hospital systems. A two-stage stochastic integer linear programming (SILP) model is formulated to determine better weekly phlebotomist schedules and blood collection assignments. The objective of the two-stage SILP model is to balance the workload of the phlebotomists within and between shifts, as reducing workload imbalance will result in improved patient care. Due to the size of the two-stage SILP model, a scenario reduction model has been proposed as a solution approach. The scenario reduction heuristic is formulated as a linear programming model and the results indicate the scenarios with the largest likelihood of occurrence. These selected scenarios will be tested in the two-stage SILP model to determine weekly scheduling policies and blood draw assignments that will balance phlebotomist workload and improve overall performance

A mathematical model for the product mixing and lot-sizing problem by considering stochastic demand

The product-mix planning and the lot size decisions are some of the most fundamental research themes for the operations research community. The fact that markets have become more unpredictable has increaed the importance of these issues, rapidly. Currently, directors need to work with product-mix planning and lot size decision models by introducing stochastic variables related to the demands, lead times, etc. However, some real mathematical models involving stochastic variables are not capable of obtaining good solutions within short commuting times. Several heuristics and metaheuristics have been developed to deal with lot decisions problems, in order to obtain high quality results within short commuting times. Nevertheless, the search for an efficient model by considering product mix and deal size with stochastic demand is a prominent research area. This paper aims to develop a general model for the product-mix, and lot size decision within a stochastic demand environment, by introducing the Economic Value Added (EVA) as the objective function of a product portfolio selection. The proposed stochastic model has been solved by using a Sample Average Approximation (SAA) scheme. The proposed model obtains high quality results within acceptable computing times

Parametric error bounds for convex approximations of two-stage mixed-integer recourse models with a random second-stage cost vector

We consider two-stage recourse models with integer restrictions in the second stage. These models are typically nonconvex and hence, hard to solve. There exist convex approximations of these models with accompanying error bounds. However, it is unclear how these error bounds depend on the distributions of the second-stage cost vector q.In this paper, we derive parametric error bounds whose dependence on the distribution of q is explicit: they scale linearly in the expected value of the `1-norm of q

Regional Electric-Power Systems Planning and Carbon Dioxide Emissions Management under Uncertainty

In this study, an interval two-stage integer programming model is formulated for planning electric-power systems and managing carbon dioxide (CO2) emissions under uncertainty. The developed model can reflect dynamic, interactive, and uncertain characteristics of regional energy systems. Besides, the model can be used for answering questions related to types, times, demands and mitigations of energy systems planning practices, with the objective of minimizing system cost over a long-time planning horizon. The developed model is also applied to a case study of planning CO2-emission mitigation for an electric-power system that involves fossil-fueled and renewable energy sources. Solutions can help generate electricity-generation schemes and capacity-expansion plans under different CO2-mitigation options and electricity-demand levels. Different CO2-emission management policies corresponding to different renewable energy development plans are analyzed. A high system cost will increase renewable energy supply and reduce CO2 emission, while a desire for a low cost will run into risks of a high energy deficiency and a high CO2 emission

Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds

An integer L-shaped algorithm for the integrated location and network restoration problem in disaster relief

Being prepared for potential disaster scenarios enables government agencies and humanitarian organizations to respond effectively once the disaster hits. In the literature, the two-stage stochastic programming models are commonly employed to develop preparedness plans before anticipated disasters. These models can be very difficult to solve as the complexity increases by several sources of uncertainty and interdependent decisions. In this study, we propose an integer L-shaped algorithm to solve the integrated location and network restoration model, which is a two-stage stochastic programming model determining the number and locations of the emergency response facilities and restoration resources under uncertainty. Our algorithm accommodates the second-stage binary decision variables which are required to indicate undamaged and restored roads of the network that can be used for relief distribution. Our computational results show that our algorithm outperforms CPLEX for the larger number of disaster scenarios as the solution time of our algorithm increases only linearly as the number of scenarios increases