Capacity planning and scheduling with applications in healthcare

Abstract

In this thesis we address capacity planning problems with different demand and service characteristics, motivated by healthcare applications. In the first application, we develop, implement, and assess the impact of analytical models, accompanied by a decision-support tool, for operating room (OR) staff planning decisions with different service lines. First, we propose a methodology to forecast the staff demand by service line. We use these results in a two-phase mathematical model that defines the staffing budget for each service line, and then decides how many staff to assign to each potential shift and day pair while considering staff overtime and pooling policies and other staff planning constraints. We also propose a heuristic to solve the model's second phase. We implement these models using historical data from a community hospital and analyze the effect of different model parameters and settings. Compared with the current practice, we reduce delays and staff pooling at no additional cost. We validate these conclusions through a simulation model. In the second application, we consider the problem of staff planning and scheduling when there is an accepted time window between each order's arrival and fulfillment, with the goal of obtaining a balanced schedule that focuses on on-time demand fulfillment but also considers staff characteristics and operational practices. Hence, solving this problem requires simultaneously scheduling the staff and the forecasted demand. We propose, implement, and analyze the results of a model for staff and demand scheduling under this setting, accompanied by a decision-support tool. We implement this model in a company that offers document processing and other back-office services to healthcare providers. We provide details on the model validation, implementation, and results, including a 25\% increase in the company's staff productivity. Finally, we provide insights on the effects of some of the model's parameters and settings, and assess the performance of a proposed heuristic to solve this problem. In the third application, we consider a non-consumable resource planning problem. Demand consists of a set of jobs, each job has a scheduled start time and duration, and belongs to a particular demand class that requires a subset of resources. Jobs can be `accepted' or `rejected,' and the service level is measured by the (weighted) percentage of accepted jobs. The goal is to find the capacity level that minimizes the total cost of the resources, subject to global and demand-class-based service level constraints. We first analyze the complexity of this problem and several of its special cases, and then we propose a model to find the optimal inventory for each type of resource. We show the convergence of the sample average approximation method to solve a stochastic extension of the model. This problem is motivated by the inventory planning decisions for surgical instruments for ORs. We study the effects of different model parameters and settings on the cost and service levels, based on surgical data from a community hospital.