Cem Saydam

A multiperiod set covering location model for dynamic redeployment of ambulances

Emergency medical service (EMS) providers continually seek ways to improve system performance particularly the response time to incidents. The demand for ambulances fluctuate throughout the week, depending on the day of week, and even the time of day, therefore EMS operators can improve system performance by dynamic relocation/redeployment of ambulances in response to fluctuating demand patters. The objective of the model is to determine the minimum number of ambulances and their locations for each time cluster in which significant changes in demand pattern occur while meeting coverage requirement with a predetermined reliability. The model is further enhanced by calculating ambulance specific busy probabilities and validated by a comprehensive simulation model. Computational results on experimental data sets and data from an EMS agency are provided.

An optimization approach for ambulance location and the districting of the response segments on highways

In this paper we present a method to optimize the configuration and operation of emergency medical systems on highways. Different from the approaches studied in the previous papers, the present method can support two combined configuration decisions: the location of ambulance bases along the highway and the districting of the response segments. For example, this method can be used to make decisions regarding the optimal location and coverage areas of ambulances in order to minimize mean user response time or remedy an imbalance in ambulance workloads within the system. The approach is based on embedding a well-known spatially distributed queueing model (hypercube model) into a hybrid genetic algorithm to optimize the decisions involved. To illustrate the application of the proposed method, we utilize two case studies on Brazilian highways and validate the findings via a discrete event simulation model.

Solving large-scale maximum expected covering location problems by genetic algorithms: A comparative study

Abstract This paper compares the performance of genetic algorithms (GAs) on large-scale maximum expected coverage problems to other heuristic approaches. We focus our attention on a particular formulation with a nonlinear objective function to be optimized over a convex set. The solutions obtained by the best genetic algorithm are compared to Daskins heuristic and the optimal or best solutions obtained by solving the corresponding integer linear programming (ILP) problems. We show that at least one of the GAs yields optimal or near-optimal solutions in a reasonable amount of time.

EMS call volume predictions: A comparative study

The demand for ambulances fluctuates throughout the week, depending on the day of week and, even more so, the time of day. Many emergency medical services (EMS) managers adjust the number of ambulances deployed using various demand pattern analyses, including moving averages. Simply forecasting the number of expected calls for an entire region does not allow managers to deploy their often-limited resources effectively so that emergency response time is minimized. In order for deployment plans, or even sophisticated optimization models, to be more effective, emergency call forecasts must be accurate for both time and location. For purposes of this study, we consider forecasts accurate for a 4x4sq.mile region if they are within +/-0.25 of actual calls for hourly forecasts and within +/-0.5 of actual calls for 3-h forecasts. An artificial neural network (ANN) designed to forecast demand volume of specific areas during different times of the day is compared to current industry practice for accuracy of prediction. Our study shows that both methods produce accurate forecasts for certain levels of time and space granularity. Results also suggest that the high level of space and time details in forecasts desired by EMS managers may be difficult to obtain regardless of which method is used.

Accurate estimation of expected coverage: revisited

Abstract As noted in several studies (Batta et al., Transp. Sci. 23 (1989) 277), (Burwell et al., Comput. Opns. Res. 20 (1993) 113), (Daskin, Network and Discrete Location, Wiley, New York, 1995), (Marianov and ReVelle, Eur. J. Opns. Res. 93 (1996) 110), (Saydam et al., Socio-Econ. Plann. Sci. 28(2) (1994) 113), the accurate estimation of expected coverage is an important and open issue. Although the maximum expected coverage model is empirically shown to prescribe a robust set of “optimal” locations, earlier findings suggest that it could also over or underestimate the coverage by a significant margin. In this study, we present a genetic algorithm (GA) that combines the expected coverage approach with the hypercube model (Jarvis, Mgmt. Sci. 31 (1985) 235), (Larson, Comput. Opns. Res. 1 (1974) 67), (Larson, Opns. Res. 23 (1975) 845) to solve the maximum expected coverage location problem with increased accuracy and realism. Our findings suggest that the GA provides at least as good solutions 94% of the time making it a viable alternative to the two-step procedures stipulated earlier.

Joint replenishment problem under continuous unit cost change

The joint replenishment problem determines order quantities and the grouping of products replenished from the same supplier. The objective is to minimize the ordering and holding cost of the purchasing firm. The problem is frequently solved assuming products with constant unit cost. An efficient algorithm for solving the joint replenishment problem for products that may be experiencing unit cost increase or decrease is developed. The proposed algorithm is tested on a sample of randomly generated problems containing up to 25 items and it is shown that it identifies the global optimal solutions for most of these problems. For the worst case where the algorithm fails to identify the global optimal solution, the solution it provides had a total cost 0.007% above the global minimum.

Developing effective meta-heuristics for a probabilistic location model via experimental design

This article employs a statistical experimental design to guide and evaluate the development of four meta-heuristics applied to a probabilistic location model. The meta-heuristics evaluated include evolutionary algorithm, tabu search, simulated annealing, and a hybridized hill-climbing algorithm. Comparative results are analyzed using ANOVA. Our findings show that all four implementations produce high quality solutions. In particular, it was found that on average tabu search and simulated annealing find their best solutions in the least amount of time, with relatively small variability. This is especially important for large-size problems when dynamic redeployment is required.

Accurate estimation of expected coverage: A comparative study

Abstract The accurate estimation of expected coverage is an important issue in the application of set covering approaches to emergency medical service (EMS) location problems. The first article to define and utilize expected coverage was published by Daskin in 1982. Batta el al . recognized the inaccuracy of solutions obtained via Daskins model and proposed an adjustment to improve the expected coverage predicted by it. Recently. Bernardo and Repede presented a modified model that reportedly estimates expected coverage more accurately relative to the previous models. In this study, each of these models was applied to a wide range of simulated EMS system scenarios. Our findings suggest that none of the expected covering models is consistently more accurate than the others. Additionally, our results support Batta et al.s recommendation that a hypercube-based model should be used for post-optimality analysis.

A comparative performance analysis of the Wagner-Whitin algorithm and lot-sizing heuristics

Abstract Lot-sizing for dynamic demand has received considerable attention in th eliterature over the past two decades. The Wagner-Whitin (WW) algorithm, although known to produce optimal ordering plants for dynamic lot-sizing problems, has not been utilized or promoted due to the unjustified claims about its inefficiency. In this paper, we show the relative performances of four popular heuristics against the WW. We use the cost performance and CPU time as our criteria. Our results show that the WW algorithm will solve problems in linear time, and among all of the algorithms tested, the Silver-Meal heuristic exhibits the best overall performance, in terms of speed (17 times faster than WW), and in quality of solution (with an average loss of 1.6% of optimality).

The dynamic redeployment coverage location model

Demand for ambulances is known to fluctuate spatially and temporally by day of the week and time of day. Faced with fluctuating demand during the day, emergency medical systems (EMS) managers utilize redeployment strategies to meet demand. Such shifting of personnel, although better able to cover a region with fluctuating demand, can cause fatigue amongst ambulance crew members. Considering these phenomena, we extend the dynamic available coverage location model to be driven by two objectives: (1) Minimize the number of ambulances, and (2) Minimize the number of redeployments for a given fleet during a given shift. We develop a heuristic search algorithm and present the comparative statistics using real data from an urban EMS agency. Our findings suggest that EMS managers can effectively balance a need for additional ambulances with those redeployments required to meet variable demand patterns.