Onur Ozturk

Makespan minimisation on parallel batch processing machines with non-identical job sizes and release dates

The problem we study in this paper arises from the washing step of hospital sterilisation services. Washers in the washing step are capable of handling more than one medical device set as long as their capacity is not exceeded. The medical device set sizes and arrival times to the sterilisation service may be different, but they all have the same washing duration. Thus, we model the washing step as a batch scheduling problem where medical device sets are treated as jobs with non-identical sizes and release dates, but equal processing times. The main findings we present in this paper are the following. First, we study two special cases for which polynomial algorithms are presented. We then develop a 2-approximation algorithm for the general problem. Finally, we develop a MILP model and compare it with another MILP model from the literature. Computational results show that our MILP model outperforms the model from the literature.

A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services

In this paper, we address the problem of parallel batching of jobs on identical machines to minimize makespan. The problem is motivated from the washing step of hospital sterilization services where jobs have different sizes, different release dates and equal processing times. Machines can process more than one job at the same time as long as the total size of jobs in a batch does not exceed the machine capacity. We present a branch and bound based heuristic method and compare it to a linear model and two other heuristics from the literature. Computational experiments show that our method can find high quality solutions within short computation time.

Optimizing the makespan of washing operations of medical devices in hospital sterilization services

In this paper, we deal with the problem of minimizing the makespan of washing operations in hospitals sterilization services. After use in operating blocs, reusable medical devices (RMD) are sent to the sterilization service which is composed of various processes. In the washing step, different sets of RMD, used for different operations, may be washed together without exceeding washer capacity. An RMD set must be washed in one cycle and so, we are not allowed to split RMD sets. In this case, we consider a batch scheduling problem where RMD sets may have different sizes and different release dates for washing. Note that if all release dates are equal, the problem is reduced to a bin packing problem. We provide a mixed integer linear programming model which aims at minimizing the makespan of washing operations. We provide and also experiment some heuristics based on classical bin packing algorithms.

A branch and bound algorithm for scheduling unit size jobs on parallel batching machines to minimize makespan

In this paper, we present a branch and bound algorithm for the parallel batch scheduling of jobs having different processing times, release dates and unit sizes. There are identical machines with a fixed capacity and the number of jobs in a batch cannot exceed the machine capacity. All batched jobs are processed together and the processing time of a batch is given by the greatest processing time of jobs in that batch. We compare our method to a mixed integer program as well as a method from the literature that is capable of optimally solving instances with a single machine. Computational experiments show that our method is much more efficient than the other two methods in terms of solution time for finding the optimal solution.

Exact and metaheuristic algorithms to minimize the total tardiness of cutting tool sharpening operations

Abstract We present in this study an algorithmic framework of an intelligent scheduling system that aims to provide an optimum planning for the production process of cutting tools taking into consideration the constraining conditions such as production characteristics, capacity, and performance criteria. Once blunt, cutting tools are sent to the sharpening service composed of parallel machines capable of sharpening more than one tool at the same time. After sharpening, tools are sent back to the departments of origins to be used in other production processes. Thus, any delay in the sharpening service provokes delays in other departments. We develop first a genetic algorithm enhanced by a dynamic programming procedure capable of optimally scheduling a given job sequence. Then we develop a branch and bound method that emulates at each node possible decisions based on a postpone or schedule strategy. Numerical results show that both methods give high quality solutions for the scheduling of tool sharpening operations. Beside the minimization of total tardiness, many other types of decision making related to minimal operation time of a sharpening service, minimal amount of cutting tool inventory and the number of required sharpening machines can be deduced thanks to applying our models.

An optimization model for freight transport using urban rail transit

In this paper, we discuss a new concept for freight transport within the borders of a city with an urban rail transit system. A rising trend in some countries, urban rail transit systems are an alternative method for freight transport through cities. In these systems, the same railway is shared between passenger trains and cargo trains. We present a decision support framework for the problem of urban freight movement by rail together with mathematical methods for the optimal distribution of goods. The problem we consider has a single rail line on which some stations can be used as loading/unloading platforms for goods. Demand is known in advance and each client desires a different time for the delivery. First, we start with the case of two stations for which an approximation algorithm and a pseudo-polynomial dynamic programming algorithm are presented. Afterwards we extend the setting to several stations and develop a heuristic method, two mixed integer models and an ϵ—constraint. We provide numerical results that demonstrate the speed at which the various methods solve different sized versions of the problem.