Integrating lean thinking and mathematical optimization: A case study in appointment scheduling of hematological treatments

This paper addresses the relationship between lean thinking and mathematical optimization. We discuss the roles of the two approaches, using as a reference case study the appointment scheduling process in a hematological center of a large Italian hospital. We report on how lean tools have been deployed to improve the process, we present a mathematical optimization model and discuss its implementation. Our aim is to show that the joint use of lean thinking and mathematical optimization can disclose large benefits when they are properly integrated in the improvement process. In our case study, simulated experiments point out that the average patient lead time could be decreased by more than 30%. Keywords: Appointment scheduling, Hematological treatments, Lean thinkin

An efficient decomposition approach for surgical planning

This talk presents an efficient decomposition approach to surgical planning. Given a set of surgical waiting lists (one for each discipline) and an operating theater, the problem is to decide the room-to-discipline assignment for the next planning period (Master Surgical Schedule), and the surgical cases to be performed (Surgical Case Assignment), with the objective of optimizing a score related to priority and current waiting time of the cases. While in general MSS and SCA may be concurrently found by solving a complex integer programming problem, we propose an effective decomposition algorithm which does not require expensive or sophisticated computational resources, and is therefore suitable for implementation in any real-life setting. Our decomposition approach consists in first producing a number of subsets of surgical cases for each discipline (potential OR sessions), and select a subset of them. The surgical cases in the selected potential sessions are then discarded, and only the structure of the MSS is retained. A detailed surgical case assignment is then devised filling the MSS obtained with cases from the waiting lists, via an exact optimization model. The quality of the plan obtained is assessed by comparing it with the plan obtained by solving the exact integrated formulation for MSS and SCA. Nine different scenarios are considered, for various operating theater sizes and management policies. The results on instances concerning a medium-size hospital show that the decomposition method produces comparable solutions with the exact method in much smaller computation time

2 Combinatorial Models for Multi-agent Scheduling Problems

Abstract Scheduling models deal with the best way of carrying out a set of jobs on given processing resources. Typically, the jobs belong to a single decision maker, who wants to find the most profitable way of organizing and exploiting available resources, and a single objective function is specified. If different objectives are present, there can be multiple objective functions, but still the models refer to a centralized framework, in which a single decision maker, given data on the jobs and the system, computes the best schedule for the whole system. This approach does not apply to those situations in which the allocation process involves different subjects (agents), each having his/her own set of jobs, and there is no central authority who can solve possible conflicts in resource usage over time. In this case, the role of the model must be partially redefined, since rather than computing "optimal" solutions, the model is asked to provide useful elements for the negotiation process, which eventually leads to a stable and acceptable resource allocation. Multi-agent scheduling models are dealt with by several distinct disciplines (besides optimization, we mention game theory, artificial intelligence etc), possibly indicated by different terms. We are not going to review the whole scope in detail, but rather we will concentrate on combinatorial models, and how they can be employed for the purpose on hand. We will consider two major mechanisms for generating schedules, auctions and bargaining models, corresponding to different information exchange scenarios

Part type selection and batch sequencing in a flexible flow system

http://deepblue.lib.umich.edu/bitstream/2027.42/35348/2/b1576495.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/35348/1/b1576495.0001.001.tx