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

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

Scheduling problems with two competing agents

We consider the scheduling problems arising when two agents, each with a set of nonpreemptive jobs, compete to perform their respective jobs on a common processing resource. Each agent wants to minimize a certain objective function, which depends on the completion times of its jobs only. The objective functions we consider in this paper are maximum of regular functions (associated with each job), number of late jobs, and total weighted completion times. We obtain different scenarios, depending on the objective function of each agent, and on the structure of the processing system (single machine or shop). For each scenario, we address the complexity of various problems, namely, finding the optimal solution for one agent with a constraint on the other agent's cost function, finding single nondominated schedules (i.e., such that a better schedule for one of the two agents necessarily results in a worse schedule for the other agent), and generating all nondominated schedules

Two is better than one? Order aggregation in a meal delivery scheduling problem

We address a single-machine scheduling problem motivated by a last-mile-delivery setting for a food company. Customers place orders, each characterized by a delivery point (customer location) and an ideal delivery time. An order is considered on time if it is delivered to the customer within a time window given by the ideal delivery time , where is the same for all orders. A single courier (machine) is in charge of delivery to all customers. Orders are either delivered individually, or two orders can be aggregated in a single courier trip. All trips start and end at the restaurant, so no routing decisions are needed. The problem is to schedule courier trips so that the number of late orders is minimum. We show that the problem with order aggregation is -hard and propose a combinatorial branch and bound algorithm for its solution. The algorithm performance is assessed through a computational study on instances derived by a real-life application and on randomly generated instances. The behavior of the combinatorial algorithm is compared with that of the best ILP formulation known for the problem. Through another set of computational experiments, we also show that an appropriate choice of design parameters allows to apply the algorithm to a dynamic context, with orders arriving over time

Covering a line segment with variable radius discs

The paper addresses the problem of locating sensors with a circular field of view so that a given line segment is under full surveillance, which is termed as the Disc Covering Problem on a Line. The cost of each sensor includes a fixed component f, and a variable component that is a convex function of the diameter of the field-of- view area. When only one type of sensor or, in general, one type of disc, is available, then a simple polynomial algorithm solves the problem. When there are different types of sensors, the problem becomes hard. A branch-and-bound algorithm as well as an efficient heuristic are developed for the special case in which the variable cost component of each sensor is proportional to the square of the measure of the field-of-view area. The heuristic very often obtains the optimal solution as shown in extensive computational testing

Part sequencing in three-machine no-wait robotic cells

Abstract A no-wait robotic cell is an automated ow shop in which a robot is used to move the parts from a machine to the next. Parts are not allowed to wait. We analyze the complexity of the part sequencing problem in a robotic cell with three machines, for di erent periodical patterns of robot moves, when the objective is productivity maximization