SCHEDULING MULTIPLE OPERATING ROOMS UNDER UNCERTAINTY

Operating room (OR) scheduling is an important operational problem for most hospitals. Uncertainty in the surgery delivery process, the existence of multiple resources and competing performance criteria are among the important aspects of OR scheduling problems in practice. Considering these aspects, this dissertation focuses on developing and efficiently solving novel stochastic programming models for multi-OR scheduling problems under uncertainty in surgery durations. We first consider a stochastic multi-OR scheduling problem with multiple surgeons where the daily scheduling decisions are made before the resolution of uncertainty. We formulate the problem as a two-stage stochastic mixed-integer program that minimizes the sum of the fixed cost of opening ORs and the expected overtime and surgeon idling cost. Decisions in our model include the number of ORs to open, the allocation of surgeries to ORs, the sequence of surgeries in each OR, and the start times for surgeons. Realistic-sized instances of our model are difficult or impossible to solve with standard stochastic programming techniques. Therefore, we exploit several structural properties of our model and describe a novel set of widely applicable valid inequalities to achieve computational advantages. We use our results to quantify the value of capturing uncertainty and the benefit of pooling ORs, and to demonstrate the impact of parallel surgery processing on surgery schedules. We then consider a stochastic multi-OR scheduling problem where the initial schedule is revised at a prespecified rescheduling point during the surgical day. We formulate the problem as a three-stage stochastic mixed-integer program that minimizes the sum of the fixed cost of opening ORs and the expected overtime cost. The number of ORs to open and the allocation of surgeries to ORs are the first-, and the revisions on the allocation of surgeries to ORs are the second-stage decisions in our model. For our computational study, we consider a special case, which is a two-stage stochastic mixed-integer program, where rescheduling decisions are made under perfect information. We use stage-wise and scenario-wise decomposition methods to solve our model. By using our results, we estimate the value of rescheduling, and illustrate the impact of different surgery sequencing rules on this value

Önleyici bakım varlığında makine çizelgeleme.

In manufacturing environments, machines are usually subject to down periods due to various reasons such as preventive maintenance activities, pre-accepted jobs and pre-known material shortages. Among these reasons, preventive maintenance, which is defined as the pre-planned maintenance activities to keep the machine in its operating state, has gained much more importance in recent years. In this thesis, we consider the single machine total flow time problem where the jobs are non-resumable and the machine is subject to preventive maintenance activities of known starting times and durations. We propose a number of optimality properties together with the upper and lower bounding procedures. Using these mechanisms, we build a branch and bound algorithm to find the optimal solution of the problem. Our extensive computational study on randomly generated test instances shows that our algorithm can solve large-sized problem instances with up to 80 jobs in reasonable times. We also study a two-alternative maintenance planning problem with minor and major maintenances. We give an optimizing algorithm to find the timing of the maintenances, when the job sequence is fixed.M.S. - Master of Scienc

Closed-loop supply chain network design under demand, return and quality uncertainty

We consider the problem of designing a closed-loop supply chain (CLSC) network in the presence of uncertainty in demand quantities, return rates, and quality of the returned products. We formulate the problem as a two-stage stochastic mixed-integer program (SMIP) that maximizes the total expected profit. The first-stage decisions in our model are facility location and capacity decisions, and the second-stage decisions are the forward/backward flows on the network and hence the production/recovery quantities defined by the flow amounts. We solve the problem by using the L-shaped method in iterative and branch-and-cut frameworks. To improve the computational efficiency, we consider various cut generation strategies. Besides testing the performance of the considered solution methods, we also use our numerical results to estimate the value of the stochastic solution (VSS), the expected value of perfect information (EVPI), and the benefit of utilizing a CLSC network. Our results indicate that the uncertainty in demand has the highest impact and the uncertainty in return rate has the lowest impact on VSS and EVPI values, and including reverse chain increases the expected profit significantly

Closed-loop supply chain network design under demand, return and quality uncertainty

We consider the problem of designing a closed-loop supply chain (CLSC) network in the presence of uncertainty in demand quantities, return rates, and quality of the returned products. We formulate the problem as a two-stage stochastic mixed-integer program (SMIP) that maximizes the total expected profit. The first-stage decisions in our model are facility location and capacity decisions, and the second-stage decisions are the forward/reverse flows on the network and hence the production/recovery quantities defined by the flow amounts. We solve the problem by using the L-shaped method in iterative and branch-and-cut frameworks. To improve the computational efficiency, we consider various cut generation strategies. Besides testing the performance of the considered solution methods, we also use our numerical results to estimate the value of the stochastic solution (VSS), the expected value of perfect information (EVPI), and the benefit of utilizing a CLSC network. Our results indicate that the uncertainty in demand has the highest impact and the uncertainty in return rate has the lowest impact on VSS and EVPI values, and including reverse chain increases the expected profit significantly

Single machine scheduling with preventive maintenances

We consider the single machine total flow time problem in which the jobs are non-resumable and the machine is subject to preventive maintenance activities of known starting times and durations. We propose a branch-and-bound algorithm that employs powerful optimality properties and bounding procedures. Our extensive computational studies show that our algorithm can solve large-sized problem instances with up to 80 jobs in reasonable times. We also study a two-alternative maintenance planning problem with minor and major maintenances. We give a polynomial-time algorithm to find the optimal maintenance times when the job sequence is fixed