MILP Formulations for Optimal Steady-State Buffer Levels and Flexible Maintenance Scheduling

Abstract

<p>In this thesis two industrially motivated problems, belonging to the same manufacturing process, are solved by mixed-integer linear programming (MILP) techniques. Initially, the problem of determining optimal steady-state buffer levels for minimizing unit failure impacts is examined. Next, a method for achieving an optimal and coordinated production and flexible maintenance schedule is studied under several different optimization goals. The process that is predominantly considered is a continuous processing plant that can be modelled as n units in series separated by (<em>n</em> - 1) buffer tanks.</p> <p>Unit shutdowns due to equipment failure result in adverse economic consequences due to reduced production and costs associated with off-specification product. Mitigation of these effects may be possible if sufficient buffer capacity is available for parts of the plant to continue operation until the affected units are back in operation. A question that arises is what the optimal levels of the buffer storage units should be for use in normal operation, with insight as to what abnormal operating conditions may occur. This is a function of the expected unit failure frequencies and failure lengths, and the process dynamics. In this study, the problem is posed within a multi-period dynamic optimization framework. Historical records are used to determine key unit failure scenarios. The objective function considers the loss of profit associated with downtime, as well as a fixed cost of induced shutdowns due to buffers being either full or empty.</p> <p>Production scheduling in coordination with maintenance scheduling is often completed simply by fixing maintenance and then scheduling production around the maintenance-associated process unit unavailability. While acknowledging that much research has been completed to determine optimal maintenance policies, allowing maintenance events to be scheduled with a small degree of flexibility may significantly improve the resulting makespan. Alternative formulations suited to batch processing and continuous processing are presented; where the key advantage to the latter formulation is the possibility of job-splitting. Flexible maintenance by means of a specified time interval, sequence-dependent cleaning, shared finite intermediate storage, and product deadlines are accounted for in this dynamic optimization problem. Considered objectives include: makespan minimization, throughput maximization, and intermediate inventory minimization.</p> <p>Several case studies are provided for both problems, with the intention of demonstrating the functionality of the formulations as well as to indicate the possible process improvements upon implementation.</p>