a b s t r a c tWe describe a polynomial-size conic quadratic reformulation for a machine-job assignment problem with separable convex cost. Because the conic strengthening is based only on the objective of the problem, it can also be applied to other problems with similar cost functions. Computational results demonstrate the effectiveness of the conic reformulation.

In this study, we determine the upper and lower bounds for the processing time of each job under controllable machining conditions. The proposed bounding scheme is used to find a set of discrete efficient points on the efficient frontier for a bi-criteria scheduling problem on a single CNC machine. We have two objectives; minimizing the manufacturing cost (comprised of machining and tooling costs) and minimizing makespan. The technological restrictions of the CNC machine along with the job specific parameters affect the machining conditions; such as cutting speed and feed rate, which in turn specify the processing times and tool lives. Since it is well known that scheduling problems are extremely sensitive to processing time data, system resources can be utilized much more efficiently by selecting processing times appropriately.

Abstract:The machine scheduling literature does not consider the issue of tool change. The parallel literature on tool management addresses this issue but assumes that the change is due only to part mix. In practice, however, a tool change is caused most frequently by tool wear. That is why we consider here the problem of scheduling a set of jobs on a single CNC machine where the cutting tool is subject to wear; our objective is to minimize the total completion time. We first describe the problem and discuss its peculiarities. After briefly reviewing available theoretical results, we then go on to provide a mixed 0 -1 linear programming model for the exact solution of the problem; this is useful in solving problem instances with up to 20 jobs and has been used in our computational study. As our main contribution, we next propose a number of heuristic algorithms based on simple dispatch rules and generic search. We then discuss the results of a computational study where the performance of the various heuristics is tested; we note that the well-known SPT rule remains good when the tool change time is small but deteriorates as this time increases and further that the proposed algorithms promise significant improvement over the SPT rule.

Airline operations are subject to frequent disruptions typically due to unexpected aircraft maintenance requirements and undesirable weather conditions. Recovery from a disruption often involves propagating delays in downstream flights and increasing cruise stage speed when possible in an effort to contain the delays. However, there is a critical trade-off between fuel consumption (and its adverse impact on air quality and greenhouse gas emissions) and cruise speed. Here we consider delays caused by such disruptions and propose a flight rescheduling model that includes adjusting cruise stage speed on a set of affected and unaffected flights as well as swapping aircraft optimally. To the best of our knowledge, this is the first study in which the cruise speed is explicitly included as a decision variable into an airline recovery optimization model along with the environmental constraints and costs. The proposed model allows one to investigate the trade-off between flight delays and the cost of recovery. We show that the optimization approach leads to significant cost savings compared to the popular recovery method delay propagation. Flight time controllability, nonlinear delay, fuel burn and CO2 emission cost functions, and binary aircraft swapping decisions complicate the aircraft recovery problem significantly. In order to mitigate the computational difficulty we utilize the recent advances in conic mixed integer programming and propose a strengthened formulation so that the nonlinear mixed integer recovery optimization model can be solved efficiently. Our computational tests on realistic cases indicate that the proposed model may be used by operations controllers to manage disruptions in real time in an optimal manner instead of relying on ad-hoc heuristic approaches.

When a machine breakdown forces a modi®ed¯ow shop (MFS) out of the prescribed state, the proposed strategy reschedules part of the initial schedule to match up with the preschedule at some point. The objective is to create a new schedule that is consistent with the other production planning decisions like material¯ow, tooling and purchasing by utilizing the time critical decision making concept. We propose a new rescheduling strategy and a match-up point determination procedure through a feedback mechanism to increase both the schedule quality and stability. The proposed approach is compared with alternative reactive scheduling methods under di erent experimental settings. Ó

In this study, an m-machine flexible robotic manufacturing cell consisting of CNC machines is considered. The flexibility of the machines leads to a new class of robot move cycles called the pure cycles. We first model the problem of determining the best pure cycle in an m-machine cell as a special travelling salesman problem in which the distance matrix consists of decision variables as well as parameters. We focus on two specific cycles among the huge class of pure cycles. We prove that, in most of the regions, either one of these two cycles is optimal. For the remaining regions we derive worst case performances of these cycles. We also prove that the set of pure cycles dominates the flowshop-type robot move cycles considered in the literature. As a design problem, we consider the number of machines in a cell as a decision variable. We determine the optimal number of machines that minimizes the cycle time for given cell parameters such as the processing times, robot travel times and the loading/unloading times of the machines.

In the literature, there exist many variations of machining economics problem in terms of modelling approaches and solution methodologies. However most of the existing studies focus on the single machining operation which is seldom in practice. On the other hand, tool management approaches at the system level fail to relate the tooling issues to the machining conditions, and ignore the tool availability and tool wear restrictions. A new solution methodology is developed to determine the optimum machining conditions and tool allocation simultaneously to minimize the production cost of a multiple operation case where there can be alternative tools for each operation. As a result, we can both improve the solution by exploiting the interaction between these two decisions, and also prevent any infeasibility that might occur for the tool allocation problem due to tool contention among the operations for a limited number of tool types by considering the tool availability and tool life limitations.

We present a literature review and classi® cation of techniques to determine both the design parameters and kanban sequences for just-in-time manufacturing systems. We summarize the model structures, decision variables, performance measures and assumptions in a tabular format. It is important to state that there is a signi® cant relationship between the design parameters, such as the number of kanbans and kanban sizes, and the scheduling decisions in a multiitem, multi-stage, multi-horizon kanban system. An experimental design is developed to evaluate the impact of operational issues, such as sequencing rules and actual lead times on the design parameters.