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Complex systems like semiconductor wafer fabrication facilities (fabs), networks of data switches, and large-scale call centers all demand efficient resource allocation. Deterministic models like linear programs (LP) have been used for capacity planning at both the design and expansion stages of such systems. LP-based planning is critical in setting a medium range or long-term goal for many systems, but it does not translate into a day-to-day operational policy that must deal with discreteness of jobs and the randomness of the processing environment. A stochastic processing network, advanced by J. Michael Harrison (2000, 2002, 2003), is a system that takes inputs of materials of various kinds and uses various processing resources to produce outputs of materials of various kinds. Such a network provides a powerful abstraction of a wide range of real-world systems. It provides high-fidelity stochastic models in diverse economic sectors including manufacturing, service, and information technology. We propose a family of maximum pressure service policies for dynamically allocating service capacities in a stochastic processing network. Under a mild assumption on network structure, we prove that a network operating under a maximum pressure policy achieves maximum throughput predicted by LPs. These policies are semilocal in the sense that each server makes its decision based on the buffer content in its serviceable buffers and their immediately downstream buffers. In particular, their implementation does not use arrival rate information, which is difficult to collect in many applications. We also identify a class of networks for which the nonpreemptive, non-processor-splitting version of a maximum pressure policy is still throughput optimal. Applications to queueing networks with alternate routes and networks of data switches are presented.

There are many situations in supply chain scheduling when the supplier finds it impossible to meet the promised due dates for some orders. We present a model for the rescheduling of orders with simultaneous assignment of attainable revised due dates to minimize due date escalation and tardiness penalties for the supplier. We show that the problem is equivalent to minimizing the total tardiness with rejection with respect to the original due dates. We prove that the problem is -hard and present a pseudopolynomial algorithm for it. We also present a fully polynomial time approximation scheme for the problem. Finally, we discuss the implications of our solution for setting fair tardiness penalties when due dates have to be renegotiated because of the delays.

We describe an approximation algorithm for the problem of finding the minimum makespan in a job shop. The algorithm is based on simulated annealing, a generalization of the well known iterative improvement approach to combinatorial optimization problems. The generalization involves the acceptance of cost-increasing transitions with a nonzero probability to avoid getting stuck in local minima. We prove that our algorithm asymptotically converges in probability to a globally minimal solution, despite the fact that the Markov chains generated by the algorithm are generally not irreducible. Computational experiments show that our algorithm can find shorter makespans than two recent approximation approaches that are more tailored to the job shop scheduling problem. This is, however, at the cost of large running times.

Increasing global competition, quality standards, environmental awareness and decreasing ore prices impose new challenges to mineral industries. Therefore, the extraction of mineral resources requires careful design and scheduling. In this research, simulated annealing (SA) is recommended to solve a mine production scheduling problem. First of all, in situ mineral characteristics of a deposit are simulated by sequential Gaussian simulation, and averaging the simulated characteristics within specified block volumes creates a three-dimensional block model. This model is used to determine optimal pit limits. A linear programming (LP) scheme is used to identify all blocks that can be included in the blend without violating the content requirements. The Lerchs-Grosmann algorithm using the blocks identified by the LP program determines optimal pit limits. All blocks that lie outside of the optimal pit limit are removed from the system and the blocks within the optimal pit are submitted to the production scheduling algorithm. Production scheduling optimization is carried out in two stages: Lagrangean parameterization, resulting in an initial sub-optimal solution, and multi-objective SA, improving the sub-optimal schedule further. The approach is demonstrated on a Western Australian iron ore body.

This paper considers the problem of minimizing resource investment required to execute the tasks in a project network by a given project due date. A project consists of non-pre-emptive tasks executed in a known and required precedence order. Each task is completed in one of its feasible modes, which may differ not only in task duration but also in consumption of renewable resources. A priority rule heuristic with polynomial computational complexity is presented for this computationally intractable problem. This heuristic simultaneously considers due date constraints and resource usage to select and schedule tasks with one decision rule. This differs from prior multi-mode priority rule scheduling heuristics that apply two consecutive decision rules to schedule tasks. Extensive computational testing indicates promising results.

For the purpose of production scheduling, open-pit mines are discretized into three-dimensional arrays known as block models. Production scheduling consists of deciding which blocks should be extracted, when they should be extracted, and what to do with the blocks once they are extracted. Blocks that are close to the surface should be extracted first, and capacity constraints limit the production in each time period. Since the 1960s, it has been known that this problem can be cast as an integer programming model. However, the large size of some real instances (3-10 million blocks, 15-20 time periods) has made these models impractical for use in real planning applications, thus leading to the use of numerous heuristic methods. In this article we study a well-known integer programming formulation of the problem that we refer to as C-PIT. We propose a new decomposition method for solving the linear programming relaxation (LP) of C-PIT when there is a single capacity constraint per time period. This algorithm is based on exploiting the structure of the precedence-constrained knapsack problem and runs in O ( mn log n ) in which n is the number of blocks and m a function of the precedence relationships in the mine. Our computations show that we can solve, in minutes, the LP relaxation of real-sized mine-planning applications with up to five million blocks and 20 time periods. Combining this with a quick rounding algorithm based on topological sorting, we obtain integer feasible solutions to the more general problem where multiple capacity constraints per time period are considered. Our implementation obtains solutions within 6% of optimality in seconds. A second heuristic step, based on local search, allows us to find solutions within 3% in one hour on all instances considered. For most instances, we obtain solutions within 1-2% of optimality if we let this heuristic run longer. Previous methods have been able to tackle only instances with up to 150,000 blocks and 15 time periods.

We provide a unified framework for the total tardiness problem by surveying the related literature in the single-machine, parallel machine, flowshop and jobshop settings. We focus on critically evaluating the heuristic algorithms; we also propose new heuristics for both the single-machine and the parallel-machine tardiness problems. Finally, we identify the areas where further research is needed and we give directions for future research.

An efficient appointment scheduling system has a defining role in controlling wait times and improving the productivity of a large variety of service systems. This study addresses the variability and length of wait times. We reduce them by a form of restricted central intake. We believe it is the first study that expands the appointment scheduling-sequencing model to include multiple sites and incorporate clients’ flexibility and priorities, and solves the large-size scheduling-sequencing problem in a decentralized manner. To make the study more practical, it should be compatible with the multi-stakeholder environment and consider their independency. Furthermore, the problem is large-size as it combines all requests from a geographical region into one stream. Therefore, a decentralized distributed algorithm is applied to solve the amended model. The solution approach is an ADMM-based combination of dual decomposition and augmented Lagrangian relaxation. For the application of this approach, this paper focuses on the outpatient appointment system due to its importance. Early diagnosis and prevention play a crucial role in community health and health system quality. However, patients often experience significant wait times for various diagnostic technologies worldwide. The approach is examined by a real situation of MRI in Ontario, Canada. It has been shown that this study provides better workload balance across hospitals, better responding to demand fluctuations, and alleviates excessive wait times. The computational results also show that the proposed solution method can be satisfactory in terms of accuracy, running time, and applicability. The approach developed in this study can be applicable to many practical applications of timing and sequencing, such as outpatient surgery, other diagnostic testing, home healthcare, and physical and mental therapies, as well as in other service industries beyond healthcare, like public consultations, government services.

We combine mixed-integer linear programming (MILP) and constraint programming (CP) to solve an important class of planning and scheduling problems. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. Tasks assigned to a facility may run in parallel subject to resource constraints (cumulative scheduling). We solve problems in which the objective is to minimize cost, makespan, or total tardiness. We obtain significant computational speedups, of several orders of magnitude for the first two objectives, relative to the state of the art in both MILP and CP. We also obtain better solutions and bounds for problems than cannot be solved to optimality.

This study is concerned with the determination of an optimal appointment schedule in an outpatient-inpatient hospital system where the inpatient exams can be cancelled based on certain rules while the outpatient exams cannot be cancelled. Stochastic programming models were formulated and solved to tackle the stochasticity in the procedure durations and patient arrival patterns. The first model, a two-stage stochastic programming model, is formulated to optimize the slot size. The second model further optimizes the inpatient block (IPB) placement and slot size simultaneously. A computational method is developed to solve the second optimization problem. A case study is conducted using the data from Magnetic Resonance Imaging (MRI) centers of Lahey Hospital and Medical Center (LHMC). The current schedule and the schedules obtained from the optimization models are evaluated and compared using simulation based on FlexSim Healthcare. Results indicate that the overall weighted cost can be reduced by 11.6% by optimizing the slot size and can be further reduced by an additional 12.6% by optimizing slot size and IPB placement simultaneously. Three commonly used sequencing rules (IPBEG, OPBEG, and a variant of ALTER rule) were also evaluated. The results showed that when optimization tools are not available, ALTER variant which evenly distributes the IPBs across the day has the best performance. Sensitivity analysis of weights for patient waiting time, machine idle time and exam cancellations further supports the superiority of ALTER variant sequencing rules compared to the other sequencing methods. A Pareto frontier was also developed and presented between patient waiting time and machine idle time to enable medical centers with different priorities to obtain solutions that accurately reflect their respective optimal tradeoffs. An extended optimization model was also developed to incorporate the emergency patient arrivals. The optimal schedules from the extended model show only minor differences compared to those from the original model, thus proving the robustness of the scheduling solutions obtained from our optimal models against the impacts of emergency patient arrivals.