A hybrid method for large-scale short-term scheduling of make-and-pack production processes

Due to the ongoing trend towards increased product variety, fast-moving consumer goods such as food and beverages, pharmaceuticals, and chemicals are typically manufactured through so-called make-and-pack processes. These processes consist of a make stage, a pack stage, and intermediate storage facilities that decouple these two stages. In operations scheduling, complex technological constraints must be considered, e.g., non-identical parallel processing units, sequence-dependent changeovers, batch splitting, no-wait restrictions, material transfer times, minimum storage times, and finite storage capacity. The short-term scheduling problem is to compute a production schedule such that a given demand for products is fulfilled, all technological constraints are met, and the production makespan is minimised. A production schedule typically comprises 500–1500 operations. Due to the problem size and complexity of the technological constraints, the performance of known mixed-integer linear programming (MILP) formulations and heuristic approaches is often insufficient. We present a hybrid method consisting of three phases. First, the set of operations is divided into several subsets. Second, these subsets are iteratively scheduled using a generic and flexible MILP formulation. Third, a novel critical path-based improvement procedure is applied to the resulting schedule. We develop several strategies for the integration of the MILP model into this heuristic framework. Using these strategies, high-quality feasible solutions to large-scale instances can be obtained within reasonable CPU times using standard optimisation software. We have applied the proposed hybrid method to a set of industrial problem instances and found that the method outperforms state-of-the-art methods.

A framework for benchmarking of homogenisation algorithm performance on the global scale

The International Surface Temperature Initiative (ISTI) is striving towards substantively improving our ability to robustly understand historical land surface air temperature change at all scales. A key recently completed first step has been collating all available records into a comprehensive open access, traceable and version-controlled databank. The crucial next step is to maximise the value of the collated data through a robust international framework of benchmarking and assessment for product intercomparison and uncertainty estimation. We focus on uncertainties arising from the presence of inhomogeneities in monthly mean land surface temperature data and the varied methodological choices made by various groups in building homogeneous temperature products. The central facet of the benchmarking process is the creation of global-scale synthetic analogues to the real-world database where both the "true" series and inhomogeneities are known (a luxury the real-world data do not afford us). Hence, algorithmic strengths and weaknesses can be meaningfully quantified and conditional inferences made about the real-world climate system. Here we discuss the necessary framework for developing an international homogenisation benchmarking system on the global scale for monthly mean temperatures. The value of this framework is critically dependent upon the number of groups taking part and so we strongly advocate involvement in the benchmarking exercise from as many data analyst groups as possible to make the best use of this substantial effort.