A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.

Optimal compliance with emission constraints: dynamic characteristics and the choice of technique

The paper analyzes how to comply with an emission constraint, which restricts the use of an established energy technique, given the two options to save energy and to invest in two alternative energy techniques. These techniques differ in their deterioration rates and the investment lags of the corresponding capital stocks. Thus, the paper takes a medium-term perspective on climate change mitigation, where the time horizon is too short for technological change to occur, but long enough for capital stocks to accumulate and deteriorate. It is shown that, in general, only one of the two alternative techniques prevails in the stationary state, although, both techniques might be utilized during the transition phase. Hence, while in a static economy only one technique is efficient, this is not necessarily true in a dynamic economy.

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.

Constraints on the thermal evolution of the Adriatic margin during Jurassic continental break-up: U–Pb dating of rutile from the Ivrea–Verbano Zone, Italy

The Ivrea–Verbano Zone (IVZ), northern Italy, exposes an attenuated section through the Permian lower crust that records high-temperature metamorphism under lower crustal conditions and a protracted history of extension and exhumation associated partly with the Jurassic opening of the Alpine Tethys ocean. This study presents SHRIMP U–Pb geochronology of rutile from seven granulite facies metapelites from the base of the IVZ, collected from locations spanning ~35 km along the strike of Paleozoic fabrics. Rutile crystallised during Permian high-temperature metamorphism and anatexis, yet all samples give Jurassic rutile U–Pb ages that record cooling through 650–550 °C. Rutile age distributions are dominated by a peak at ~160 Ma, with a subordinate peak at ~175 Ma. Both ~160 and ~175 Ma age populations show excellent agreement between samples, indicating that the two distinctive cooling stages they record were synchronous on a regional scale. The ~175 Ma population is interpreted to record cooling in the footwall of rift-related faults and shear zones, for which widespread activity in the Lower Jurassic has been documented along the western margin of the Adriatic plate. The ~160 Ma age population postdates the activity of all known rift-related structures within the Adriatic margin, but coincides with extensive gabbroic magmatism and exhumation of sub-continental mantle to the floor of the Alpine Tethys, west of the Ivrea Zone. We propose that this ~160 Ma early post-rift age population records regional cooling following episodic heating of the distal Adriatic margin, likely related to extreme lithospheric thinning and associated advection of the asthenosphere to shallow levels. The partial preservation of the ~175 Ma age cluster suggests that the post-rift (~160 Ma) heating pulse was of short duration. The regional consistency of the data presented here, which is in contrast to many other thermochronometers in the IVZ, demonstrates the value of the rutile U–Pb technique for probing the thermal evolution of high-grade metamorphic terrains. In the IVZ, a significant decoupling between Zr-in-rutile temperatures and U–Pb ages of rutile is observed, with the two systems recording events ~120 Ma apart.