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.

Advanced production scheduling for batch plants in process industries

An Advanced Planning System (APS) offers support at all planning levels along the supply chain while observing limited resources. We consider an APS for process industries (e.g. chemical and pharmaceutical industries) consisting of the modules network design (for long–term decisions), supply network planning (for medium–term decisions), and detailed production scheduling (for short–term decisions). For each module, we outline the decision problem, discuss the specifi cs of process industries, and review state–of–the–art solution approaches. For the module detailed production scheduling, a new solution approach is proposed in the case of batch production, which can solve much larger practical problems than the methods known thus far. The new approach decomposes detailed production scheduling for batch production into batching and batch scheduling. The batching problem converts the primary requirements for products into individual batches, where the work load is to be minimized. We formulate the batching problem as a nonlinear mixed–integer program and transform it into a linear mixed–binary program of moderate size, which can be solved by standard software. The batch scheduling problem allocates the batches to scarce resources such as processing units, workers, and intermediate storage facilities, where some regular objective function like the makespan is to be minimized. The batch scheduling problem is modelled as a resource–constrained project scheduling problem, which can be solved by an efficient truncated branch–and–bound algorithm developed recently. The performance of the new solution procedures for batching and batch scheduling is demonstrated by solving several instances of a case study from process industries.

Resource allocation with project management software

We present results of a benchmark test evaluating the resource allocation capabilities of the project management software packages Acos Plus.1 8.2, CA SuperProject 5.0a, CS Project Professional 3.0, MS Project 2000, and Scitor Project Scheduler 8.0.1. The tests are based on 1560 instances of precedence– and resource–constrained project scheduling problems. For different complexity scenarios, we analyze the deviation of the makespan obtained by the software packages from the best feasible makespan known. Among the tested software packages, Acos Plus.1 and Project Scheduler show the best resource allocation performance. Moreover, our numerical analysis reveals a considerable performance gap between the implemented methods and state–of–the–art project scheduling algorithms, especially for large–sized problems. Thus, there is still a significant potential for improving solutions to resource allocation problems in practice.

Batch scheduling in process industries: an application of resource-constrained project scheduling

The paper deals with batch scheduling problems in process industries where final products arise from several successive chemical or physical transformations of raw materials using multi–purpose equipment. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. The production start of a batch at a given level requires the availability of all input products. We consider the problem of scheduling the production of given batches such that the makespan is minimized. Constraints like minimum and maximum time lags between successive production levels, sequence–dependent facility setup times, finite intermediate storages, production breaks, and time–varying manpower contribute to the complexity of this problem. We propose a new solution approach using models and methods of resource–constrained project scheduling, which (approximately) solves problems of industrial size within a reasonable amount of time.

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.

Heuristic decomposition and LP-based scheduling in make-and-pack production

In this paper, we are concerned about the short-term scheduling of industrial make-and-pack production processes. The planning problem consists in minimizing the production makespan while meeting given end-product demands. Sequence-dependent changeover times, multi-purpose storage units with finite capacities, quarantine times, batch splitting, partial equipment connectivity, material transfer times, and a large number of operations contribute to the complexity of the problem. Known MILP formulations cover all technological constraints of such production processes, but only small problem instances can be solved in reasonable CPU times. In this paper, we develop a heuristic in order to tackle large instances. Under this heuristic, groups of batches are scheduled iteratively using a novel MILP formulation; the assignment of the batches to the groups and the scheduling sequence of the groups are determined using a priority rule. We demonstrate the applicability by means of a real-world production process.