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.

A mixed-integer linear programming approach to the optimization of event-bus schedules: a scheduling application in the tourism sector

This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.

Dynamic Optimization of SLA-Based Services Scaling Rules

Current advanced cloud infrastructure management solutions allow scheduling actions for dynamically changing the number of running virtual machines (VMs). This approach, however, does not guarantee that the scheduled number of VMs will properly handle the actual user generated workload, especially if the user utilization patterns will change. We propose using a dynamically generated scaling model for the VMs containing the services of the distributed applications, which is able to react to the variations in the number of application users. We answer the following question: How to dynamically decide how many services of each type are needed in order to handle a larger workload within the same time constraints? We describe a mechanism for dynamically composing the SLAs for controlling the scaling of distributed services by combining data analysis mechanisms with application benchmarking using multiple VM configurations. Based on processing of multiple application benchmarks generated data sets we discover a set of service monitoring metrics able to predict critical Service Level Agreement (SLA) parameters. By combining this set of predictor metrics with a heuristic for selecting the appropriate scaling-out paths for the services of distributed applications, we show how SLA scaling rules can be inferred and then used for controlling the runtime scale-in and scale-out of distributed services. We validate our architecture and models by performing scaling experiments with a distributed application representative for the enterprise class of information systems. We show how dynamically generated SLAs can be successfully used for controlling the management of distributed services scaling.