Přemysl Šůcha

Production scheduling with alternative process plans

This paper deals with a scheduling problem with alternative process plans that was motivated by a production of wire harnesses where certain parts can be processed manually or automatically by different types of machines. Only a subset of all the given activities will form the solution, so the decision whether the activity will appear in the final schedule has to be made during the scheduling process. The problem considered is an extension of the resource constrained project scheduling problem (RCPSP) with unary resources, positive and negative time-lags and sequence dependent setup times. We extend classic RCPSP problem by a definition of alternative branchings, represented by the Petri nets formalism allowing one to define alternatives and parallelism within one data structure. For this representation of the problem, an integer linear programming model is formulated and the reduction of the problem, using time symmetry mapping, is shown. Finally, a heuristic algorithm based on priority schedule construction with an unscheduling step is proposed for the nested version of the problem and it is used to solve the case study of the wire harnesses production.

Nash equilibria for the multi-agent project scheduling problem with controllable processing times

This paper considers a project scheduling environment in which the activities of the project network are partitioned among a set of agents. Activity durations are controllable, i.e., every agent is allowed to shorten the duration of its activities, incurring a crashing cost. If the project makespan is reduced with respect to its normal value, a reward is offered to the agents and each agent receives a given ratio of the total reward. Agents want to maximize their profit. Assuming a complete knowledge of the agents’ parameters and of the activity network, this problem is modeled as a non-cooperative game and Nash equilibria are analyzed. We characterize Nash equilibria in terms of the existence of certain types of cuts on the project network. We show that finding one Nash equilibrium is easy, while finding a Nash strategy that minimizes the project makespan is NP-hard in the strong sense. The particular case where each activity belongs to a different agent is also studied and some polynomial-time algorithms are proposed for this case.

Scalable and efficient configuration of time-division multiplexed resources

Branch-and-price to configure resources shared by Time-Division Multiplexing.Numerous computation time optimizations for branch-and-price are proposed.The proposed approach improves scalability of the existing approaches.The practical relevance is demonstrated by applying it to a case study. Consumer-electronics systems are becoming increasingly complex as the number of integrated applications is growing. Some of these applications have real-time requirements, while other non-real-time applications only require good average performance. For cost-efficient design, contemporary platforms feature an increasing number of cores that share resources, such as memories and interconnects. However, resource sharing causes contention that must be resolved by a resource arbiter, such as Time-Division Multiplexing. A key challenge is to configure this arbiter to satisfy the bandwidth and latency requirements of the real-time applications, while maximizing the slack capacity to improve performance of their non-real-time counterparts. As this configuration problem is NP-hard, a sophisticated automated configuration method is required to avoid negatively impacting design time.The main contributions of this article are: (1) an optimal approach that takes an existing integer linear programming (ILP) model addressing the problem and wraps it in a branch-and-price framework to improve scalability. (2) A faster heuristic algorithm that typically provides near-optimal solutions. (3) An experimental evaluation that quantitatively compares the branch-and-price approach to the previously formulated ILP model and the proposed heuristic. (4) A case study of an HD video and graphics processing system that demonstrates the practical applicability of the approach.

A cyclic scheduling problem with an undetermined number of parallel identical processors

This paper presents two integer linear programming (ILP) models for cyclic scheduling of tasks with unit/general processing time. Our work is motivated by digital signal processing (DSP) applications on FPGAs (Field-Programmable Gate Arrays)—hardware architectures hosting several sets of identical arithmetic units. These hardware units can be formalized as dedicated sets of parallel identical processors. We propose a method to find an optimal periodic schedule of DSP algorithms on such architectures where the number of available arithmetic units must be determined by the scheduling algorithm with respect to the capacity of the FPGA circuit. The emphasis is put on the efficiency of the ILP models. We show the advantages of our models in comparison with common ILP models on benchmarks and randomly generated instances.

Scheduling of Iterative Algorithms with Matrix Operations for Efficient FPGA Design--Implementation of Finite Interval Constant Modulus Algorithm

This paper deals with the optimization of iterative algorithms with matrix operations or nested loops for hardware implementation in Field Programmable Gate Arrays (FPGA), using Integer Linear Programming (ILP). The method is demonstrated on an implementation of the Finite Interval Constant Modulus Algorithm. It is an equalization algorithm, suitable for modern communication systems (4G and behind). For the floating-point calculations required in the algorithm, two arithmetic libraries were used in the FPGA implementation: one based on the logarithmic number system, the other using floating-point number system in the standard IEEE format. Both libraries use pipelined modules. Traditional approaches to the scheduling of nested loops lead to a relatively large code, which is unsuitable for FPGA implementation. This paper presents a new high-level synthesis methodology, which models both, iterative loops and imperfectly nested loops, by means of the system of linear inequalities. Moreover, memory access is considered as an additional resource constraint. Since the solutions of ILP formulated problems are known to be computationally intensive, an important part of the article is devoted to the reduction of the problem size.

Time symmetry of resource constrained project scheduling with general temporal constraints and take-give resources

The paper studies a lacquer production scheduling problem formulated as a resource constrained project scheduling problem with general temporal constraints (i.e., positive and negative time-lags). This real-world scheduling problem requires so-called take-give resources that are needed from the beginning of an activity to the completion of another activity of the production process. Furthermore, we consider sequence dependent changeover times on take-give resources. We formulate this problem by mixed integer linear programming and we suggest a parallel heuristic to solve the problem. This heuristic exploits a time symmetry mapping which allows an easy construction of a schedule in the backward time orientation. In the second part of the paper, it is proven that the time symmetry mapping is bijective and involutive even for the problem with general temporal constraints, changeover times, and take-give resources. The motivation to use this mapping is to improve the performance of the heuristic and to simplify its implementation. Finally, the performance of the heuristic algorithm is evaluated on a set of lacquer production benchmarks requiring take-give resources and on standard benchmarks for the resource constrained project scheduling problem with general temporal constraints where we found new better solutions in 16 and 12 instances out of 90 for UBO500 and UBO1000 respectively.

A multistage approach for an employee timetabling problem with a high diversity of shifts as a solution for a strongly varying workforce demand

Abstract This work deals with the employee rostering problem at the airport. Such problems, related to the time varying demand of the transport services, use many (e.g., about a hundred) diverse shifts to cover the workforce demand during the day. Together with the strict constraints, given by the collective agreement, the problem becomes difficult to solve. Algorithms commonly used for solving the usual employee rostering problems produce poor quality rosters, which are unusable in practice. This paper suggests a three stage approach allowing one to solve the employee rostering problems where a huge set of different shifts is used to satisfy the coverage requirements. The solution is based on the problem transformation to a simpler problem, thereupon, an evolutionary algorithm is used to determine a rough position of the shifts in the roster. Afterwards, the maximal weighted matching in the bipartite graph is applied as the inverse transformation of the problem and the final roster is obtained by the optimization based on a Tabu Search algorithm. This multistage approach is compared to other approaches. Furthermore, an evaluation methodology was proposed in order to make a complex and fair comparison. Its objective is to verify the contribution of the particular stages used in the different approaches applied on the different personnel scheduling problems.

Accelerating the Branch-and-Price Algorithm Using Machine Learning

Abstract This study presents a widely applicable approach to accelerate the computation time of the Branch-and-Price (BaP) algorithm, which is a very powerful exact method used for solving complex combinatorial problems. Existing studies indicate that the most computationally demanding element of the BaP algorithm is the pricing problem. The case-studies presented in this paper show that more than 90% of the total Central Processing Unit (CPU) processing time is consumed by solving the pricing problem. The pricing problem is repetitive in nature and it solves the same problem from scratch differing only in the input dual prices. In this study, we demonstrate how to utilize the knowledge gained from previous executions of the pricing problem to reduce the solution space of pricing problems solved in future iterations. The solution is based on an online machine learning method that is not tailor-made for a specific problem (but needs a proper problem-dependent feature selection) and uses a very fast regression model that generates negligible overhead compared to the total CPU processing time of the BaP algorithm. The method predicts a tight upper bound for the current iteration of the pricing problem while preserving the exactness of the BaP algorithm. The efficiency of the proposed approach is demonstrated by two distinct case-studies: the nurse rostering problem and the scheduling of time-division multiplexing for multi-core platforms. The experiments carried out for both case-studies using benchmark instances from the literature show a 40% and 22% average CPU time reduction for the entire BaP algorithm.

Algorithms for robust production scheduling with energy consumption limits

Abstract In this work, we consider a scheduling problem faced by production companies with large electricity consumption. Due to the contract with the electric utility, the production companies are obligated to comply with the total energy consumption limits in the specified time intervals (usually 15-min long); otherwise, the companies pay substantial penalty fees. Although it is possible to design production schedules that consider these limits as hard constraints, uncertainties occurring during the execution of the schedules are usually not taken into account. This may lead to situations in which the unexpected delays of the operations cause the violations of the energy consumption limits. Our goal is to design robust production schedules pro-actively guaranteeing that the energy consumption limits are not violated for the given set of uncertainty scenarios. We consider scheduling on one machine with release times of the operations and total tardiness as the objective function. To tackle this problem, we first propose a pseudo-polynomial algorithm for finding the optimal robust schedule for the given permutation of the operations. This algorithm is then utilised in three different algorithms for finding the optimal permutation: two exact (Branch-and-Bound and logic-based Benders decomposition) and one heuristic algorithm (tabu search). All the algorithms were experimentally evaluated on random instances with different sizes of the uncertainty scenarios set. Using the tabu search algorithm, we are able to solve large instances within one minute.

Optimizing energy consumption of robotic cells by a Branch & Bound algorithm

Abstract Nowadays, robotic cells are mostly designed with the main goal to meet the desired production rate without any consideration of the energy efficiency, therefore, it is often possible to achieve significant energy savings without downsizing the production. In our previous study, we established the mathematical formulation of the energy optimization problem, proposed a parallel heuristic, and optimized an existing robotic cell in Skoda Auto, the results of which revealed a 20% reduction in the energy consumption of robot drive systems. This study proposes a novel parallel Branch & Bound algorithm to optimize the energy consumption of robotic cells without deterioration in throughput. The energy saving is achieved by changing robot speeds and positions, applying robot power-saving modes (brakes, bus power off), and selecting an order of operations. The core part of the algorithm is our tight lower bound, based on convex envelopes. Besides the bounding, a Deep Jumping approach is introduced to guide the search to the promising parts of the Branch & Bound tree, and the parallelization accelerates the exploration of the tree. The experimental results revealed that the performance of the parallel algorithm scales almost linearly up to 12 processor cores, and the quality of obtained solutions is better or comparable to other existing works.