Energy Cost-Efficient Task Positioning in Manufacturing Systems

Abstract

A problem to determine a production schedule which minimises the cost of energy used for manufacturing is studied. The scenario assumes that each production task has assigned constant power consumption, price of power from conventional electrical grid system is defined by time-of-use tariffs, and a component of free of charge renewable energy is available for the manufacturing system. The objective is to find the most cost-efficient production plan, subject to constraints involving predefined precedence relationships between the tasks and a bounded makespan. Two independent optimisation approaches have been developed, based on significantly different paradigms, namely mixed-integer linear programming and tabu search metaheuristic. Both of them have been verified and compared in extensive computational experiments. The tabu search-based approach has turned out to be generally more efficient in the sense of the obtained objective function values, but advantages of the use of linear programming have also been identified. The results confirm that it is possible to develop efficient computational methods to optimise energy cost under circumstances typical of manufacturing companies. The set of numerous benchmark instances and their solutions have been archived and it can be reused in further research.

Communication Time Optimization of Register-Based Data Transfer

“…We have chosen two mathematical programming techniques, namely MILP and constraint programming, which are widely used for hard optimization problems. We have also implemented the tabu search metaheuristic which can often overperform mathematical programming solvers due to use of problem encoding dedicated directly for a specific case [19,20]. Finally, we have developed deterministic algorithms based on greedy or heuristic rules which are guided by locally defined optima rather than the global objective function; hence, they may be less efficient at objective minimization, but competitive in industrial applications due to simple implementation and low computational complexity.…”

“…, r q } ⊆ R are to be transferred in the k-th consecutive frame. As a consequence, the constraints (23) obtain the form r k ≤ r i and r k ≥ r i for i ∈ I k , which implies that the value r q − r p + 1 will be assigned to ω k , according to (20). There are expressions (20) reserved for the maximum possible number of frames equal to n, but not all of them are needed in a typical solution, and then κ n < n. In such a case, no constraints are activated for r k , r k with k > κ n , according to (23).…”

“…As a consequence, the constraints (23) obtain the form r k ≤ r i and r k ≥ r i for i ∈ I k , which implies that the value r q − r p + 1 will be assigned to ω k , according to (20). There are expressions (20) reserved for the maximum possible number of frames equal to n, but not all of them are needed in a typical solution, and then κ n < n. In such a case, no constraints are activated for r k , r k with k > κ n , according to (23). As a result, the solver can freely choose the r k and r k values giving ω k ≤ 0 in (20), hence ε k = γ k = 0 in (21), and the k-th frame does not contribute to (22).…”

“…There are expressions (20) reserved for the maximum possible number of frames equal to n, but not all of them are needed in a typical solution, and then κ n < n. In such a case, no constraints are activated for r k , r k with k > κ n , according to (23). As a result, the solver can freely choose the r k and r k values giving ω k ≤ 0 in (20), hence ε k = γ k = 0 in (21), and the k-th frame does not contribute to (22). The maximum frame sizes are limited in (24), and these restrictions should be removed if s = ∞.…”

Analysis of Energy Efficient Scheduling of the Manufacturing Line with Finite Buffer Capacity and Machine Setup and Shutdown Times

“…The growing cost of energy is one of the most important factors related to the cost of production, therefore the literature considers various ways to solve this problem, e.g., production of renewable energy [3], prosumer parallel production and consumption of energy [4], local electricity trading [5], flexible distribution of energy in the smart grid [6], modern energy saving technologies [7], and intelligent energy management in the whole supply chain [8][9][10][11].…”