scholarly journals Order Acceptance and Scheduling Problem with Carbon Emission Reduction and Electricity Tariffs on a Single Machine

2019 ◽  
Vol 11 (19) ◽  
pp. 5432 ◽  
Author(s):  
Shih-Hsin Chen ◽  
Yeong-Cheng Liou ◽  
Yi-Hui Chen ◽  
Kun-Ching Wang
Keyword(s):  
Single Machine ◽  
Carbon Emission ◽  
Carbon Dioxide Emission ◽  
Mixed Integer ◽  
Order Acceptance ◽  
Due Dates ◽  
Electricity Cost ◽  
Order Acceptance And Scheduling ◽  
The One ◽  
Dependent Setup Times

Order acceptance and scheduling (OAS) problems are realistic for enterprises. They have to select the appropriate orders according to their capacity limitations and profit consideration, and then complete these orders by their due dates or no later than their deadlines. OAS problems have attracted significant attention in supply chain management. However, there is an issue that has not been studied well. To our best knowledge, no prior research examines the carbon emission cost and the time-of-use electricity cost in the OAS problems. The carbon emission during the on-peak hours is lower than the one in mid-peak and off-peak hours. However, the electricity cost during the on-peak hours is higher than the one during mid-peak and off-peak hours when time-of-use electricity (TOU) tariff is used. There is a trade-off between sustainable scheduling and the electricity cost. To calculate the objective value, a carbon tax and carbon dioxide emission factor are included when we evaluate the carbon emission cost. The objective function is to maximize the total revenue of the accepted orders and then subtract the carbon emission cost and the electricity cost under different time intervals on a single machine with sequence-dependent setup times and release date. This research proposes a mixed-integer linear programming model (MILP) and a relaxation method of MILP model to solve this problem. It is of importance because the OAS problems are practical in industry. This paper could attract the attention of academic researchers as well as the practitioners.

scholarly journals Hybrid Differential Evolution Optimisation for Earth Observation Satellite Scheduling with Time-Dependent Earliness-Tardiness Penalties

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Guoliang Li ◽  
Cheng Chen ◽  
Feng Yao ◽  
Renjie He ◽  
Yingwu Chen
Keyword(s):  
Differential Evolution ◽  
Programming Model ◽  
Earth Observation ◽  
Time Dependent ◽  
Mixed Integer ◽  
Order Acceptance ◽  
Due Dates ◽  
Earth Observation Satellite ◽  
Satellite Scheduling ◽  
Dependent Setup Times

We study the order acceptance and scheduling (OAS) problem with time-dependent earliness-tardiness penalties in a single agile earth observation satellite environment where orders are defined by their release dates, available processing time windows ranging from earliest start date to deadline, processing times, due dates, sequence-dependent setup times, and revenues. The objective is to maximise total revenue, where the revenue from an order is a piecewise linear function of its earliness and tardiness with reference to its due date. We formulate this problem as a mixed integer linear programming model and develop a novel hybrid differential evolution (DE) algorithm under self-adaptation framework to solve this problem. Compared with classical DE, hybrid DE employs two mutation operations, scaling factor adaptation and crossover probability adaptation. Computational tests indicate that the proposed algorithm outperforms classical DE in addition to two other variants of DE.

scholarly journals A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Yujian Song ◽  
Ming Xue ◽  
Changhua Hua ◽  
Wanli Wang
Keyword(s):  
Column Generation ◽  
Mixed Integer Linear Programming ◽  
Parallel Machines ◽  
Set Partitioning ◽  
Mixed Integer ◽  
Order Acceptance ◽  
Generation Algorithm ◽  
Order Acceptance And Scheduling ◽  
Linear Programming Formulation ◽  
Integer Linear Programming Formulation

In this paper, we investigate the resource-constrained order acceptance and scheduling on unrelated parallel machines that arise in make-to-order systems. The objective of this problem is to simultaneously select a subset of orders to be processed and schedule the accepted orders on unrelated machines in such a way that the resources are not overutilized at any time. We first propose two formulations for the problem: mixed integer linear programming formulation and set partitioning. In view of the complexity of the problem, we then develop a column generation approach based on the set partitioning formulation. In the proposed column generation approach, a differential evolution algorithm is designed to solve subproblems efficiently. Extensive numerical experiments on different-sized instances are conducted, and the results demonstrate that the proposed column generation algorithm reports optimal or near-optimal solutions that are evidently better than the solutions obtained by solving the mixed integer linear programming formulation.

scholarly journals Bi-criteria parallel batch machine scheduling to minimize total weighted tardiness and electricity cost

2020 ◽  
Vol 90 (9) ◽  
pp. 1345-1381
Author(s):  
Jens Rocholl ◽  
Lars Mönch ◽  
John Fowler
Keyword(s):  
Genetic Algorithms ◽  
Pareto Front ◽  
Total Weighted Tardiness ◽  
Mixed Integer ◽  
Due Dates ◽  
Semiconductor Wafer ◽  
Weighted Tardiness ◽  
Electricity Cost ◽  
Problem Instances ◽  
Special Case

Abstract A bi-criteria scheduling problem for parallel identical batch processing machines in semiconductor wafer fabrication facilities is studied. Only jobs belonging to the same family can be batched together. The performance measures are the total weighted tardiness and the electricity cost where a time-of-use (TOU) tariff is assumed. Unequal ready times of the jobs and non-identical job sizes are considered. A mixed integer linear program (MILP) is formulated. We analyze the special case where all jobs have the same size, all due dates are zero, and the jobs are available at time zero. Properties of Pareto-optimal schedules for this special case are stated. They lead to a more tractable MILP. We design three heuristics based on grouping genetic algorithms that are embedded into a non-dominated sorting genetic algorithm II framework. Three solution representations are studied that allow for choosing start times of the batches to take into account the energy consumption. We discuss a heuristic that improves a given near-to-optimal Pareto front. Computational experiments are conducted based on randomly generated problem instances. The $$ \varepsilon $$ ε -constraint method is used for both MILP formulations to determine the true Pareto front. For large-sized problem instances, we apply the genetic algorithms (GAs). Some of the GAs provide high-quality solutions.

scholarly journals Multiobjective Order Acceptance and Scheduling on Unrelated Parallel Machines with Machine Eligibility Constraints

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Bailin Wang ◽  
Haifeng Wang
Keyword(s):  
Parallel Machines ◽  
Mixed Integer ◽  
List Scheduling ◽  
Unrelated Parallel Machines ◽  
Order Acceptance ◽  
Trade Off ◽  
Pareto Ranking ◽  
Machine Eligibility ◽  
Net Profit ◽  
Order Acceptance And Scheduling

This paper studies the order acceptance and scheduling problem on unrelated parallel machines with machine eligibility constraints. Two objectives are considered to maximize total net profit and minimize the makespan, and the mathematical model of this problem is formulated as multiobjective mixed integer linear programming. Some properties with respect to the objectives are analysed, and then a classic list scheduling (LS) rule named the first available machine rule is extended, and three new LS rules are presented, which focus on the maximization of the net profit, the minimization of the makespan, and the trade-off between the two objectives, respectively. Furthermore, a list-scheduling-based multiobjective parthenogenetic algorithm (LS-MPGA) is presented with parthenogenetic operators and Pareto-ranking and selection method. Computational experiments on randomly generated instances are carried out to assess the effectiveness and efficiency of the four LS rules under the framework of LS-MPGA and discuss their application environments. Results demonstrate that the performance of the LS-MPGA developed for trade-off is superior to the other three algorithms.

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