High-quality Solutions In Reasonable Time Research Articles

Scheduling shuttles in deep-lane shuttle-based storage systems

Deep-lane shuttle-based storage systems with forklifts are widely used in bulk storage and finished-goods warehouses that require dense storage paired with high operational efficiency. In such a system, automated shuttles take care of the movements of loads within the storage lanes, and forklifts take care of the horizontal and vertical movements of loads. Since shuttles are expensive, the number of shuttles in the system is typically smaller than the number of storage lanes, so shuttle transfers are required with the help of the forklift. This paper focuses on optimizing the schedule: Given a set of retrieval requests and shuttles, how can the shuttle transfer sequence and the retrieval request sequence be arranged to minimize the makespan? A mathematical model is formulated. Since the problem is NP-hard, an efficient two-stage heuristic is proposed to compute near-optimal solutions. This study’s numerical results show that the two-stage heuristic can provide high-quality solutions in reasonable time. Compared to straightforward heuristics used in practice and in the literature, the makespan can be reduced considerably. The proposed two-stage heuristic can also be used to decide the optimal shuttle fleet size.

A mixed integer formulation and an efficient metaheuristic for the unrelated parallel machine scheduling problem: Total tardiness minimization

In this paper, the unrelated parallel machine scheduling problem with the objective of minimizing the total tardiness is addressed. For such a problem, a mixed-integer linear programming (MILP) formulation, that considers assignment and positional variables, is presented. In addition, an iterated local search (ILS) algorithm that produces high-quality solutions in reasonable times is proposed for higher size instances. The ILS robustness was determined by comparing its performance with the results provided by the MILP. The instances used in this paper were constructed under a new approach which results in tighter due dates than the previous generation method for this problem. The proposed MILP formulation was able to solve instances of up to 150 jobs and 20 machines. Regarding the ILS, it yielded high-quality solutions in a reasonable time, solving instances of a size up to 400 jobs and 20 machines. Experimental results confirm that both approaches are efficient and promising. • A new mixed integer programming formulation for the Unrelated Parallel Machine Scheduling Problem. • The formulation uses positional variables, is linear and does not use the Big-M technique. • The formulation solves instances up to 150 jobs and 20 machines to optimality. • An efficient iterated local search metaheuristic is presented. • A potential issue in the commonly used instance-generation procedure is discussed and a new set of instances is proposed.

Stochastic forestry harvest planning under soil compaction conditions

We present a study of annual forestry harvesting planning considering the risk of compaction generated by the transit of heavy forestry machinery. Soil compaction is a problem that occurs when the soil loses its natural resistance to resist the movement of machinery, causing the soil to be compacted in excess. This compaction generates unwanted effects on both the ecosystem and its economic sustainability. Therefore, when the risk of compaction is considerable, harvest operations must be stopped, complicating the annual plan and incurring in excessive costs to alleviate the situation. To incorporate the risk of compaction into the planning process, it is necessary to incorporate the analysis of the soil's hydrological balance, which combines the effect of rainfall and potential evapotranspiration. This requires analyzing the uncertainty of rainfall regimes, for which we propose a stochastic model under different scenarios. This stochastic model yields better results than the current deterministic methods used by lumber companies. Initially, the model is solved analyzing monthly scenarios. Then, we change to a biweekly model that provides a better representation of the dynamics of the system. While this improves the performance of the model, this new formulation increases the number of scenarios of the stochastic model. To address this complexity, we apply the Progressive Hedging method, which decomposes the problem in scenarios, yielding high-quality solutions in reasonable time.

Constraint programming models for integrated container terminal operations

Although operations in container terminals are highly interdependent, they are traditionally optimized by decomposing the overall problem into a sequence of smaller sub-problems, each focusing on a single operation. Recent studies, however, have demonstrated the need and potential of optimizing these interdependent operations jointly. This paper proposes the Integrated Port Container Terminal Problem (IPCTP) that considers the joint optimization of quay crane assignment and scheduling, yard crane assignment and scheduling, yard location assignments, and yard truck assignment and scheduling. The IPCTP aims at minimizing the turnover times of the vessels and maximize terminal throughput. It also considers inbound and outbound containers simultaneously and models the safety distance and the interference constraints for the quay cranes. To solve the IPCTP, the paper proposes several constraint programming (CP) models. Computational results show that CP provides exact solutions in acceptable time to IPCTP instances derived from an actual (small) container terminal in Turkey. For hard IPCTP instances, the CP model can be generalized in a two-stage optimization approach to produce high-quality solutions in reasonable times.

Two-stage fully distributed approach for unit commitment with consensus ADMM

This paper discusses a two-stage fully distributed approach for the unit commitment (UC) problem, which solves the UC of each individual unit. This approach, based on the augmented Lagrangian relaxation method (ALR) and alternating direction method of multipliers (ADMM), consists of two stages: the solution of the single-unit optimization problem and the distributed update of the multiplier. In the first stage, using the proximal term to effectively improve the oscillation phenomenon and the convergence speed of the improved distributed augmented Lagrangian relaxation method (ID-ALR). In the second stage of multiplier updating, using ADMM to solve dual subgradient problem in fully distributed way for obtaining subgradients. In addition, the multiplier is updated with the improved multiplier update strategy. Finally, the subgradients are also used to reduce the constraint violation degree of the UC and enhance the soft constraint ability of the ID-ALR. The simulation results show that the ID-ALR can not only obtain high-quality solutions in reasonable times but also obtain good speedup in a parallel environment. The proposed ID-ALR enables each unit to keep its information secret and achieves a fully distributed solution for UC.

Benders decomposition for the inventory vehicle routing problem with perishable products and environmental costs

We consider the problem of inventory routing in the context of perishable products and find near-optimal replenishment scheduling and vehicle routes when the objective is to maximize the supplier’s profit and minimize the costs due to fuel consumption, inventory holding, and greenhouse gas emissions. Greenhouse gas emissions are calculated as a function of fuel consumed, and fuel consumption levels are accurately calculated as a function of vehicle speed, load and traveled distance. To solve the problem efficiently, we develop an exact method based on Benders decomposition to find high-quality solutions in reasonable time. To enhance the convergence rate of the Benders decomposition algorithm, we present several acceleration strategies, such as addition of valid inequalities to the master problem and warm-up start. The warm-up start acceleration strategy itself is a meta-heuristic based on the greedy random adaptive search procedure (GRASP) and mathematical programming formulations. We present computational results which illustrate the superior performance of the proposed solution methodology in solving large-scale instances with 60 customers and 6 planning periods with 4 vehicles using Benders decomposition. Additionally, we show that utilizing a more comprehensive model to calculate the fuel cost results in fuel savings of 2 to 11% on the tested instances compared to traditional models that assume that the fuel cost is solely a function of the distance traveled during delivery.

Bi-objective offshore supply vessel planning with costs and persistence objectives

This paper introduces a bi-objective model for the offshore supply vessel planning problem (SVPP) in the oil & gas industry. The SVPP consists of determining a new weekly plan for sailing the platform supply vessels whenever the sailing plan needs revising due to some major events, such as the arrival or removal of drilling rigs, and demand increase or reduction in the current platforms. Apart from remaining cost-efficient, the new weekly plan is required to be persistent, i.e., exhibiting few changes from the previous plan. To achieve this, we propose a bi-objective optimization framework that enables the planners to simultaneously take into account both costs and persistence-related objectives. The framework encompasses a bi-objective SVPP model and a genetic search algorithm adapted from Borthen et al. (2018). We show that the proposed algorithm is able to provide high-quality solutions in reasonable time and has the decision support capability in real offshore operation planning.

A hierarchical alternating direction method of multipliers for fully distributed unit commitment

The mechanism of energy supply has been greatly changed due to the liberalization of electricity, which creates major challenges in power system operations. As such, in this paper, a hierarchical alternating direction method of multipliers (ADMM) approach for the unit commitment (UC) problem is presented, which is proposed to solve the UC problem of each individual unit in parallel. This approach consists of two-layers ADMM. In outer layer, the x-update and v-update steps can be decoupled for each unit and executed in parallel after rearranging and grouping the variables and constraints of the UC mixed integer quadratic programming (MIQP) model according to each unit. The difficulty in this approach is the z-update steps, which couple all units because of system constraints. We used an inner consensus ADMM to solve their Lagrangian dual problems, which are decoupled for each individual unit. Then, the UC problem with a different number of units without transmission constraints is used to test the effectiveness of the algorithm. The simulation results show that the proposed hierarchical ADMM can obtain high-quality solutions in reasonable times and keep the units’ information secret. It can also help to obtain a good speedup and is suitable for solving large-scale distributed unit commitment (D-UC) problems.

Energy-Efficient Scheduling of Periodic Applications on Safety-Critical Time-Triggered Multiprocessor Systems

Energy optimization for periodic applications running on safety/time-critical time-triggered multiprocessor systems has been studied recently. An interesting feature of the applications on the systems is that some tasks are strictly periodic while others are non-strictly periodic, i.e., the start time interval between any two successive instances of the same task is not fixed as long as task deadlines can be met. Energy-efficient scheduling of such applications on the systems has, however, been rarely investigated. In this paper, we focus on the problem of static scheduling multiple periodic applications consisting of both strictly and non-strictly periodic tasks on safety/time-critical time-triggered multiprocessor systems for energy minimization. The challenge of the problem is that both strictly and non-strictly periodic tasks must be intelligently addressed in scheduling to optimize energy consumption. We introduce a new practical task model to characterize the unique feature of specific tasks, and formulate the energy-efficient scheduling problem based on the model. Then, an improved Mixed Integer Linear Programming (MILP) method is proposed to obtain the optimal scheduling solution by considering strict and non-strict periodicity of the specific tasks. To decrease the high complexity of MILP, we also develop a heuristic algorithm to efficiently find a high-quality solution in reasonable time. Extensive evaluation results demonstrate the proposed MILP and heuristic methods can on average achieve about 14.21% and 13.76% energy-savings respectively compared with existing work.

Green transportation scheduling with speed control: trade-off between total transportation cost and carbon emission

Abstract Transportation has a significant portion in greenhouse gas emission. Efficient transportation scheduling can decrease transportation costs and environmental damages by reducing fuel consumption and greenhouse gas emission. These advantages have made green transportation scheduling more attractive. This paper addresses the problem of integrated green truck transportation scheduling and driver assignment. We propose a bi-objective mixed integer nonlinear programming (MINLP) model to minimize total transportation-related costs (TTC) and total carbon emission (TCE). We consider TTC and TCE as manufacturer measure and environmental sustainability measure respectively. There is a contradiction between two objectives. We consider the ability of speed control for trucks to create the trade-off between TTC and TCE. A linearization technique is utilized to reduce the complexity of the proposed model. The Augmented e-constraint method is used to solve the model. Also, we develop a constructive heuristic (CH) approach to get high-quality solutions in an efficient CPU time. Some scenarios are applied to evaluate the model and heuristic approach. The results show the model achieves high-quality solutions in reasonable time. Also, the model and heuristic have a better performance compared to scenarios. Statistical tests are done to approve the comparisons.

Integrated production and delivery with single machine and multiple vehicles

This paper considers a class of multi-objective production–distribution scheduling problem with a single machine and multiple vehicles. The objective is to minimize the vehicle delivery cost and the total customer waiting time. It is assumed that the manufacturer’s production department has a single machine to process orders. The distribution department has multiple vehicles to deliver multiple orders to multiple customers after the orders have been processed. Since each delivery involves multiple customers, it involves a vehicle routing problem. Most previous research work attempts at tackling this problem focus on single-objective optimization system. This paper builds a multi-objective mathematical model for the problem. Through deep analysis, this paper proposes that for each non-dominated solution in the Pareto solution set, the orders in the same delivery batch are processed contiguously and their processing order is immaterial. Thus we can view the orders in the same delivery batch as a block. The blocks should be processed in ascending order of the values of their average workload. All the analysis results are embedded into a non-dominated genetic algorithm with the elite strategy (PD-NSGA-II). The performance of the algorithm is tested through random data. It is shown that the proposed algorithm can offer high-quality solutions in reasonable time.

Multi-Cuts Outer Approximation Method for Unit Commitment

This letter introduces a deterministic global optimization methods for unit commitment (UC) problem based on outer approximation method (OAM). The proposed Multi-cuts OAM (MCs-OAM) decomposes the UC problem into a mixed integer linear programming (MILP) master problem and several nonlinear programming (NLP) subproblems, whereas only one NLP in classic OAM. After elaborately designing the terminating criterion for solving the bigger but tighter MILP master problems, MCs-OAM can obtained higher quality solutions with fewer main iterations and less total CPU times, although solving more NLPs consumes more CPU times than OAM. The numerical results on 42 test systems of up to 200 units show that the MCs-OAM is very promising for large scale UC problems because that it can obtain high-quality solutions in reasonable time.

Buffer dimensioning and control stations positioning with a space partitioning-tabu search approach

We propose an efficient heuristic method based on Space Partitioning (SP) and Tabu Search (TS) to solve the buffer sizing problem in unreliable production lines with several inspection stations. In such problem, we have an unreliable production line consisting of a certain number of machines and fixed-size buffers. These machines produce a single part with two different quality levels: conforming and non-conforming parts. The production line may contain inspection stations whose job is to reject the non-conforming parts from the line. The production line must meet a constant rate of demand for the conforming finished parts. The objective is to minimize the average long term combined storage and shortage costs, while also specifying the optimal location of inspection stations. This design problem is a difficult mixed integer nonlinear program. Solving even a small instance of 10 machines and one inspection station using a direct dynamic programming method takes hours. If we especially increase the number of machines or the inspection stations, the dynamic programming approach becomes drastically inefficient. The method we propose divides the search space into a set of disjoint subspaces using a space partitioning technique. Tabu search is used to intensify the search in the selected subspaces. This combined method finds optimal solutions for small instances in a fraction of dynamic programming time. For the largest instances (up to 20 machines) the dynamic programming approach was unable to solve, our method finds high-quality solutions in reasonable times.

Hybridization of harmony search with variable neighborhood search for restrictive single-machine earliness/tardiness problem

Earliness/tardiness scheduling, in connection with Just-In-Time manufacturing philosophy, is crucial in reducing the production cost while maintaining a high service level. In this article, the well-known restrictive single-machine earliness/tardiness scheduling problem (RSMETP) is addressed. A novel hybrid metaheuristic, named as PHVNS, is developed for this NP-hard problem. There are three main innovative aspects in the proposed PHVNS. First, a permutation-based harmony search (PHS) is developed in compliance with the RSMETP features and optimality properties. Secondly, in order to provide an effective balance between the global diversification and local intensification, an enhanced basic variable neighborhood search (EBVNS) is incorporated into the iterative PHS. Thirdly, several problem-dependent mechanisms are introduced to facilitate the search process of PHVNS, such as the distinctive schedule representation, specific tweaks and speed-ups to the new harmony vector, and local search strategies within a neighborhood. An extensive calibration for the main parameters in PHVNS is carried out with the aid of a carefully designed set of experiments. To evaluate and validate the fine-tuned PHVNS, computational experiments are conducted upon the test suite of 280 benchmark instances. As demonstrated in the results, the tuned PHVNS is capable of reaching the high-quality solutions in reasonable time for most of the instances. Compared with some state-of-the-art metaheuristics for RSMETP, PHVNS shows high competitiveness.

An effective hybrid simulated annealing and two mixed integer linear formulations for just-in-time open shop scheduling problem

This paper addresses open shop scheduling problem from the viewpoint of just-in-time management in which the objective function is to minimize the sum of weighted earliness/tardiness penalties. The problem is formulated as two different mixed integer linear programming models. To solve the problem, a novel hybrid two-phase algorithm is presented. In the first phase, a simulated annealing is applied to search the appropriate sequences of jobs on machines. Based on the job sequences obtained in the first phase, one of the proposed mathematical formulations can be reduced to a linear programming model and in the second phase by solving the linear programming model, the start time of jobs on machines can be determined. In order to evaluate the quality of solutions, a specific branching strategy is applied in solving the other mathematical model to obtain a lower bound. Computational results show that the algorithm obtains high-quality solutions in reasonable time.