Total Compression Cost Research Articles

제어가능한 공정시간과 납기 지연 조건을 고려한 선점적 단일 머신 일정계획 문제

In classical scheduling problems, jobs are usually assumed to be non-preemptive with constant processing times. In many practical cases, however, restrictions on preemption can be released by outsourcing and the job processing times are controllable by allocating additional resources to the job operations. In this paper, we consider a single- machine scheduling problem with preemption such that each job processing time can be reduced linearly by using additional resource. The objective is to minimize the sum of total late work and total compression cost. We show that the problem can be solved in polynomial time.

Preemptive scheduling of parallel jobs of two sizes with controllable processing times

AbstractIn parallel machine scheduling, a size of a job is defined as the number of machines that are simultaneously required for its processing. This paper considers a scheduling problem in which the set of jobs consists of jobs of two sizes: the conventional jobs (each job requires a single machine for its processing) and parallel jobs (each job to be simultaneously processed on more than one machine). The processing times are controllable, and they have to be chosen from given intervals in order to guarantee the existence of a preemptive schedule in which all jobs are completed by a common deadline. The objective is to minimize the total compression cost which reflects possible reductions in processing times. Unlike problems of classical scheduling with conventional jobs, the model under consideration cannot be directly handled by submodular optimization methods. We reduce the problem to maximizing the total weighted work of all jobs parametrized with respect to total work of the parallel jobs. The solution is delivered by separately finding the breakpoints for the maximum total weighted work of the parallel jobs and for the maximum total weighted work of the conventional jobs. This results in a polynomial-time algorithm that is no slower than needed to perform sorting of jobs’ parameters.

Single-machine scheduling of multiple projects with controllable processing times

This paper studies the single-machine multiple-project scheduling problem with controllable processing times, in which the cost of a project refers to the total compression cost of its jobs plus the weighted number of tardy jobs in a schedule satisfying some given precedence constraints. It involves four specific problems: (i) minimizing the total cost of an arbitrary number of projects, (ii) being the same as (i) except the jobs from the same project having a common due date, (iii) having a fixed number of projects and minimizing the cost of one project subject to the cost of each of other projects not exceeding a given threshold, and (iv) being the same as (iii) except all jobs having identical weights. We show that a special version of (i) in which each project has only two jobs and all jobs have unit weights and cannot be compressed is strongly NP-hard (it implies the strong NP-hardness of (i)), (ii) is weakly NP-hard and admits a pseudo-polynomial algorithm and a fully polynomial time approximation scheme, (iii) is pseudo-polynomially solvable by a two-phase transformation, and (iv) is weakly NP-hard even if there are only two projects and all jobs have identical maximum compression amounts and identical processing times.

A Time–Cost Tradeoff Problem with Multiple Assessments and Release Times on a Chain Precedence Graph

We consider two variants of a time–cost tradeoff problem with multiple assessments on a chain precedence graph. Furthermore, each job can only be started after a release time, and a penalty cost is incurred when a job is not finished before its due date. The motivation is from the project such that a project owner can control the duration of each job and the support level of each project partner to avoid the penalty cost from the tardy jobs. We describe the penalty costs of the first and the second variants as the total weighted number of tardy jobs and the total weighted tardiness, respectively. These can be avoided by compressing the processing times or advancing the release times, which incurs a compression cost or release cost according to the linear and the piecewise constant functions, respectively. The objective is to minimize the total penalty, compression cost and release cost. In this paper, we propose the procedure based on the reduction to a shortest path problem, and show that the procedure can solve two variants in strongly polynomial time.

A note on parallel-machine scheduling with controllable processing times and job-dependent learning effects

This note studies a unrelated parallel-machine scheduling problem with controllable processing times and job-dependent learning effects, where the objective function is to minimize the weighted sum of total completion time, total load, and total compression cost. We show that the problem can be solved in O(nm+2) time, where m and n are the numbers of machines and jobs. We also show how to apply the technique to several single-machine scheduling problems with total criteria.

The cold high-pressure approach to hydrogen delivery

In view of the very expensive and wasteful nature of today's approaches to H2 delivery, we explore the possibility of transporting cold (200 K) high pressure (875 bar) H2 in thermally insulated trailers and dispensing H2 directly from the trailer, with the potential to eliminate station compressor, cascade, and refrigerator, leading to major reductions in station complexity, maintenance, electricity consumption, and cost, while improving functionality by enabling essentially unlimited back to back refuels, and improving safety due to reduced H2 expansion energy at low temperature.Detailed techno-economic analysis shows promise for substantial delivery cost reductions through cold high pressure H2 dispensed directly from the trailer. Results indicate that: (1) Terminal operations for cold high pressure H2 delivery are $0.32/kg H2 more expensive than for 350 bar compressed gas delivery (today's lowest cost H2 delivery technology) due to higher level of pressurization (to 1000 bar) and chilling needs (to 165 K). (2) Trailer cost drops slightly ($0.73 vs. $0.81/kg H2 for a 350 bar trailer) due to increased capacity (1035 kg H2 delivered vs. 700 kg) compensating for increased capital cost ($906,900 for cold high pressure H2 vs. $634,000 for 350 bar trailer). (3) Cold hydrogen delivery presents major advantages in fueling station cost, reduced from $1.27 to $0.46/kg H2 due to elimination of major system components: compressor, cascade, and chiller. (4) Total compression cost (terminal + station) drops from $0.92/kg H2 ($0.32 terminal and $0.60 station) for 350 bar trailers to $0.55/kg H2 (all at the terminal) for cold high pressure H2. (5) Elimination of small-scale station compressors is the main contributor to reduced delivery cost due to their inefficiency, capital expense, and maintenance needs. In summary, total delivery cost reduction vs. 350 bar trailer equals $0.58/kg H2 (from $2.96 to 2.38/kg H2), equivalent to 24% of the total delivery cost. This large cost advantage will improve the economics of H2 vehicles facilitating the transition to a future of zero emission transportation.

Scheduling two projects with controllable processing times in a single-machine environment

We consider two single-machine scheduling problems in which two competing projects share one common resource. Each project has multiple interim assessments, and its own jobs are ordered completely. A tardy job incurs a tardiness penalty cost which can be avoided by compressing some jobs, which requires an additional cost. The performance measure of each project is the total tardiness penalty cost plus the total compression cost. The first problem minimizes the weighted sum of the performance measures of two projects, and the second problem minimizes the performance measure of one project with a constraint on that of the other. We show that the first problem is solvable in strongly polynomial time and the second is weakly NP-hard. Furthermore, we analyze how the computational complexity of each problem changes if the number of projects is more than two.

A linear time–cost tradeoff problem with multiple milestones under a comb graph

We consider a linear time–cost tradeoff problem (LTCTP) with multiple milestones under a comb graph. A time–cost tradeoff problem decides whether and how much to spend a cost to compress processing time of a job in order to meet promised due dates. This is common in managing a project because additional labors or resources are expensive. It is called linear where the compression cost linearly increases with reduced time. An objective of the LTCTP that this study addresses is to minimize the weighted number of tardy milestones plus the total compression cost. This study considers a special precedence structure, which is called a comb graph. A chain of jobs that sequentially precede each other forms a main process of a project, and other chains of jobs, corresponding to sub processes, precede each job in the main process. For this structure, we developed a strongly-polynomial-time algorithm. This is the first result of unveiling complexity of the multi-milestone LTCTP under a non-chain structure.

Communication scheduling in data gathering networks of heterogeneous sensors with data compression: Algorithms and empirical experiments

We consider a communication scheduling problem to address data compression and data communication together, arising from the data gathering wireless sensor networks with data compression. In the problem, the deployed sensors are heterogeneous, in that the data compression ratios, in terms of size reduction, the compression time, and the compression costs, in terms of energy consumption, on different sensors are different. The bi-objective is to minimize the total compression cost and to minimize the total time to transfer all the data to the base station. The problem reduces to two mono-objective optimization problems in two separate ways: in the original problem a time bound is given and the mono-objective is to minimize the total compression cost, and in the complementary problem a global compression budget is given and the mono-objective is to minimize the makespan. We present a unified exact algorithm for both of them based on dynamic programming; this exact algorithm is then developed into a fully polynomial time approximation scheme for the complementary problem, and a dual fully polynomial time approximation scheme for the original problem. All these approximation algorithms have been implemented and extensive computational experiments show that they run fast and return the optimal solutions almost all the time.

Algorithms for Communication Scheduling in Data Gathering Network with Data Compression

We consider a communication scheduling problem that arises within wireless sensor networks, where data is accumulated by the sensors and transferred directly to a central base station. One may choose to compress the data collected by a sensor, to decrease the data size for transmission, but the cost of compression must be considered. The goal is to designate a subset of sensors to compress their collected data, and then to determine a data transmission order for all the sensors, such that the total compression cost is minimized subject to a bounded data transmission completion time (a.k.a. makespan). A recent result confirms the NP-hardness for this problem, even in the special case where data compression is free. Here we first design a pseudo-polynomial time exact algorithm, articulated within a dynamic programming scheme. This algorithm also solves a variant with the complementary optimization goal—to minimize the makespan while constraining the total compression cost within a given budget. Our second result consists of a bi-factor $$(1 + \epsilon , 2)$$ -approximation for the problem, where $$(1 + \epsilon )$$ refers to the compression cost and 2 refers to the makespan, and a 2-approximation for the variant. Lastly, we apply a sparsing technique to the dynamic programming exact algorithm, to achieve a dual fully polynomial time approximation scheme for the problem and a usual fully polynomial time approximation scheme for the variant.

An Efficient Multiobjective Backtracking Search Algorithm for Single Machine Scheduling with Controllable Processing Times

The scheduling problem with controllable processing times (CPT) is one of the most important research topics in the scheduling field due to its widespread application. Because of the complexity of this problem, a majority of research mainly addressed single-objective small scale problems. However, most practical problems are multiobjective and large scale issues. Multiobjective metaheuristics are very efficient in solving such problems. This paper studies a single machine scheduling problem with CPT for minimizing total tardiness and compression cost simultaneously. We aim to develop a new multiobjective discrete backtracking search algorithm (MODBSA) to solve this problem. To accommodate the characteristic of the problem, a solution representation is constructed by a permutation vector and an amount vector of compression processing times. Furthermore, two major improvement strategies named adaptive selection scheme and total cost reduction strategy are developed. The adaptive selection scheme is used to select a suitable population to enhance the search efficiency of MODBSA, and the total cost reduction strategy is developed to further improve the quality of solutions. For the assessment of MODBSA, MODBSA is compared with other algorithms including NSGA-II, SPEA2, and PAES. Experimental results demonstrate that the proposed MODBSA is a promising algorithm for such scheduling problem.

Some Special Cases of a Continuous Time-Cost Tradeoff Problem with Multiple Milestones under a Chain Precedence Graph

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

Integrated rescheduling and preventive maintenance for arrival of new jobs through evolutionary multi-objective optimization

In this paper, we study a rescheduling problem in response to arrival of new jobs in single machine layout, where preventive maintenance should be determined. Preventive maintenance together with controllable processing time could alleviate the inherent deteriorating effect in manufacturing system. Processing sequence of original and new jobs, compression of each job, and position of maintenance should be optimized simultaneously with regards to total operational cost (job's total completion times, maintenance cost and compression cost) and total completion time deviation. An improved elitist non-dominated sorting genetic algorithm (NSGA-II) has been proposed to solve the rescheduling problem. To address the key problem of balancing between exploration and exploitation, we hybridize differential evolution mutation operation with NSGA-II to enhance diversity, constitute high-quality initial solution based on assignment model for exploitation, and incorporate analytic property of non-dominated solutions for exploration. Finally computational study is designed by randomly generating various instances with regards to the problem size from given distributions. By use of existing performance indicators for convergence and diversity of Pareto fronts, we illustrate the effectiveness of the hybrid algorithm and the incorporation of domain knowledge into evolutionary optimization in rescheduling.

A continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs

We consider a continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs. If a milestone is tardy, a penalty cost may be imposed. The processing times of jobs can be compressed by additional resources or activities that incur compression costs. The objective is to minimize the total penalty cost plus the total compression cost. We show that the problem is NP-hard, even if the compression cost is described as a concave function, and we present a pseudo-polynomial time algorithm for that case. Furthermore, we show that the problem is polynomially solvable if the compression cost function is convex.

Research on scheduling with job-dependent learning effect and convex resource-dependent processing times

We study resource allocation scheduling with job-dependent learning effect on a single machine with or without due date assignment considerations. For a convex resource processing time function, we provide a polynomial time algorithm to find the optimal job sequence, and resource allocations that minimise the schedule criterion (the total compression cost) subject to the constraint that the total compression cost (the schedule criterion) is less than or equal to a fixed amount.

Decomposition algorithms for submodular optimization with applications to parallel machine scheduling with controllable processing times

In this paper we present a decomposition algorithm for maximizing a linear function over a submodular polyhedron intersected with a box. Apart from this contribution to submodular optimization, our results extend the toolkit available in deterministic machine scheduling with controllable processing times. We demonstrate how this method can be applied to developing fast algorithms for minimizing total compression cost for preemptive schedules on parallel machines with respect to given release dates and a common deadline. Obtained scheduling algorithms are faster and easier to justify than those previously known in the scheduling literature.

Scheduling with Discretely Compressible Processing Times to Minimize Makespan

In this paper, we address the scheduling model with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost on identical parallel machines. Jobs may have simultaneous release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

Single Machine Scheduling with Discretely Compressible Processing Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

Unrelated Parallel-Machine Scheduling with Controllable Processing Time

This paper explores an unrelated parallel-machine resource allocation scheduling problem with controllable processing time. The objective is to minimize the cost function containing the weighted of total load, total completion time, total absolute deviation of completion time, and total compression cost. We show that the proposed problem is polynomial time solvable. We also discuss a special case of the problem and show that it can be optimally solved by lower order algorithm.

CO2 purification. Part II: Techno-economic evaluation of oxygen and water deep removal processes

According to the findings of the first part of this work, the two impurities in the CO2 stream, from post-combustion capture, which require deep removal, are oxygen and water, down to 10 and 50ppmv, respectively. In addition, a review and preliminary evaluation of the possible technologies which can be used for oxygen and water deep removal were conducted. The results showed that the promising technologies are: catalytic oxidation of hydrogen for oxygen removal and refrigeration and condensation for water removal.In this paper, detailed process modeling, design and a techno-economic evaluation are performed on these two technologies. Both selected technologies were designed and proved their potential by reducing the impurities to the required levels with a total cost of treating and compressing one ton of CO2 of $13.09 for the coal-fired power plant full purification case and $17.23 for the NGCC full purification process. The cost of CO2 compression without the purification step was found to be approximately $10.12/ton of CO2 for the coal-fired case and $11.98/ton CO2 for the NGCC case. This means that adding the purification technologies will increase the cost of CO2 compression by around 29.3% for the coal-fired case and 43.8% for the NGCC case. Assuming a total CO2 capture and compression cost of $73–94/ton of CO2 shows that the total CO2 purification cost is roughly 3–4% of the overall capture cost for the coal-fired case and 5.5–7% for the NGCC case.