A note on a paper by W. Szwarc

In this note the authors call for a change of the optimality criteria given by Theorem 3 in section 5 of the paper of W. Szwarc “On Some Sequencing Problems” in NRLQ Vol. 15, No. 2 [2]. Further, two cases of the three machine problem, namely, (i) ≦ and (ii) ≦ are considered, and procedures for obtaining optimal sequences in these cases are given. In these cases the three-machine problem is solved by solving n (the number of jobs) two-machine problems.     

On equivalence between the proportionate flow shop and single‐machine scheduling problems

We derive sufficient conditions which, when satisfied, guarantee that an optimal solution for a single‐machine scheduling problem is also optimal for the corresponding proportionate flow shop scheduling problem. We then utilize these sufficient conditions to show the solvability in polynomial time of numerous proportionate flow shop scheduling problems with fixed job processing times, position‐dependent job processing times, controllable job processing times, and also problems with job rejection. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 595–603, 2015     

Scheduling for parallel dedicated machines with a single server

This paper examines scheduling problems in which the setup phase of each operation needs to be attended by a single server, common for all jobs and different from the processing machines. The objective in each situation is to minimize the makespan. For the processing system consisting of two parallel dedicated machines we prove that the problem of finding an optimal schedule is N P‐hard in the strong sense even if all setup times are equal or if all processing times are equal. For the case of m parallel dedicated machines, a simple greedy algorithm is shown to create a schedule with the makespan that is at most twice the optimum value. For the two machine case, an improved heuristic guarantees a tight worst‐case ratio of 3/2. We also describe several polynomially solvable cases of the later problem. The two‐machine flow shop and the open shop problems with a single server are also shown to be N P‐hard in the strong sense. However, we reduce the two‐machine flow shop no‐wait problem with a single server to the Gilmore—Gomory traveling salesman problem and solve it in polynomial time. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 304–328, 2000     

双舰编队协同制导防空作战的动态拦截排序问题

针对双舰编队协同制导作战条件下如何对空袭目标进行排序这一问题,依据作战时间给出了排序算法。首先对平台的作战时间进行分析和求解,将射击周期分成了2段,把静态拦截排序问题转化为了2台处理机的同顺序作业排序问题,然后根据输入信息的改变而不断调整空袭目标的顺序以解决动态拦截排序问题,最后在想定条件下仿真计算,结果表明该算法具有较好的适用性。     

Scheduling jobs,with exponentially distributed processing times,on two machines of a flow shop

This paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.     

链约束下加工时间恶化的Flow Shop排序问题

讨论作业具有线性加工时间,作业间具有链约束的两台处理机流水作业排序问题,目标函数为极小化完工时间。在作业加工时间简单线性恶化下,提出作业的非负开始和停止延迟恶化率,构造了满足约束条件的复合作业。在此基础上,给出作业间具有平行链约束的两台处理机流水作业排序问题的最优多项式算法。     

Open shop scheduling to minimize the number of late jobs

We develop polynomial algorithms for several cases of the NP-hard open shop scheduling problem of minimizing the number of late jobs by utilizing some recent results for the open shop makespan problem. For the two machine common due date problem, we assume that either the machines or the jobs are ordered. For the m machine common due date problem, we assume that one machine is maximal and impose a restriction on its load. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 525–532, 1998     

The two-machine permutation flow shop with state-dependent processing times

If the processing time of each job in a flow shop also depends on the time spent prior to processing, then the choice of a sequence influences processing times. This nonstandard scheduling problem is studied here for the minimum makespan schedule in a flow shop with two machines. The problem is NP-hard in the strong sense and already contains the main features of the general case [10]. Restricting to the case of permutation schedules, we first determine the optimal release times of the jobs for a given sequence. Permutation schedules are evaluated for this optimal policy, and the scheduling problem is solved using branch-and-bound techniques. We also show the surprising result that the optimal schedule may not be a permutation schedule. Numerical results on randomly generated data are provided for permutation schedules. Our numerical results confirm our preliminary study [10] that fairly good approximate solutions can efficiently be obtained in the case of limited computing time using the heuristics due to Gilmore and Gomory [7]. © 1993 John Wiley & Sons, Inc.     

Flowshop sequencing problem with ordered processing time matrices: A general case

The ordered matrix flow shop problem with no passing of jobs is considered. In an earlier paper, the authors have considered a special case of the problem and have proposed a simple and efficient algorithm that finds a sequence with minimum makespan for a special problem. This paper considers a more general case. This technique is shown to be considerably more efficient than are existing methods for the conventional flow shop problems.     

Two machine flow shop scheduling problems with sequence dependent setup times: A dynamic programming approach

This paper considers the two different flow shop scheduling problems that arise when, in a two machine problem, one machine is characterized by sequence dependent setup times. The objective is to determine a schedule that minimizes makespan. After establishing the optimally of permutation schedules for both of these problems, an efficient dynamic programming formulation is developed for each of them. Each of these formulations is shown to be comparable, from a computational standpoint, to the corresponding formulation of the traveling salesman problem. Then, the relative merits of the dynamic programming and branch and bound approaches to these two scheduling problems are discussed.     

Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function

We consider open‐shop scheduling problems where operation‐processing times are a convex decreasing function of a common limited nonrenewable resource. The scheduler's objective is to determine the optimal job sequence on each machine and the optimal resource allocation for each operation in order to minimize the makespan. We prove that this problem is NP‐hard, but for the special case of the two‐machine problem we provide an efficient optimization algorithm. We also provide a fully polynomial approximation scheme for solving the preemptive case. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Scheduling and lot streaming in two‐machine open shops with no‐wait in process

We study the problem of minimizing the makespan in no‐wait two‐machine open shops producing multiple products using lot streaming. In no‐wait open shop scheduling, sublot sizes are necessarily consistent; i.e., they remain the same over all machines. This intractable problem requires finding sublot sizes, a product sequence for each machine, and a machine sequence for each product. We develop a dynamic programming algorithm to generate all the dominant schedule profiles for each product that are required to formulate the open shop problem as a generalized traveling salesman problem. This problem is equivalent to a classical traveling salesman problem with a pseudopolynomial number of cities. We develop and test a computationally efficient heuristic for the open shop problem. Our results indicate that solutions can quickly be found for two machine open shops with up to 50 products. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Scheduling target illuminators in naval battle-group anti-air warfare

We schedule a set of illuminators (homing devices) to strike a set of targets using surface-to-air missiles in a naval battle. The task is viewed as a production floor shop scheduling problem of minimizing the total weighted flow time, subject to time-window job availability and machine downtime side constraints. A simple algorithm based on solving assignment problems is developed for the case when all the job processing times are equal and the data are all integer. For the general case of scheduling jobs with unequal processing times, we develop two alternate formulations and analyze their relative strengths by comparing their respective linear programming relaxations. We select the better formulation in this comparison and exploit its special structures to develop several effective heuristic algorithms that provide good-quality solutions in real time; this is an essential element for use by the Navy. © 1995 John Wiley & Sons, Inc.     

Optimal flowshop schedules with no intermediate storage space

In this paper the problem of finding an optimal schedule for the n-job, M-machine flowshop scheduling problem is considered when there is no intermediate space to hold partially completed jobs and the objective function is to minimize the weighted sum of idle times on all machines. By assuming that jobs are processed as early as possible, the problem is modeled as a traveling salesman problem and solved by known solution techniques for the traveling salesman problem. A sample problem is solved and a special case, one involving only two machines, is discussed.     

A convex property of an ordered flow shop sequencing problem

A flow shop sequencing problem with ordered processing time matrices is considered. A convex property for the makespan sequences of such problems is discussed. On the basis of this property an efficient optimizing algorithm is presented. Although the proof of optimality has not been developed, several hundred problems were solved optimally with this procedure.     

An exact algorithm for the batch sequencing problem in a two-machine flow shop with limited buffer

This paper deals with the problem of makespan minimization in a flow shop with two machines when the input buffer of the second machine can only host a limited number of parts. Here we analyze the problem in the context of batch processing, i.e., when identical parts must be processed consecutively. We propose an exact branch-and-bound algorithm, in which the bounds exploit the batching nature of the problem. Extensive computational results show the effectiveness of the approach, and allow us to compare it with a previous heuristic approach. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 141–164, 1998     

Time minimizing flows in directed networks

An important class of network flow problems is that class for which the objective is to minimize the cost of the most expensive unit of flow while obtaining a desired total flow through the network. Two special cases of this problem have been solved, namely, the bottleneck assignment problem and time-minimizing transportation problem. This paper addresses the more general case which we shall refer to as the time-minimizing network flow problem. Associated with each arc is an arc capacity (static) and a transferral time. The objective is to find a maximal flow for which the length (in time) of the longest path carrying flow is minimized. The character of the problem is discussed and a solution algorithm is presented.     

On the asymptotic optimality of algorithms for the flow shop problem with release dates

We consider the nonpermutation flow shop problem with release dates, with the objective of minimizing the sum of the weighted completion times on the final machine. Since the problem is NP‐hard, we focus on the analysis of the performance of several approximation algorithms, all of which are related to the classical Weighted Shortest Processing Time Among Available Jobs heuristic. In particular, we perform a probabilistic analysis and prove that two online heuristics and one offline heuristic are asymptotically optimal. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Flow‐shop batch scheduling with identical processing‐time jobs

In many practical situations of production scheduling, it is either necessary or recommended to group a large number of jobs into a relatively small number of batches. A decision needs to be made regarding both the batching (i.e., determining the number and the size of the batches) and the sequencing (of batches and of jobs within batches). A setup cost is incurred whenever a batch begins processing on a given machine. This paper focuses on batch scheduling of identical processing‐time jobs, and machine‐ and sequence‐independent setup times on an m‐machine flow‐shop. The objective is to find an allocation to batches and their schedule in order to minimize flow‐time. We introduce a surprising and nonintuitive solution for the problem. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

A shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop

We present a shifting bottleneck heuristic for minimizing the total weighted tardiness in a job shop. The method decomposes the job shop into a number of single‐machine subproblems that are solved one after another. Each machine is scheduled according to the solution of its corresponding subproblem. The order in which the single machine subproblems are solved has a significant impact on the quality of the overall solution and on the time required to obtain this solution. We therefore test a number of different orders for solving the subproblems. Computational results on 66 instances with ten jobs and ten machines show that our heuristic yields solutions that are close to optimal, and it clearly outperforms a well‐known dispatching rule enhanced with backtracking mechanisms. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 1–17, 1999