Comments on “A bicriteria flowshop scheduling problem with setup times”

The aim of this paper is to point out that the integer programming model proposed by Eren and Güner [T. Eren, E. Güner, A bicriteria flowshop scheduling problem with setup times, Appl. Math. Comput. 183 (2006) 1292-1300] is incorrect. We propose a new integer programming model for the same scheduling problem based on their model.     

Comments on “A bicriteria m-machine flowshop scheduling with sequence-dependent setup times”

The purpose of this paper is to point out that the programming model proposed by Eren [A bicriteria m-machine flowshop scheduling with sequence-dependent setup times, Appl. Math. Model. 34 (2010) 284–293] is incorrect. We propose a mixed 0–1 programming model for the same scheduling problem based on their model.     

Comments on “A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect”

The purpose of this paper is to point out that if there are some machines that do not process any job then the mathematical programming model provided by Eren [T. Eren, A note on minimizing maximum lateness in an m-machine scheduling problem with a learning effect, Applied Mathematics and Computation 209 (2009) 186-190] may not be a valid one. A simple way to fix this problem is given. Furthermore, based on the idea of Eren’s model, a general mathematical programming model is proposed.     

A note on “A mixed integer programming model for advanced planning and scheduling (APS)”

In a recent paper, Chen and Ji [Chen, K., Ji, P., 2007. A mixed integer programming model for advanced planning and scheduling (APS). European Journal of Operational Research 181, 515–522] develop a mixed integer programming model for advanced planning and scheduling problem that considers capacity constraints and precedence relations between the operations. The orders require processing of several operations on eligible machines. The model presented in the above paper works for the case where each operation can be processed on only one machine. However, machine eligibility means that only a subset of machines are capable of processing a job and this subset may include more than one machine. We provide a general model for advanced planning and scheduling problems with machine eligibility. Our model can be used for problems where there are alternative machines that an operation can be assigned to.     

Comments on “A bicriteria parallel machine scheduling with a learning effect of setup and removal times”

The purpose of this paper is to point out some errors in Eren [Applied Mathematical Modelling, 33 (2009) 1141–1150]. We also suggest some methods to fix them.     

Chance constrained programming models for refinery short-term crude oil scheduling problem

The main objective of this work is to put forward chance constrained mixed-integer nonlinear stochastic and fuzzy programming models for refinery short-term crude oil scheduling problem under demands uncertainty of distillation units. The scheduling problem studied has characteristics of discrete events and continuous events coexistence, multistage, multiproduct, nonlinear, uncertainty and large scale. At first, the two models are transformed into their equivalent stochastic and fuzzy mixed-integer linear programming (MILP) models by using the method of Quesada and Grossmann [I. Quesada, I E. Grossmann, Global optimization of bilinear process networks with multicomponent flows, Comput. Chem. Eng. 19 (12) (1995) 1219–1242], respectively. After that, the stochastic equivalent model is converted into its deterministic MILP model through probabilistic theory. The fuzzy equivalent model is transformed into its crisp MILP model relies on the fuzzy theory presented by Liu and Iwamura [B.D. Liu, K. Iwamura, Chance constrained programming with fuzzy parameters, Fuzzy Sets Syst. 94 (2) (1998) 227–237] for the first time in this area. Finally, the two crisp MILP models are solved in LINGO 8.0 based on scheduling time discretization. A case study which has 267 continuous variables, 68 binary variables and 320 constraints is effectively solved with the solution approaches proposed.     

Retail store scheduling for profit

In spite of its tremendous economic significance, the problem of sales staff schedule optimization for retail stores has received relatively scant attention. Current approaches typically attempt to minimize payroll costs by closely fitting a staffing curve derived from exogenous sales forecasts, oblivious to the ability of additional staff to (sometimes) positively impact sales. In contrast, this paper frames the retail scheduling problem in terms of operating profit maximization, explicitly recognizing the dual role of sales employees as sources of revenues as well as generators of operating costs. We introduce a flexible stochastic model of retail store sales, estimated from store-specific historical data, that can account for the impact of all known sales drivers, including the number of scheduled staff, and provide an accurate sales forecast at a high intra-day resolution. We also present solution techniques based on mixed-integer (MIP) and constraint programming (CP) to efficiently solve the complex mixed integer non-linear scheduling (MINLP) problem with a profit-maximization objective. The proposed approach allows solving full weekly schedules to optimality, or near-optimality with a very small gap. On a case-study with a medium-sized retail chain, this integrated forecasting–scheduling methodology yields significant projected net profit increases on the order of 2–3% compared to baseline schedules.     

A (0–1) goal programming model for scheduling the tour of a marketing executive

This paper addresses the problem of scheduling the tour of a marketing executive (ME) of a large electronics manufacturing company in India. In this problem, the ME has to visit a number of customers in a given planning period. The scheduling problem taken up in this study is different from the various personnel scheduling problems addressed in the literature. This type of personnel scheduling problem can be observed in many other situations such as periodical visits of inspection officers, tour of politicians during election campaigns, tour of mobile courts, schedule of mobile stalls in various areas, etc. In this paper the tour scheduling problem of the ME is modeled using (0–1) goal programming (GP). The (0–1) GP model for the data provided by the company for 1 month has 802 constraints and 1167 binary variables. The model is solved using LINDO software package. The model takes less than a minute (on a 1.50 MHz Pentium machine with 128 MB RAM) to get a solution of the non-preemptive version and about 6 days for the preemptive version. The main contribution is in problem definition and development of the mathematical model for scheduling the tour.     

A probabilistic scheduling period inventory model for deteriorating items with lead time

A probabilistic scheduling period inventory model is developed for continuously decaying items. The model assumes no shortages, deterministic lead time and a general deterioration function. The developed model is shown to be related to the similar model without lead time and also to the similar model for non-deteriorating items. Two special cases are considered and an example is also furnished.

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Zusammenfassung Es wird ein probabilistisches Lagerhaltungsmodell für sich stetig verschlechternde Güter entwickelt. Im Modell wird angenommen, da\ kein Mangel eintritt, die Verschlechterung durch eine allgemeine Funktion beschrieben wird und deterministische Lieferzeiten vorliegen. Es wird gezeigt, da\ das entwickelte Modell bekannte Modelle ohne Lieferzeiten sowie für sich nicht verschlechternde Güter als Spezialfälle enthält. Ferner werden zwei weitere Spezialfälle und ein numerisches Beispiel angegeben.

     

Scheduling interfering job sets on parallel machines

We consider bicriteria scheduling on identical parallel machines in a nontraditional context: jobs belong to two disjoint sets, and each set has a different criterion to be minimized. The jobs are all available at time zero and have to be scheduled (non-preemptively) on m parallel machines. The goal is to generate the set of all non-dominated solutions, so the decision maker can evaluate the tradeoffs and choose the schedule to be implemented. We consider the case where, for one of the two sets, the criterion to be minimized is makespan while for the other the total completion time needs to be minimized. Given that the problem is NP-hard, we propose an iterative SPT–LPT–SPT heuristic and a bicriteria genetic algorithm for the problem. Both approaches are designed to exploit the problem structure and generate a set of non-dominated solutions. In the genetic algorithm we use a special encoding scheme and also a unique strategy – based on the properties of a non-dominated solution – to ensure that all parts of the non-dominated front are explored. The heuristic and the genetic algorithm are compared with a time-indexed integer programming formulation for small and large instances. Results indicate that the both the heuristic and the genetic algorithm provide high solution quality and are computationally efficient. The heuristics proposed also have the potential to be generalized for the problem of interfering job sets involving other bicriteria pairs.     

Kundenzeitschranken in der computergestützten Tourenplanung

Zusammenfassung Tourenplanungsprobleme der Praxis weisen gegenüber dem Grundmodell der Literatur in der Regel vielfältige, z.T. erhebliche Abweichungen auf. Nach einer kurzen Diskussion dieser Problemmodifikationen wird eine in der Praxis besonders wichtige und ohne Computerunterstützung schwer zu bewältigende Klasse von Nebenbedingungen, spezifische Kundenzeitschranken, näher untersucht. Insbesondere wird eine im Softwarepaket TRAFIC der Firma Siemens erfolgreich implementierte Lösungsheuristik entwickelt. Rechenexperimente zeigen die Auswirkungen von Kundenzeitschranken auf die Güte von Tourenmustern.

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Summary Real world vehicle scheduling problems often deviate in important aspects from the basic theoretic model of vehicle scheduling. Variable time restrictions for customers are especially difficult to meet in vehicle scheduling planning. A heuristic procedure for solving this problem is developed. Computational experiments show the effects of time restrictions on the quality of vehicle scheduling plans.

     

Minimizing makespan and total completion time for parallel batch processing machines with non-identical job sizes

This paper considers the scheduling problem of parallel batch processing machines with non-identical job sizes. The jobs are processed in batches and the machines have the same capacity. The models of minimizing makespan and total completion time are given using mixed integer programming method and the computational complexity is analyzed. The bound on the number of feasible solutions is given and the properties of the optimal solutions are presented. Then a polynomial time algorithm is proposed and the worst case ratios for minimizing total completion time and makespan is proved to be 2 and (8/3–2/3 m) respectively. To test the proposed algorithm, we generate different levels of random instances. The computational results demonstrate the effectiveness of the algorithm for minimizing the two objectives.     

A bicriteria flowshop scheduling with a learning effect

In many situations, a worker’s ability improves as a result of repeating the same or similar tasks; this phenomenon is known as the learning effect. In this paper the learning effect is considered in a two-machine flowshop. The objective is to find a sequence that minimizes a weighted sum of total completion time and makespan. Total completion time and makespan are widely used performance measures in scheduling literature. To solve this scheduling problem, an integer programming model with n² + 6n variables and 7n constraints where n is the number of jobs is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 30 jobs can be solved. A heuristic algorithm and a tabu search based heuristic algorithm are presented to solve large size problems. Experimental results show that the proposed heuristic methods can solve this problem with up to 300 jobs rapidly. According to the best of our knowledge, no work exists on the bicriteria flowshop with a learning effect.     

Note on “A note on single-machine group scheduling problems with position-based learning effect”

In a recent paper, Lee and Wu [W.-C. Lee, C.-C. Wu, A note on single-machine group scheduling problems with position-based learning effect, Appl. Math. Model. 33 (2009) 2159–2163] proposed a new group scheduling learning model where the learning effect not only depends on the job position, but also depends on the group position. They investigate the makespan and the total completion time minimization problems on a single-machine. As for the total completion time minimization problem, they assumed that the numbers of jobs in each group are the same and the group normal setup and the job normal processing times are agreeable. Under the assumption conditions, they showed that the total completion time minimization problem can be optimally solved in polynomial time solution. However, the assumption conditions for the total completion time minimization problem do not reflect actual practice in many manufacturing processes. Hence, in this note, we propose other agreeable conditions and show that the total completion time minimization problem remains polynomially solvable under the agreeable conditions.     

Multi-mode project payment scheduling problems with bonus–penalty structure

This paper involves the multi-mode project payment scheduling problem with bonus–penalty structure where activities can be performed with several modes and a bonus–penalty structure exists at the deadline of the project. In the problem the decisions on when to schedule events and payments, the magnitude of each payment, and the performing mode of each activity need to be optimized. A two-module simulated annealing heuristic is proposed to solve the mixed integer non-linear programming models for the contractor and the client, and a satisfactory solution, which consists of payment event set, event schedule, and payment amount set, may be found through iterations between the heuristic’s two modules. The profits of the two parties of the contract are changed significantly by the bonus–penalty structure and the structure may be considered as a coordination mechanism essentially, which may enhance the flexibility of payment scheduling and be helpful for the two parties to get more profits from the project. Through solving and analyzing an instance the insight that the bonus–penalty structure may advance the project completion effectively and improve the profits of the two parties in the meantime can be obtained.     

考虑碳排放的多机可持续调度问题

考虑多机器生产环境下,研究在加工空档期允许关闭机器的可持续调度问题。同时对工件的指派、工件的开始加工时刻和机器在空档期是否开关机进行决策,以最小化碳排放为目标建立数学规划模型。设计了禁忌搜索混合算法求解模型,首先通过一个企业案例验证了模型和算法的有效性,然后通过仿真算例分析了算法的效率。计算结果表明,可持续调度方式在机器调度层面为企业减少了大量的碳排放。     

基于动态列生成算法的飞机排班问题研究

飞机排班是航空运输生产计划的重要环节,对航空公司的正常运营和整体效益有着决定性影响;飞机排班通常构建为大规模整数规划问题,是航空运筹学研究的重要课题,构建的模型属于严重退化的NP-Hard问题.在考虑对多种机型的飞机进行排班时,大大增加了问题的复杂性.针对航空公司实际情况,建立多种机型的飞机排班模型;为实现模型的有效求解,提出了基于约束编程的动态列生成算法;即用约束编程快速求解航班连线(航班串)并计算航班串简约成本,动态选择列集并与限制主问题进行迭代.最后,利用国内某航空公司干线航班网络实际数据验证模型和算法的有效性.     

A branch-and-price approach for large-scale employee tour scheduling problems

We present a new methodology for solving large-scale employee tour scheduling problems. An integer programming model is proposed where tours are decomposed into shifts and start times. This formulation can model complex shift and start time rules for both continuous and discontinuous scheduling problems. A branch-and-price approach is devised to solve this model efficiently. The methodology was tested on the largest tour scheduling problems found in the open literature. In comparison with an alternative implicit model, our approach showed superior computational performance.     

Solving a multi-objective multi-skilled manpower scheduling model by a fuzzy goal programming approach

Manpower scheduling is an intricate problem in production and service environments with the purpose of generating fair schedules that consider employers’ objectives and employees’ preferences as much as possible. However, sometimes, vagueness of information related to employers’ objectives and employees’ preferences leads to the fuzzy nature of the problem. This paper presents a multi-objective manpower scheduling model regarding the lack of clarity on the target values of employers’ objectives and employees’ preferences. Hence, a fuzzy goal programming model is developed for the presented model. Afterwards, two fuzzy solution approaches are used to convert the fuzzy goal programming model to two single-objective models. Finally, the results obtained by both single-objective models are compared with each other to select the solution that has the greatest degree of the satisfaction level of employers’ objectives and employees’ preferences.