More MILP models for hybrid flow shop scheduling problem and its extended problems

In this paper, a hybrid flow shop scheduling problem with a new approach considering time lags and sequence-dependent setup time in realistic situations is presented. Since few works have been implemented in this field, the necessity of finding better solutions is a motivation to extend heuristic or meta-heuristic algorithms. This type of production system is found in industries such as food processing, chemical, textile, metallurgical, printed circuit board, and automobile manufacturing. A mixed integer linear programming (MILP) model is proposed to minimize the makespan. Since this problem is known as NP-Hard class, a meta-heuristic algorithm, named Genetic Algorithm (GA), and three heuristic algorithms (Johnson, SPTCH and Palmer) are proposed. Numerical experiments of different sizes are implemented to evaluate the performance of presented mathematical programming model and the designed GA in compare to heuristic algorithms and a benchmark algorithm. Computational results indicate that the designed GA can produce near optimal solutions in a short computational time for different size problems.

Solving a large-scale industrial scheduling problem using MILP combined with a heuristic procedure

This research addresses scheduling problem of n jobs on a Hybrid Flow Shop (HFS) with unrelated parallel machines in each stage. A monolithic mixed integer linear programming (MILP) model is presented to minimize the maximum completion time (makespan). As the research problem is shown to be strongly NP-hard, a Lagrangian relaxation (LR) algorithm is developed to handle the HFS scheduling problem. We design two approaches, simplification of subproblems and dominance rules, to solve the subproblems which are generated in each iteration. For evaluation purposes, numerical experiments with small and large size problems are randomly generated with up to 50 jobs and four stages. The experimental results show that the Lagrangian relaxation approaches outperform the MILP model with respect to CPU time. Furthermore, from the results, it can be conclude that the simplification of subproblems shows slightly better solutions in comparison with dominance rules to solve the subproblems.

Purpose: The main purpose of the paper is to evaluate the impact of diverse personnel policies around personnel promotion in the design of the strategic staff plan for a public university. The strategic staff planning consists in the determination of the size and composition of the workforce for an organization.Design/methodology/approach: The staff planning is solved using a Mixed Integer Linear Programming (MILP) model. The MILP model represents the organizational structure of the university, the personnel categories and capacity decisions, the demand requirements, the required service level and budget restrictions. All these aspects are translated into a set of data, as well as the parameters and constraints building up the mathematical model for optimization. The required data for the model is adopted from a Spanish public university.Findings: The development of appropriate policies for personnel promotion can effectively reduce the number of dismissals while proposing a transition towards different preferable workforce structures in the university.Research limitations/implications: The long term staff plan for the university is solved by the MILP model considering a time horizon of 8 years. For this time horizon, the required input data is derived from current data of the university. Different scenarios are proposed considering different temporal trends for input data, such as in demand and admissible promotional ratios for workers.Originality/value: The literature review reports a lack of formalized procedures for staff planning in universities taking into account, at the same time, the regulations on hiring, dismissals, promotions and the workforce heterogeneity, all considered to optimize workforce size and composition addressing not only an economic criteria, but also the required workforce expertise and the quality in the service offered. This paper adopts a formalized procedure developed by the authors in previous works, and exploits it to assess the impact of various personnel policies in the staff planning for a particular university case, and this is the principal contribution of the paper.

Passive Optical Network (PON) deployments have recently been aiming to combine the capacity of metro and access networks in the last mile of the Internet service provisioning. Deployment of PONs by running fiber to the premises introduces the advantage of huge capacity but at the same time, it calls for a robust design in order to avoid long service outage durations in case of network failures where survivable network design is mostly limited to the deployment budget. In this paper, we propose three mixed integer linear programming (MILP) models for various survivability policies to deploy reliable long-reach PONs under the budget limitations. Each MILP model aims to place the ONUs in optimal locations so that the covered area is maximized while availability requirements of the users are satisfied within the deployment budget. We solve the MILP models under the uniform and heterogeneous availability requirement scenarios and show that service availability and coverage introduce a trade-off so as the coverage and deployment cost do. Two out of the three survivability policies can guarantee 99.99% service availability while the third one is able to guarantee 99.999% by running the proposed MILP models. However, the first two schemes are able to cover larger area when compared to the third scheme which is the most reliable protection policy.

Modeling side slopes in vertical alignment resource road construction using convex optimization

Due to the large size of open-pit mines’ long-term production scheduling (OPMPS) problem in large-scale deposits, it is challenging to solve that problem as the mixed integer linear programming (MILP) model. This study used an approach of the genetic algorithm (GA) to tackle this challenge. So, in a small hypothetical deposit, based on the blocks in the ultimate pit limit and scenarios with 2–6 phases, net present values (NPV) and computational times obtained from the GA and MILP model were compared to evaluate the GA. Also, the GA was applied to a large-scale deposit to determine the efficiency of the GA in real deposits. The maximum NPV was obtained for the four-phase scenario in the hypothetical deposit and the six-phase scenario in the large-scale deposit. Although the GA’s NPV decreased slightly compared to the global optimum solution from the MILP model, the computational time was significantly reduced.

To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium. The food lists generated by the MILP model have good performance in terms of length, coverage and R 2 (explained variance) of all nutrients. MILP-generated food lists were 32-40 % shorter than a benchmark food list, whereas their quality in terms of R 2 was similar to that of the benchmark. The results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

To design a cellular manufacturing system, many decisions have to be taken into consideration; grouping machines into cells, determining the system and intracellular layouts, and dividing the resources between the cells. In this paper, a novel mixed integer linear programming (MILP) model is proposed for the integrated cell formation, cellular layout and worker assignment problem. The workers are assumed to have different skill levels, and worker load is based on manual workload and material handling tasks. A genetic algorithm (GA) is further proposed to solve the problem, where the GA chromosome represents locations of machines and assignment of workers to machines. A numerical study is finally conducted to evaluate the performance of the proposed GA with regards to solutions attained by solving the MILP model. Results demonstrate the efficiency of the proposed GA in solving the integrated problem, as well as the competence in the developed MILP model.

This article studies a distributed heterogeneous hybrid flow shop scheduling problem under nonidentical time-of-use electricity tariffs (DHHFSP-NTOU). The makespan and the total electricity charge are considered as the optimization objectives from the view of production and management. The DHHFSP-NTOU considers different processing capabilitie and time-of-use electricity tariffs for each factory. The mixed-integer linear programming (MILP) model of DHHFSP-NTOU is established. To solve the DHHFSP-NTOU, this article proposes an ant colony optimization behavior-based multiobjective evolutionary algorithm based on decomposition (ACO_MOEA/D). A problem-specific ant colony behavior is presented to construct offspring individuals. Eight neighborhoods within the factory and between factories are adopted to improve the quality of the individuals in the archive set. A right-shift movement is used to reduce the electricity charge. A large number of numerical experiments and comprehensive investigations are carried out to test the efficiency and effectiveness of ACO_MOEA/D. The experimental results show that each component (e.g., ant colony behavior, neighborhoods move operators, right-shift movement) contributes to the performance of ACO_MOEA/D. The comparisons with several related algorithms show the superiority of ACO_MOEA/D for solving the DHHFSP-NTOU. Note to Practitioners—From the managers' insights, the electricity charge is a large cost in the production. The scheduling is an economical approach to reduce the electricity charge. For the time-of-use (TOU) tariffs, the managers can adjust the schedule to reduce the idle time or move some operations to the interval period with a lower electric price. This article studies a distributed heterogeneous hybrid flow shop scheduling problem under nonidentical TOU (UTOU) electricity. This model can be used in many manufacturing enterprises that have several heterogeneous factories. This article proposes an ant colony optimization behavior-based multiobjective evolutionary algorithm based on decomposition (ACO_MOEA/D) to minimize the makespan and the total electricity charge. The ACO_MOEA/D can provide the economy and high-efficiency schedules for practitioners. The computational results confirm its effectiveness and efficiency.

Mixed integer linear programming for the design of solar thermal energy systems with short-term storage

In this research, a bi-criteria group scheduling problem is investigated in a hybrid flow shop (HFS) environment, wherein the parallel machines are unrelated. The objective of the problem is to minimize a linear combination of the total weighted completion time being mindful of the producer and the total weighted tardiness being mindful of the customers. The underlying assumption is that the jobs are released into the system in dynamic times. The machine ready times are considered to be dynamic as well. Sequence-dependent setup times are required for changing the process between groups of jobs. The runtimes of jobs are assumed to be decreasing as the workers learn how to process similar jobs. A mixed-integer linear programing model is developed for the problem. However, since the problem is non-deterministic polynomial-time hard (NP-hard), it may not be solved to optimality within a reasonable time. This research comprehensively addresses the question of what type of meta-heuristic algorithm is more appropriate for solving these problems. In particular, local search algorithms are compared to the population-based algorithms with respect to the permutation or non-permutation properties of the optimal solution. Three algorithms based on tabu search as well as three algorithms based on simulated annealing are developed to represent the local search algorithms. Two other algorithms are developed based on genetic algorithm (GA) to exemplify the population-based algorithms. The results of a comprehensive experimental design reveal that GA-based algorithms have greater potential for identifying better quality solutions in HFS scheduling problems compared to the local search algorithms.

Mixed Integer Linear Programming Model for Vehicle Routing Problem for Hazardous Materials Transportation

Matheuristic is an optimisation methodology that integrates mathematical approaches and heuristics to address intractable combinatorial optimisation problems, where a common framework is to insert mixed integer linear programming (MILP) models as local search functions for evolutionary algorithms. However, since a mathematical programming formulation only tries to find the solution with the best objective value, matheuristics are rarely adopted to multi‐objective scenarios asking for a set of Pareto optimal solutions, for example, vehicle routing problems and production scheduling problems. In this situation, the ɛ ‐constraint, which transforms multi‐objective problems into single‐objective formulations by considering selected objectives as constraints, seems to be a promising approach. First, an augmented ɛ ‐constraint‐based matheuristic methodology ( ɛ ‐MH) is proposed to apply the idea of ɛ ‐constraint to embedded MILP models, so that Pareto fronts obtained by meta‐heuristics can be further improved by solving a set of MILP models. Afterwards, four speed‐up strategies are developed to alleviate the computational burden resulting from repeatedly solving mathematical formulations, which also imply preferable scenarios for taking advantages of the ɛ ‐MH. Finally, several real‐world bi‐objective scheduling problems are discussed to present potential applications for the proposed methodology.

Cellular manufacturing systems (CMS) are production systems that typically comprise a number of manufacturing cells served by a centralized material handling system. Designing such systems includes three major decisions; cell formation (CF), group layout (GL), and group scheduling (GS). Traditionally, these three decisions have been dealt with separately, which has usually lead to less than optimal system performance. In this paper, a new mixed integer linear programming (MILP) model is proposed for the integrated CF, GL and GS problem, to efficiently design and operate CMSs. The model solves the integrated problem, taking into consideration intercellular and intracellular transportation times to determine the optimal cell formation, layout of machines and schedule of parts on the machines, simultaneously. Sequence-dependent set up times are also considered in the model. The performance of the model is tested by solving problems previously introduced in the literature considering two objectives; minimizing the makespan or minimizing the mean flow time in the system. The results show that the proposed model is efficient in solving small to medium-sized problems.