Mathematical modeling for a multiproduct manufacturing system featuring postponement, external suppliers, overtime, and scrap

Manufacturing firms operating in today’s competitive global markets must continuously find the appropriate manufacturing scheme and strategies to effectively meet customer needs for various types of quality of merchandise under the constraints of short order lead-time and limited in-house capacity. Inspired by the offering of a decision-making model to aid smooth manufacturers’ operations, this study builds an analytical model to expose the influence of the outsourcing of common parts, postponement policies, overtime options, and random scrapped items on the optimal replenishment decision and various crucial system performance indices of the multiproduct problem. A two-stage fabrication scheme is presented to handle the products’ commonality and the uptime-reduced strategies to satisfy the short amount of time before the due dates of customers’ orders. A screening process helps identify and remove faulty items to ensure the finished lot’s anticipated quality. Mathematical derivation assists us in finding the manufacturing relevant total cost function. The differential calculus helps optimize the cost function and determine the optimal stock-replenishing rotation cycle policy. Lastly, a simulated numerical illustration helps validate our research result’s applicability and demonstrate the model’s capability to disclose the crucial managerial insights and facilitate manufacturing-relevant decision making.

Discounted costs and obsolescence with the Joint replenishment problem

Real life inventory lot sizing problems are frequently challenged with the need to order different types of items within the same batch. The Joint Replenishment Problem (JRP) addresses this setting of coordinated ordering by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. The complexity of this problem increases when some or all item types are prone to obsolescence. In fact, the items may experience an abrupt decline in demand because they are no longer needed, due to rapid advancements in technology, going out of fashion, or ceasing to be economically viable. This article proposes an extension of the Joint Replenishment Problem (JRP) where the items may suddenly become obsolete at some time in the future. The model assumes constant demand and the items’ lifetimes follow independent negative exponential distributions. The optimization process considers the time value of money by using the expected discounted total cost as the minimization criterion. The proposed model was applied to some test cases, and sensitivity analyses were performed, in order to assess the impact of obsolescence on the ordering policy. The increase in the obsolescence risk, through the progressive increase of the obsolescence rates of the item types, determines smaller lot sizes on the ordering policy. The increase in the discount rate causes smaller quantities to be ordered as well.

A granular tabu search for the refrigerated vehicle routing problem with homogeneous fleet

The Refrigerated Capacitated Vehicle Routing Problem (RCVRP) considers a homogeneous fleet with a refrigerated system to decide the selection of routes to be performed according to customers' requirements. The aim is to keep the energy consumption of the routes as low as possible. We use a thermodynamic model to understand the unloading of products from trucks and the variables' efficiency, such as the temperature during the day influencing energy consumption. By considering various neighborhoods and a shaking procedure, this paper proposes a Granular Tabu Search scheme to solve the RCVRP. Computational tests using adapted benchmark instances from the literature demonstrate that the suggested method delivers high-quality solutions within short computing times, illustrating the refrigeration system's effect on routing decisions.

Cockpit crew pairing Pareto optimisation in a budget airline

Crew pairing is the primary cost checkpoint in airline crew scheduling. Because the crew cost comes second after the fuel cost, a substantial cost saving can be gained from effective crew pairing. In this paper, the cockpit crew pairing problem (CCPP) of a budget airline was studied. Unlike the conventional CCPP that focuses solely on the cost component, many more objectives deemed to be no less important than cost minimisation were also taken into consideration. The adaptive non-dominated sorting differential algorithm III (ANSDE III) was proposed to optimise the CCPP against many objectives simultaneously. The performance of ANSDE III was compared against the NSGA III, MOEA/D, and MODE algorithms under several Pareto optimal measurements, where ANSDE III outperformed the others in every metric.

Optimization of Bayesian repetitive group sampling plan for quality determination in Pharmaceutical products and related materials

Sampling plans are extensively used in pharmaceutical industries to test drugs or other related materials to ensure that they are safe and consistent. A sampling plan can help to determine the quality of products, to monitor the goodness of materials and to validate the yields whether it is free from defects or not. If the manufacturing process is precisely aligned, the occurrence of defects will be an unusual occasion and will result in an excess number of zeros (no defects) during the sampling inspection. The Zero Inflated Poisson (ZIP) distribution is studied for the given scenario, which helps the management to take a precise decision about the lot and it can certainly reduce the error rate than the regular Poisson model. The Bayesian methodology is a more appropriate statistical procedure for reaching a good decision if the previous knowledge is available concerning the production process. This article proposed a new design of the Bayesian Repetitive Group Sampling plan based on Zero Inflated Poisson distribution for the quality assurance in pharmaceutical products and related materials. This plan is studied through the Gamma-Zero Inflated Poisson (G-ZIP) model to safeguard both the producer and consumer by minimizing the Average Sample Number. Necessary tables and figures are constructed for the selection of optimal plan parameters and suitable illustrations are provided that are applicable for pharmaceutical industries.

MILP of multitask scheduling of geographically distributed maintenance tasks

Due to its proactive impact on the serviceability of components in a system, preventive maintenance plays an important role particularly in systems of geographically spread infrastructure such as utilities networks in commercial buildings. What makes such systems differ from the classical schemes is the routing and technicians' travel times. Besides, maintenance in commercial buildings is characterized by its short tasks’ durations and spatial distribution within and between different buildings, a class of problems that has not been suitably investigated. Although it is not trivial to assign particular duties solely to multi-skilled teams under limited time and capacity constraints, the problem becomes more challenging when travel routes, durations and service levels are considered during the execution of the daily maintenance tasks. To address this problem, we propose a Mixed Integer Linear Programming Model that considers the above settings. The model exact solution recommends collaborative choices that include the number of maintenance teams, the selected tasks, routes, tasks schedules, all detailed to days and teams. The model will reduce the cost of labor, replacement parts, penalties on service levels and travel time. The optimization model has been tested using different maintenance scenarios taken from a real maintenance provider in the UAE. Using CPLEX solver, the findings demonstrate an inspiring time utilization, schedules of minimal routing and high service levels using a minimum number of teams. Different travel speeds of diverse assortment of tasks, durations and cost settings have been tested for further sensitivity analysis.

Minimizing total tardiness for the order scheduling problem with sequence-dependent setup times using hybrid matheuristics

This paper aims at presenting a customer order scheduling environment in which the setup times are explicit and depend on the production sequence. The considered objective function is the total tardiness minimization. Since the variant under study is NP-hard, we propose a mixed-integer linear programming (MILP) model, an adaptation of the Order-Scheduling Modified Due-Date heuristic (OMDD) (referred to as Order-Scheduling Modified Due-Date Setup (OMMD-S)), an adaptation of the Framinan and Perez-Gonzalez heuristic (FP) (hereinafter referred to as Framinan and Perez-Gonzalez Setup (FP-S)), a matheuristic with Same Permutation in All Machines (SPAM), and the hybrid matheuristic SPAM-SJPO based on Job-Position Oscillation (JPO). The algorithms under comparison have been compared on an extensive benchmark of randomly generated test instances, considering two performance measures: Relative Deviation Index (RDI) and Success Rate (SR). For the small-size evaluated instances, the SPAM is the most efficient algorithm, presenting the better values of RDI and SR. For the large-size evaluated instances, the hybrid matheuristic SPAM-JPO and MILP model are the most efficient methods.

An extensive and systematic literature review for hybrid flowshop scheduling problems

Hybrid flowshop scheduling problem (HFSP) is a mixture of two classical scheduling problems as parallel machine scheduling (PMS) and flowshop scheduling (FS). In the HFSP, a series of jobs are processed respectively in a set of stages that at least one of these stages has more than one parallel machine (identical, uniform or unrelated). HFSP is a widespreadly studied subject in the literature and there are various application areas such as transportation, healthcare management, agricultural activities, cloud computing, and the most common manufacturing. Therefore, it will be useful to present a review study including recent papers and developments related to this problem for researchers. For this aim, in this paper, a systematic literature survey has been conducted with respect to HFSPs by means of Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology which enables to realize systematic review and meta-analyses in a specified subject. 172 articles which are published in the 2010-2020 year interval, related to production scheduling and including a mathematical programming model to express scheduling problems have been determined as a result of this methodological review process. These articles have been statistically analyzed according to many features such as year, country, journal, number of stages, type of parallel machines, constraints, objective functions, solution methods, test instances and type of parameters. The results of statistical analyses have been presented through charts so as to provide a visual demonstration to researchers. Furthermore, it has been aimed to answer 14 predetermined research questions by means of analyses realized in the scope of this review study. Consequently, it has revealed the existing literature, recent developments and future research suggestions related to HFSP and therefore it is possible to say that this review paper provides a beneficial road map for researchers studying in this field.

An algorithm for a no-wait flowshop scheduling problem for minimizing total tardiness with a constraint on total completion time

We consider a no-wait m-machine flowshop scheduling problem which is common in different manufacturing industries such as steel, pharmaceutical, and chemical. The objective is to minimize total tardiness since it minimizes penalty costs and loss of customer goodwill. We also consider the performance measure of total completion time which is significant in environments where reducing holding cost is important. We consider both performance measures with the objective of minimizing total tardiness subject to the constraint that total completion time is bounded. Given that the problem is NP-hard, we propose an algorithm. We conduct extensive computational experiments to compare the performance of the proposed algorithm with those of three well performing benchmark algorithms in the literature. Computational results indicate that the proposed algorithm reduces the error of the best existing benchmark algorithm by 88% under the same CPU times. The results are confirmed by extensive statistical analysis. Specifically, ANOVA analysis is conducted to justify the difference between the performances of the algorithms, and a test of hypothesis is performed to justify that the proposed algorithm is significantly better than the best existing benchmark algorithm with a significance level of 0.01.

A new hybrid algorithm based on MVO and SA for function optimization

Hybrid algorithms are widely used today to increase the performance of existing algorithms. In this paper, a new hybrid algorithm called IMVOSA that is based on multi-verse optimizer (MVO) and simulated annealing (SA) is used. In this model, a new method called the black hole selection (BHS) is proposed, in which exploration and exploitation can be increased. In the BHS method, the acceptance probability feature of the SA algorithm is used to increase exploitation by searching for the best regions found by the MVO algorithm. The proposed IMVOSA algorithm has been tested on 50 benchmark functions. The performance of IMVOSA has been compared with other latest and well-known metaheuristic algorithms. The consequences show that IMVOSA produces highly successful and competitive results.