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Main constraints for an assembly line balancing problem (ALBP) are cycle time/number of stations and task precedence relations. However, due to the technological and organizational limitations, several other restrictions can be encountered in real production systems. These restrictions are called as assignment restrictions and can be task assignment, station, resource and distance limitations. The purpose of the study is to evaluate the effects of these restrictions on ALBP using constraint programming (CP) model.

A novel CP model is proposed and compared to mixed-integer programming (MIP) as a benchmark. The objective is to minimize the cycle time for a given number of stations. The authors also provide explicit anthology of the assignment restriction effects on line efficiency, the solution quality and the computation time.

The proposed approach is verified with the literature test instances and a real-life problem from a furniture manufacturing company. Computational experiments show that, despite the fact that additional assignment restrictions are problematic in mathematical solutions, CP is a versatile exact solution alternative in modelling and the solution quality.

Assembly line is a popular manufacturing system in the making of standardized high volume products. The problem of assembly line balancing is a crucial challenge in these settings and consists of assigning tasks to the stations by optimizing one or more objectives. Type-2 AR-ALBP is a specific case with the objective function of minimizing the cycle time for a given number of stations. It further assumes assignment restrictions that can be confronted due to the technological limitations or the strategic decisions of the company management. This is especially encountered in rebalancing lines.

Several solution approaches such as mathematical modelling, heuristic and meta-heuristic are proposed to solve the ALBP in the literature. In this study, a new approach has been presented using CP. Efficient models are developed for Type-2 ALBP with several assignment restrictions. Previous studies have not considered the problem to the presented extent. Furthermore, to the best of the authors’ knowledge, the paper is the first study that solves ALBP with assignment restrictions using CP.

Environmental issues have become an important concern in modern supply chain management. The structure of closed-loop supply chain (CLSC) networks, which considers both forward and reverse logistics, can greatly improve the utilization of materials and enhance the performance of the supply chain in coping with environmental impacts and cost control.

A biobjective mixed-integer programming model is developed to achieve the balance between environmental impact control and operational cost reduction. Various factors regarding the capacity level and the environmental level of facilities are incorporated in this study. The scenario-based method and the Epsilon method are employed to solve the stochastic programming model under uncertain demand.

The proposed stochastic mixed-integer programming (MIP) model is an effective way of formulating and solving the CLSC network design problem. The reliability and precision of the Epsilon method are verified based on the numerical experiments. Conversion efficiency calculation can achieve the trade-off between cost control and CO₂ emissions. Managers should pay more attention to activities about facility operation. These nodes might be the main factors of costs and environmental impacts in the CLSC network. Both costs and CO₂ emissions are influenced by return rate especially costs. Managers should be discreet in coping with cost control for CO₂ emissions barely affected by return rate. It is advisable to convert the double target into a single target by the idea of “Efficiency of CO₂ Emissions Control Reduction.” It can provide managers with a way to double-target conversion.

We proposed a biobjective optimization problem in the CLSC network considering environmental impact control and operational cost reduction. The scenario-based method and the Epsilon method are employed to solve the mixed-integer programming model under uncertain demand.

Resource capacity and product changeovers must be both considered in the preparation of a realistic production plan. The purpose of this paper is to present a heuristic for enforcing resource availability and the accompanying changeover realities into a continuous‐variable linear programming formulation that would otherwise require a mixed‐integer model. The results from both approaches are compared in terms of objective function values and computational requirements; the effectiveness of the heuristic approach is demonstrated.

A case study search was conducted to identify relevant data sets that could be used to exercise the optimization and heuristic models. The case studies found in the literature were too small and simple compared to the problem complexity desired. The authors developed a case study based on the development of a production plan for a typical flashlight. It includes two end‐products that differ in their bills of materials and process requirements. Basic processes include plastic part preparation and final assembly; various raw materials with pre‐defined lead times are purchased from external suppliers. The results of the LP‐based heuristic and the mixed‐integer programming (MIP) optimization algorithm are then compared through a statistical experiment. The experiment includes four factors: number of products, number of periods, number of machines, and percentage line capacity utilization.

When a MIP algorithm is applied to obtain the results, most of the time the planner would have to wait days or even weeks for the algorithm to provide a solution. However, the authors' linear programming‐based procedure provides the same quality of solution in minutes and for some problems in seconds.

The originality of the heuristic approach resides on the avoidance of the lengthy MIP computer runs. At each iteration, the authors solve the LP production planning problem without changeover considerations, and then subtract from the original capacity the time associated with the changeovers resulting from the last LP solution. After a small number of iterations the heuristic always converges to the optimal MIP solution. The contribution of this research can be appreciated by someone who is using this tool to generate a production plan in a real world factory where setups are important and the results can immediately suggest changes to some of the assumptions or parameters used in the planning exercise.

This research is designed to optimize the business process of a green tea dealer, who is a key supply chain partner of the Sri Lankan tea industry. The most appropriate trips for each vehicle in multiple trip routing systems are identified to minimize the total cost by considering the traveling distance.

The study has followed the concepts in vehicle routing problems and mixed-integer programming mathematical techniques. The model was coded with the Python programming language and was solved with the CPLEX Optimization solver version 12.10. In total, 20 data instances were used from the subjected green tea dealer for the validation of the model.

The result of the numerical experiment showed the ability to access supply over the full capacity of the available fleet. The model achieved optimal traveling distance for all the instances, with the capability of saving 17% of daily transpiration cost as an average.

This study contributes to the three index mixed-integer programing model formulation through in-depth analysis and combination of several extensions of vehicle routing problem.

This study contributes to the three index mixed-integer programming model formulation through in-depth analysis and combination of several extensions of the vehicle routing problem.

The proposed model provides a cost-effective optimal routing plan to the green tea dealer, which satisfies all the practical situations by following the multiple trip vehicle routing problems. Licensee green tea dealer is able to have an optimal fleet size, which is always less than the original fleet size. Elimination of a vehicle from the fleet has the capability of reducing the workforce. Hence, this provides managerial implication for the optimal fleet sizing and route designing.

Developing an optimization model for a tea dealer in Sri Lankan context is important, as this a complex real world case which has a significant importance in export economy of the country and which has not been analyzed or optimized through any previous research effort.

This paper aims to correct the existing mixed integer programming (MIP) model proposed by Yadav et al. (2019) [“Bi-objective optimization for sustainable supply chain network design in omnichannel.”, Journal of Manufacturing Technology Management, Vol. 30 No. 6, pp. 972–986].

This paper first presents a counterexample to show that the existing MIP model is incorrect and then proposes an improved mixed integer linear programming (MILP) model for the considered problem. Last, a numerical experiment is conducted to test our improved MILP model.

This paper demonstrates that the formulations of the facility capacity constraints and the product flow balance constraints in the existing MIP model are incorrect and incomplete. Due to this reason, infeasible solutions could be identified as feasible ones by the existing MIP model. Hence, the optimal solution obtained with the existing MIP model could be infeasible. A counter-example is used to verify our observations. Computational results verify the effectiveness of our improved MILP model.

This paper gives a complete and correct formulation of the facility capacity constraints and the product flow balance constraints, and conducts other improvements on the existing MIP model. The improved MILP model can be easily implemented and would help companies to have more effective distribution networks under the omnichannel environment.

This paper aims to introduce a new mixed integer programming formulation and associated heuristic algorithm to solve the Military Nodal Capacity Problem, which is a type of supply chain network design problem that involves determining the amount of capacity expansion required at theater nodes to ensure the on-time delivery of military cargo.

Supply chain network design, mixed integer programs, heuristics and regression are used in this paper.

This work helps analysts at the United States Transportation Command identify what levels of throughput capacities, such as daily processing rates of trucks and railcars, are needed at theater distribution nodes to meet warfighter cargo delivery requirements.

This research assumes all problem data are deterministic, and so it does not capture the variations in cargo requirements, transit times or asset payloads.

This work gives military analysts and decision makers prescriptive details about nodal capacities needed to meet demands. Prior to this work, insights for this type of problem were generated using multiple time-consuming simulations often involving trial-and-error to explore the trade space.

This work merges research of supply chain network design with military theater distribution problems to prescribe the optimal, or near-optimal, throughput capacities at theater nodes. The capacity levels must meet delivery requirements while adhering to constraints on the proportion of cargo transported by mode and the expected payloads for assets.

The traveling purchaser problem (TPP) has gained attention in academics to deal with different variants in real business world. This study aims to study a green TPP with quantity discounts and soft time windows (TPPQS), in which a firm needs to purchase products from a set of available markets and deliver the products to a set of customers.

Vehicles are available to visit the markets, which offer products at different prices and with different quantity discount schemes. Soft time windows are present for the markets and the customers, and earliness cost and tardiness may incur if a vehicle cannot arrive a market or a customer within the designated time interval. The environmental impact of transportation activities is considered. The objective of this research is to minimize the total cost, including vehicle-assigning cost, vehicle-traveling cost, purchasing cost, emission cost, earliness cost and tardiness cost, while meeting the total demand of the customers and satisfying all the constraints. A mixed integer programming (MIP) model and a genetic algorithm (GA) approach are proposed to solve the TPPQS.

The results show that both the MIP and the GA can obtain optimal solutions for small-scale cases, and the GA can generate near-optimal solutions for large-scale cases within a short computational time.

The proposed models can help firms increase the performance of customer satisfaction and provide valuable supply chain management references in the service industry.

The proposed models for TPPQS are novel and can facilitate firms to design their green traveling purchasing plans more effectively in today’s environmental conscious and competitive market.

Maintenance control plays a key role in achieving the stated objective of effectiveness and efficiency of the maintenance system. In a recent paper, Gits proposed a reference framework that guides in the design and structuring of maintenance control. The framework is conceptual in nature and its use in practice is limited. Poses Gits’ framework as a set of mathematical programming models. Extends some of Gits’ procedure for maintenance control, then outlines the required expansion in the maintenance management information system (MMIS) in order to provide the needed data to execute the models. The models provide operational plans and schedules ready for implementation.

Supplier selection in the supply chain network (SCN) has strategic importance and involves multiple factors. The multi-criteria nature of the problem coupled with environmental uncertainty requires several procedures and considerations. The issue of decision-making in selecting the best among various qualified suppliers remains the major challenge in the pharmaceutical industry. This study investigated the multi-criteria multi-supplier decision-making process and proposed a model for supplier selection problems based on mixed-integer linear programming.

The concept of principal component analysis (PCA) was used to reduce data dimensionality, and the four best criteria have been considered and selected. The result is subjected to decision-makers’ (DMs’) reliability test using the concept of a triangular fuzzy number (TFN). The importance of each supplier to each measure is established using fuzzy technique for order preference by similarity to an ideal solution approach, and the suppliers have ranked accordingly.

This study proposes a mixed integer linear programming model for supplier selection in a pharmaceutical company. The effectiveness of the proposed model has been demonstrated using a numerical example. The solution shows the model's applicability in making a sound decision in pharmaceutical companies in the space of reality. The model proposed is simple. Readily commercial packages such as LINDO/LINGO and GAMS can solve the model.

This research contributed to the systematic manner of supplier selection considering DMs’ value judgement under a fuzzy environment and is limited to the case study area. However, interested researchers can apply the study in other related manufacturing industries. However, the criteria have to be revisited to suit that system and might require varying ratings based on the experts' opinions in that field.

This work suggests more insights practically by considering a realistic and precise investigation based on a real-life case study of pharmaceutical companies with six primary criteria and twenty-four sub-criteria. The study outcome will assist organizations and managers in conducting the best decision objectively by selecting the best suppliers with their various standards and terms among many available contenders in the manufacturing industry.

In this paper, the authors attempted to identify the most critical attributes to be preserved by the top managers (DMs) while selecting suppliers in pharmaceutical companies. The study proposed an MILP model for supplier selection in the pharmaceutical company using fuzzy TOPSIS.

For many years, facilities location problems have attracted a great deal of attention in the literature. As a result, there is now a variety of methods for solving these problems. However, due to the recent interest, little research is found relating to the issues concerning international facilities location problems. Furthermore, in spite of the extensive modelling work done on facilities location, little modelling research exists on location problems. Provides a capacitated multi‐period, 0‐1 mixed integer programming formulation for the international facilities location problem and discusses its applications to an actual company case. This application is carried out to demonstrate not only how the model can be applied in practice but also to show its potential benefits when compared to other methods.