A mixed integer programming model for a closed-loop supply-chain network

In this paper, a new mixed integer mathematical model for a closed-loop supply-chain network that includes both forward and reverse flows with multi-periods and multi-parts is proposed. The proposed model guarantees the optimal values of transportation amounts of manufactured and disassembled products in a closed-loop supply chain while determining the location of plants and retailers. Finally, computational results are presented for a number of scenarios to show and validate the applicability of the model.     

Closed loop supply chain network design and optimisation using fuzzy mixed integer linear programming model

Owing to the revolution in sustainable and green manufacturing the production planning and network design of closed loop supply chain concept has got the attention of researchers and managers. In this paper, a multi-product, multi-facility capacitated closed-loop supply chain framework is proposed in an uncertain environment including reuse, refurbish, recycle and disposal of parts. The uncertainty related to demand, fraction of parts recovered for different product recovery processes, product acquisition cost, purchasing cost, transportation cost, processing, and set-up cost is handled with fuzzy numbers. A fuzzy mixed integer linear programming model is proposed to decide optimally the location and allocation of parts at each facility and number of parts to be purchased from external suppliers in order to maximise the profit of organisation. The proposed solution methodology is able to generate a balanced solution between the feasibility degree and degree of satisfaction of the decision maker. The proposed model has been tested with an illustrative example.     

Blood supply chain network design considering blood group compatibility under uncertainty

This paper addresses the design of a blood supply chain (SC) network considering blood group compatibility. To this aim, a bi-objective mathematical programming model is developed which minimises the total cost as well as the maximum unsatisfied demand. Due to uncertain nature of some input parameters, two novel robust possibilistic programming models are proposed based on credibility measure. The data of a real case study are then used to illustrate the applicability and performance of the proposed models as well as validating the proposed robust possibilistic programming approach. The obtained results show the superiority of the developed models and significant cost savings compared to current existed blood SC network.     

Reverse supply chain optimisation with disassembly line balancing

Due to responding environmental issues, conforming governmental legislations and providing economic benefits, there has been a growing interest in recycling activities through the supply chains. Reverse supply chain (RSC) optimisation problem has a great potential as an efficient tactic to achieve this goal. While disassembly, one of the main activities in RSC, enables reuse and recycling of products and prevents the overuse, disassembly line balancing problem involves determination of a line design in which used products are partially/completely disassembled to obtain available components. The aim of this study is to optimise a RSC, involving customers, collection/disassembly centres and plants, that minimises the transportation costs while balancing the disassembly lines, which minimises the total fixed costs of opened workstations, simultaneously. A non-linear mixed-integer programming model, which simultaneously determines: (i) optimal distribution between the facilities with minimum cost, (ii) the number of disassembly workstations that will be opened with minimum cost, (iii) the cycle time in each disassembly centre and (iv) optimal assignment of tasks to workstations, is developed. A numerical example is given to illustrate the applicability of the proposed model. Different scenarios have been conducted to show the effects of sensitivity analyses on the performance measures of the problem.     

Multi-objective analysis of an integrated supply chain scheduling problem

We study the problem of minimising the total weighted tardiness and total distribution costs in an integrated production and distribution environment. Orders are received by a manufacturer, processed on a single production line, and delivered to customers by capacitated vehicles. Each order (job) is associated with a customer, weight (priority), processing time, due time, and size (volume or storage space required in the transportation unit). A mathematical model is presented in which a number of weighted linear combinations of the objectives are used to aggregate both objectives into a single objective. Because even the single objective problem is NP-hard, different heuristics based on a genetic algorithm (GA) are developed to further approximate a Pareto-optimal set of solutions for our multi-objective problem.     

An integer linear programming model to support customer-driven material planning in synchronised,multi-tier supply chains

This paper describes an integer linear programming model conceived as an alternative to a traditional material requirements planning (MRP) system for extending the concept of supply chain synchronisation upstream in a multi-tier supply chain. In this model, we assume there is an incumbent application for transmitting original equipment manufacturer (OEM) requirements to first-, second- and third-tier suppliers. The proposed model is regarded as being embedded within a web-enabled, multi-tier, supply chain information system that provides the application for transmitting the production requirements. The principal motivation for having second- and third-tier suppliers that are synchronised with OEM and first-tier activity is the significant inventory, lead time and responsiveness gains that can potentially be achieved. Here, inventory is considered as a whole across a supply chain, and stock-outs are prohibited for the first-tier supplier. For illustration purposes, an example based on a real, automotive case study is provided. The model results proved better in terms of inventory and bullwhip reduction than those found in a previous simulation-based approach. Also, a comparison of the proposed case results with those of a conventional MRP application is provided.     

Multi-objective resource assignment problem in a product-driven supply chain using a Taguchi-based DNA algorithm

This paper conceptualises the integration of tangible and intangible factors into the design consideration of a resource assignment problem for a product-driven supply chain. The problem is formulated mathematically as a multi-objective optimisation model to maximise the broad objectives of profit, ahead of time of delivery, quality, and volume flexibility. Product characteristics are associated with the design requirements of a supply chain. Different types of resources are considered, each differing in its characteristics, thereby providing various alternatives during the design process. The aim is to design integrated supply chains that maximise the weighted sum of the objectives, the weights being decided by the desired product characteristics. The problem is solved through the proposed Taguchi-based DNA algorithm that draws its traits from random search optimisation and the statistical design of experiments. In order to minimise the effect of the causes of variations, the fundamental Taguchi method is integrated with the DNA-metaheuristic. The suggested methodology exhibits the global exploration capability to exploit the optimal or near-optimal DNA strands with a faster convergence rate. In order to authenticate the performance of the proposed solution methodology, a set of ten problem instances are considered and the results obtained are compared with that of the basic DNA, particle swarm optimisation (PSO) and its variant (PSO — time varying acceleration coefficients). The results demonstrate the benefits of the proposed algorithm for solving this type of problem.     

Monolithic versus hierarchical approach to integrated scheduling in a supply chain

The two approaches, monolithic and hierarchical, with a set of mixed integer programming formulations are proposed and compared for multi-objective integrated scheduling in a customer driven supply chain. The supply chain consists of multiple manufacturers (suppliers) of parts, a single producer of finished products and a set of customers who generate final demand for the products. Each supplier has a number of identical production lines in parallel for the manufacture of parts, and the producer has a flexible assembly line for assembly of products. Given a set of orders, the problem objective is to determine which orders are to be provided with parts by each supplier, find a schedule for the manufacture of parts by each supplier and for the delivery parts from each supplier to the producer, and find a schedule for the assembly of products for each order by the producer, such that a certain performance measure of the supply chain is optimised. The selection of the parts supplier for each order is combined with due date setting for some orders, subject to the suppliers and the producer available capacity. Different objective functions are considered that take into account both customer service level and total manufacturing, delivery and production cost. Numerical examples are presented that are modelled by real-world integrated scheduling in a customer driven supply chain of high-tech products, and some computational results are reported to compare the two approaches.     

Optimisation of the broiler production supply chain

In this paper, we propose a mixed integer programming (MIP) model for the Chicken Flock Sizing, Allocation and Scheduling Problem (CFSASP), which is an important planning problem in the broiler production supply chain. To solve the CFSASP efficiently, two variants of rolling horizon heuristics (RHHs) have been developed and applied on the case of a Norwegian broiler production company. Computational results show that the RHHs successfully obtain high-quality solutions within a reasonable time. The value of optimisation is verified through comparison with the case company's plans, where the solutions from optimisation outperforms the current solutions. Sensitivity analyses are also conducted to provide managerial insights regarding certain strategic decisions, such as how many and which days to use for hatching of chickens. Due to the promising results, the case company is now implementing an optimisation-based decision support system based on the MIP model and solution methods shown in this paper.     

A strategic model for exact supply chain network design and its application to a global manufacturer

This paper presents a comprehensive model that captures significant strategic decisions involved in designing or redesigning high-performance supply chains from the perspective of the manufacturer. The problem considers deterministic demand by multiple clients, for multiple products, over the periods of a long-term horizon. The design decisions involve selection of suppliers, establishment or resizing of production facilities and distribution centres, possible subcontracting of related activities, and selection of transportation modes and routes. The problem is formulated by a Mixed Integer Linear Programming model. Its objective is to minimise the overall costs associated with procurement, production, inventory, warehousing, and transportation over the design horizon. Appropriate constraints model the complex relationships among the links of the supply chain. The proposed model has been applied to a large case study of a global manufacturing firm, providing valuable insights into the transformation of the firm’s current supply chain network, as well as into the potential of the proposed approach.     

An optimisation model for purchase,production and distribution in fish supply chain – a case study

This paper presents an optimisation model for spawn purchase, fish culturing production process and harvested fish distribution in a fish supply chain. Due to the complexity and variety of real-world fish supply chains, the model is built based on a case study for a real trout fish farm to illustrate the methodology on how to incorporate influential factors from both warm chain and cold chain. Warm chain mainly considers the biological factors while fish is alive and cold chain mainly considers the economic factors after fish is ready for harvest, harvested, and processed. The model seeks to improve the trout farm production planning to help decision-making on spawn purchase quantity, the best time to harvest fish, and the farming periods. In addition, the model adopts a customer classification method in distribution planning that is able to prioritise the delivery of fresh fish to the most profitable customers. A mixed integer linear programming (MILP) model was developed to maximise the total profit. The experimental results demonstrate that farmers’ total profit can be increased after applying the proposed optimisation strategy, compared to the traditional farming strategy.     

A comparison of mixed integer programming formulations of the capacitated lot-sizing problem

We propose a novel mixed integer programming formulation for the capacitated lot-sizing problem with set-up times and set-up carryover. We compare our formulation to two earlier formulations, the Classical and Modified formulations, and a more recent formulation due to Suerie and Stadtler. Extensive computational experiments show that our formulation consistently outperforms the Classical and Modified formulations in terms of CPU time and solution quality. It is competitive with the Suerie–Stadtler (S&S) formulation, but outperforms all other formulations on the most challenging instances, those with low-capacity slack and a dense jobs matrix. We show that some of the differences in the performance of these various formulations arise from their different use of binary variables to represent production or set-up states. We also show that the LP relaxation of our Novel formulation provides a tighter lower bound than that of the Modified formulation. Our experiments demonstrate that, while the S&S formulation provides a much tighter LP bound, the Novel formulation is better able to exploit the intelligence of the CPLEX solution engine.     

Fuzzy scheduling of a build-to-order supply chain

The overwhelming majority of the literature in the area of supply chain planning and scheduling considers the traditional make-to-stock (MTS) environment. However, manufacturers of assembled products such as cars, computers, furniture, etc. adopt the build-to-order supply chain (BOSC) to become agile in a mass customization process in order to meet diversified customer requirements. In this paper we propose an integrated production–distribution planning model for a multi-echelon, multi-plant and multi-product supply chain operating in a build-to-order (BTO) environment. The uncertainties associated with estimation of the various operational cost parameters are represented by fuzzy numbers. The BOSC scheduling model is thus constructed as a mixed-integer fuzzy programming (MIFP) problem with the goal of reducing the overall operating costs related to component fabrication, procurement, assembling, inspection, logistics and inventory, while improving customer satisfaction by allowing product customization and meeting delivery promise dates at each market outlet. An efficient compromise solution approach by transforming the problem into an auxiliary multi-objective linear programming model is also suggested.     

Large neighbourhood search based on mixed integer programming and ant colony optimisation for car sequencing

We investigate the problem of scheduling a sequence of cars to be placed on an assembly line. Stations, along the assembly line install options (e.g. air conditioning), but have limited capacities, and hence cars requiring the same options need to be distributed far enough apart. The desired separation is not always feasible, leading to an optimisation problem that minimises the violation of the ideal separation requirements. In order to solve the problem, we use a large neighbourhood search (LNS) based on mixed integer programming (MIP). The search is implemented as a sliding window, by selecting overlapping subsequences of manageable sizes, which can be solved efficiently. Our experiments show that, with LNS, substantial improvements in solution quality can be found.     

A fuzzy goal programming approach for green supply chain optimisation under activity-based costing and performance evaluation with a value-chain structure

Supply chain operation with sustainable consideration has become an increasingly important issue in recent years. However, the decision framework with integrated costing and performance evaluation for green supply chain (GSC) has not been well developed so far in the literature. For this reason, this paper is aimed to propose a fuzzy goal programming (FGP) approach that integrates activity-based costing (ABC) and performance evaluation in a value-chain structure for optimal GSC supplier selection and flow allocation. The FGP approach is particularly suitable for such a decision model which includes flexible goals, financial and non-financial measures, quantitative and qualitative methods, multi-layer structure, multiple criteria, multiple objectives, and multiple strategies. An activity-based example of structural GSC with relevant costs and performances is presented for computing the composite performance indices of the GSC suppliers. A green supply chain of a mobile phone is used as an illustrative case. Several objective structures and their results are compared. The sensitivity analyses show that pure maximisation of financial profit can achieve the highest profit level, which also has the largest Euclidean distance to the multiple aspiration goals. In order to determine the final objective structure, an analytic hierarchy process (AHP) is used. This paper provides a new approach to assess and control a complex GSC based on value-chain activities, and obtain a more precise solution. The establishment of this GSC model not only helps decision-makers to monitor GSC comprehensive performance but also can facilitate further improvement and development of GSC management.     

The impact of supply chain disruption on the closed-loop supply chain configuration profit: a study of sourcing policies

A closed-loop supply chain configuration (CLSCC) encompasses the decisions related to the optimal selection of options at each stage of a closed-loop supply chain (CLSC) for the introduction and reconstruction of new products. The extant literature ignores the impact of supply chain disruptions on CLSCC. An attempt is made to fill this gap in this study. Thus, an integrated multi-sourcing CLSCC optimisation model for new and reconstructed products is developed. The optimisation model presented is a mixed-integer nonlinear programming (MINLP) model. Based on a real-world case study of an auto-parts manufacturer in India presented, a comprehensive set of computational experiments, scenario analyses are conducted. The key finding/observation that resulted from our computational experiments is that multi-sourcing generates higher net present value of total profit compared to single sourcing under the risk of supply chain disruption. Several other observations and managerial insights are drawn from computational experiments, and scenario analyses. Firms interested in configuring their CLSC under the risk of supply chain disruption may use the study's outcomes to understand the profit impact of various CLSCC parameters, individually and in combination.     

A decision support framework for global supply chain modelling: an assessment of the impact of demand,supply and lead-time uncertainties on performance

We developed a decision support framework for a global manufacturer of specialty chemicals to study the relative impact of demand, supply and lead-time uncertainties on cost and customer service performance. Our approach combines optimisation and simulation methodologies as follows: mathematical models provide optimal plans via a novel approach to the supply chain planning mechanism of the Company. Simulation models execute the supply chain plans so as to allow the examination of the outcomes under the various sources of uncertainty. The iterative use of optimisation and simulation methodologies allows the user the benefit of obtaining optimal solutions while revealing the impact of uncertainties on system performance. Our results indicate that demand uncertainty has the greatest negative impact on performance for the supply chain that we modelled in this study, emphasising the importance of effective forecasting. The relative importance of supply and lead-time uncertainties varies according to the performance measures. While our results are valid for the specific supply chain and the operating environment we modelled, our study emphasises the importance of the ability to model supply chains realistically to obtain valid and useful results.     

A real option-based supply chain project evaluation and scheduling method

Supply chain departments spend their time managing numerous projects that will improve and maintain their supply chains. Recent literature has most frequently described the content of these projects and their scheduling but neglected to include risk and uncertainty in the expected cost, profits and time durations of these projects. In this article, we have introduced real option valuation (ROV) to supply chain project scheduling as a flexible method to quantify those risks. Our proposed two-step framework links ROV to all relevant constraints of a multi-project set-up by binary fuzzy goal programming. We applied the framework to a real-life case study data of 21 projects that were facing numerous risks and resource constraints. The results show how scheduling performance improved in comparison to methods ignoring risk and uncertainty (e.g. net present value-based scheduling). For validation we conducted hypothesis tests and sensitivity analysis, and provide an in-depth discussion. The findings contribute to research and practice by capturing project-related risks and managerial flexibilities in general and in supply chains in particular.     

Biomass feedstock supply chain design – a taxonomic review and a decomposition-based methodology

In this paper, we present a taxonomic review of the literature devoted to the use of operations research approaches for the design and operation of biomass feedstock supply chains (BFSCs). A total of 185 publications that have appeared from 1989 to 2017 are classified based on (1) the embedded optimisation subproblems; (2) the modelling methodologies used for their formulations; and (3) the methods employed for their solution. Our objective of using this classification scheme is to highlight the presence of some useful substructures in a BFSC problem that can, then, be exploited in developing its solution procedure. We illustrate this idea on some generic BFSC problems and present a Dantzig–Wolfe decomposition-based methodology for developing customised approaches to effectively tackle these difficult and large-sized BFSC problems. Finally, we suggest several promising future research directions.