Multi-product Supply Research Articles

Optimization formulations for multi-product supply chain networks

We present optimization formulations for multi-product supply chain networks. The formulations use a general graph representation that captures dependencies between an arbitrary number of products, technologies, and transportation paths. We discuss how to use the framework to compute compromise solutions that resolve geographical and stakeholder conflicts. We present case studies in which we seek to design supply chains to collect and process organic waste from a large number of farms in the State of Wisconsin to mitigate point phosphorus and methane emissions.

Applying a hybrid transportation system to design an agile multi-product and multi-echelon dynamic supply chain

Making optimum decisions under complicated circumstances, requires using appropriate mathematical modelling techniques and optimisation methods. In many cases, supply and demand are different in principal. These major differences force producers to make various decisions for supplying required raw materials and meeting demands. Respecting the low operational and high strategic costs of applying the rail transport, it is highly recommended to use this method of transportation for the purpose of transporting huge load of materials/products in a centralised network. However, using vehicles and road transport is more suitable for small loads of materials/products in widespread networks. Current study is devoted to design an efficient hybrid transportation system and an agile multi-product supply chain. A mathematical model is presented in order to formulate the problem at hand. Numerical results demonstrate the validity of the presented model and the applied optimisation procedure in making optimum and applicable decisions. In fact, numerical results reveal the promising ability of the applied optimisation procedure confronting real-world situations.

Applying a hybrid transportation system to design an agile multi-product and multi-echelon dynamic supply chain

Applying a hybrid transportation system to design an agile multi-product and multi-echelon dynamic supply chain

Maximisation of total supply chain profit and minimisation of bullwhip effect in a multi-echelon supply chain network using particle swarm optimisation and genetic algorithm

The presence of numerous sources, nature of uncertainties and complex interrelationships among various entities make supply chain a complex network. Bullwhip effect is one of the major issues of complexity. This research intended to maximise profit as well as to reduce bullwhip effect in a supply chain by finding optimal forecasted sales quantities for each entity. A multi-product, multi-stage and multi-period supply chain model was developed considering previous market demands where the objective function was developed to maximise total supply chain profit. Later, the proposed model was applied to analyse a realistic case of supply chain network. Simulations were conducted using genetic algorithm and particle swarm optimisation to find optimal forecasted sales quantities and were then compared. Results revealed that total profit of the entire supply chain network significantly increased and the resulting optimal forecasted sales quantities reduced order variability, which consequently minimised the bullwhip effect in supply chain network.

Material flow optimisation in a multi-echelon and multi-product supply chain

This paper addresses a distribution problem in a multi-product, multi-echelon supply chain. We develop a mixed integer linear programming formulation that considers allocation of vehicles with varying capacities for the transportation of products between the stages of the supply chain. The cost of transportation includes the fixed and variable costs of using the vehicles. The proposed formulations are solved optimally up to certain sizes, and we propose a heuristic based on total opportunity penalty cost method to solve the large sized problems. These proposed solution procedure is tested over a set of hypothetical problem sets. The results indicate that the proposed heuristic algorithm yields solutions within 5% from the optimal solutions.

WCVaR-Based Risk Coordination Model for Multi-Product Supply

The paper develops a multi-product supply chain model where supplyproduction- sale integration is considered and the worst-case conditional value at risk (WCVaR) model is applied as the risk measure, and also provides a coordination strategy to minimize the supply chain risk. First, by analyzing the source demand of market in the supply chain, three WCVaR models consisting of three tiers—the supplier, the manufacturer and the retailer in the supply chain are proposed to measure the market risk. Then, a risk coordination model is proposed to cover the whole supply chain including producing, order, inventory and sales. Finally, the numerical results show the efficiency of the model in mitigating risks. And we make a summary of supply chain risk management strategies.

Optimal ordering policies in a multi-sourcing supply chain with supply and demand disruptions-a CVaR approach

In this study, we propose a conditional value at risk (CVaR) model for supply chain disruptions planning of a multi-agent, multi-product supply chain subject to supply and demand disruptions. Our focus is on building and comparing ordering policies under CVaR and expected cost criteria. The proposed formulation is illustrated through some numerical instances. The results present that the CVaR model shows a considerable difference in response policies compared to the expected cost model. Ordering quantities in response to supply and demand disruption are lower in the CVaR model than the expected cost model. In many instances, it is also seen that ordering quantities in response to disruptions tend to become lower when a decision maker becomes more risk-averse. It is expected that the proposed CVaR model would outperform to optimise the supply chain of an organisation, in particular, for the purpose of reducing the risk of high cost.

Material flow optimisation in a multi-echelon and multi-product supply chain

This paper addresses a distribution problem in a multi-product, multi-echelon supply chain. We develop a mixed integer linear programming formulation that considers allocation of vehicles with varying capacities for the transportation of products between the stages of the supply chain. The cost of transportation includes the fixed and variable costs of using the vehicles. The proposed formulations are solved optimally up to certain sizes, and we propose a heuristic based on total opportunity penalty cost method to solve the large sized problems. These proposed solution procedure is tested over a set of hypothetical problem sets. The results indicate that the proposed heuristic algorithm yields solutions within 5% from the optimal solutions.

A Three-Echelon Multi-Objective Multi-Period Multi-Product Supply Chain Network Design Problem: A Goal Programming Approach

In this paper, a multi-objective multi-period multi-product supply chain network design problem is introduced. This problem is modeled using a multi-objective mixed integer mathematical programming. The objectives are maximizing the total profit of logistics, maximizing service level, and minimizing inconsistency of operations. Several sets of constraints are considered to handle the real situations of three-echelon supply chains. As the optimum value of conflictive objective functions of the proposed model cannot be met concurrently, so a goal programming approach is used. An illustrative numerical example is provided to show the mechanism of proposed model and the solution procedure. In a numerical example, 1 manufacture, 2 warehouses, 2 distribution centers (DCs), and 2 types of final products are considered in a planning horizon consists of 3 time periods. Products are shipped from the manufacturer to warehouses and then are shipped from the two warehouses to two distribution centers. The distribution centers are the point from which the product are shipped to final consumers. The Model is coded using GAMS software on a Core i7 CPU, using 8GB of RAM with MS-Windows 8.0. The optimum design of supply chain, inventory level for warehouses and distributors, and amount of shipments between echelons are determined.

A large neighborhood search heuristic for supply chain network design

Many exact and approximate solution techniques have been used to solve facility location problems and, more generally, supply chain network design problems. Yet, the Large Neighborhood Search technique (LNS) has almost never been suggested for solving such problems, although it has proven its efficiency and flexibility in solving other complex combinatorial optimization problems. In this paper, we propose an LNS framework for solving a four-layer single period multi-product supply chain network design problem. One important feature of the model is that it includes inter-modality: the itinerary followed by the cargo from origin to destination may take several transportation modes. Moreover, several modes may compete on some arcs. Location decisions for intermediate facilities (e.g. plants and distribution centers) are determined by the LNS while transportation modes and product flow decisions are determined by a greedy heuristic. As a post-optimization step, linear programming is used to optimize product flows once the structure of the logistics network is fixed. Extensive experiments, based on randomly generated instances of different sizes and characteristics, show the effectiveness of the method compared with a state-of-the-art solver.

Uncertain Centralized/Decentralized Production-Distribution Planning Problem in Multi-Product Supply Chains: Fuzzy Mathematical Optimization Approaches

Complex and uncertain issues in supply chain result in integrated decision making processes in supply chains. So decentralized (distributed) decision making (DDM) approach is considered as a crucial stage in supply chain planning. In this paper, an uncertain DDM through coordination mechanism is addressed for a multi-product supply chain planning problem. The main concern of this study is comparison of DDM approach with centralized decision making (CDM) approach while some parameters of decision making are assumed to be uncertain. The uncertain DDM problem is modeled through fuzzy mathematical programming in which products’ demands are assumed to be uncertain and modeled using fuzzy sets. Moreover, a CDM approach is customized and developed in presence of fuzzy parameters. Both approaches are solved using three fuzzy mathematical optimization methods. Hence, the contribution of this paper can be summarized as follows: 1) proposing a DDM approach for a multi-product supply chain planning problem; 2) Introducing a coordination mechanism in the proposed DDM approach in order to utilize the benefits of a CDM approach while using DDM approach; 3) Modeling the aforementioned problem through fuzzy mathematical programming; 4) Comparing the performance of proposed DDM and a customized uncertain CDM approach on multiproduct supply chain planning; 5) Applying three fuzzy mathematical optimization methods in order to address and compare the performance of both DDM and CDM approaches. The results of these fuzzy optimization methods are compared. Computational results illustrate that the proposed DDM approach closely approximates the optimal solutions generated by the CDM approach while the manufacturer’s and retailers’ decisions are optimized through a coordination mechanism making lasting relationship.

Global sensitivity analysis and aggregation of risk in multi-product supply chain networks

Manufacturing firms manage complex supply chain networks which are exposed to a plethora of hazard events. An essential part of the risk management process is the calculation of the stand-alone risk exposures of the product-specific supply chains, but also of the entire multi-product system. In this paper, first, a global sensitivity analysis of the statistical supply chain risk model is conducted. This method helps the decision-makers to understand the risk of the model they are using. Second, a methodology for risk aggregation in multi-product supply chain networks is proposed. The real-world data is used to analyse and validate the model. Supply chain managers equipped with the proposed method will better cope with the risk in supply chains for different product configurations.

An integrated approach to solve a robust forward/reverse supply chain for short lifetime products

An integrated robust supply chain problem for short lifetime products is developed.A cyclic feedback procedure is proposed in between location and allocation models.A new method is developed to linearize the mixed integer nonlinear programming model.DE outperforms TS algorithm at the expense of longer running time. Supply chain management plays a key role in optimizing manufacturing costs in competitive markets. In this paper, a multi period, multi product, multi echelon and capacitated supply chain problem for short lifetime products was solved using both exact method and metaheuristic algorithms. The considered echelons in a forward/reverse supply chain network design include suppliers, hybrid production-inspection centers, hybrid warehouse-collection centers, retailers, disposal centers and recovery centers. To tackle both strategic and tactical nature of the problem and due to its complexity, the location problem is first solved using an exact method in which strategic decisions are made aiming to minimize the location costs. Then the allocation problem is solved using both exact and metaheuristic algorithms, namely Tabu Search and Differential Evolution, in which based on the results obtained from the location problem, the profit is maximized and tactical decisions are made. A cyclic feedback procedure is proposed in between the location and allocation models to obtain the best solution. The allocation model is linearized using a new method and to handle the uncertainty, a robust mixed integer programming model is developed which can retain the linearity of the model. The computational results confirm the effectiveness of the exact method for the location problem while testifies the proposed algorithms can obtain effective solutions compared with that of the exact solutions for the allocation problem in both deterministic and uncertain environment. In addition, the results show that in terms of preciseness and convergence, the proposed Differential Evolution algorithm outperforms the other algorithm.

Multi-echelon Supply Chain Flexibility Enhancement Through Detecting Bottlenecks

This study suggests a supply chain design deploying a novel idea from production planning. The idea of capacity bottlenecks is used to improve flexibility in a multi-echelon multi-product supply chain. We suggest an optimization model that focuses on optimal capacity allocations to bottleneck points in order to enhance overall flexibility. The proposed mixed-integer linear programming model minimizes the total cost of facility establishment as well as their utilization and transportation cost. The performance of suggested model is investigated by several test problems with uncertainty in demand, cost, capacity, and product specifications. The results indicate the superiority of the suggested model to the previous flexibility formulation method. According to the numerical results, the proposed model decreases the total supply chain cost by up to 16 % on average. Another advantageous feature of the proposed model is its capability of solving previously insolvable test problems by optimizing flexibility levels.

Determining an optimal hierarchical forecasting model based on the characteristics of the data set: Technical note

AbstractThe efficient flow of goods and services involves addressing multilevel forecast questions, and careful consideration when aggregating or disaggregating hierarchical estimates. Assessing all possible aggregation alternatives helps to determine the statistically most accurate way of consolidating multilevel forecasts. However, doing so in a multilevel and multiproduct supply chain may prove to be a very computationally intensive and time‐consuming task. In this paper, we present a new, two‐level oblique linear discriminant tree model, which identifies the optimal hierarchical forecast technique for a given hierarchical database in a very time‐efficient manner. We induced our model from a real‐world dataset, and it separates all historical time series into the four aggregation mechanisms considered. The separation process is a function of both the positive and negative correlation groups' variances at the lowest level of the hierarchical datasets. Our primary contributions are: (1) establishing a clear‐cut relationship between the correlation metrics at the lowest level of the hierarchy and the optimal aggregation mechanism for a product/service hierarchy, and (2) developing an analytical model for personalized forecast aggregation decisions, based on characteristics of a hierarchical dataset.

A design model and a production–distribution and inventory planning model in multi-product supply chain networks

Supply chain network (SCN) design implicates decision-making at a strategic level. That includes selecting the right suppliers and determining the number and the location of plants, distribution centres and retailers. An apt design model of the supply chain is imperative for the proper function of the supply chain and consequently for making better operational decisions in an attempt of a continuous improvement. In this paper, we propose two models. The first model is a mixed-integer linear programming model which is concerned with the SCN design problem, whereas the second operational model is a mixed-integer non-linear programming model in respect to the production–distribution and inventory planning problem in a supply chain network. The number of customers and suppliers as well as their demand and capacities are assumed to be known in both models. Two steady-state genetic algorithms were implemented in MATLAB in order to solve both the design and the operational model. The results were compared with GAMS. Some examples were devised in order to demonstrate potential ways of use for the designer of the supply chain network, as well as for the supply chain manager.

Two Echelon Supply Chain Integrated Inventory Model for Similar Products: A Case Study

The purpose of this paper is to develop a mathematical model towards minimization of total cost across echelons in a multi-product supply chain environment. The scenario under consideration is a two-echelon supply chain system with one manufacturer, one retailer and M products. The retailer faces independent Poisson demand for each product. The retailer and the manufacturer are closely coupled in the sense that the information about any depletion in the inventory of a product at a retailer’s end is immediately available to the manufacturer. Further, stock-out is backordered at the retailer’s end. Thus the costs incurred at the retailer’s end are the holding costs and the backorder costs. The manufacturer has only one processor which is time shared among the M products. Production changeover from one product to another entails a fixed setup cost and a fixed set up time. Each unit of a product has a production time. Considering the cost components, and assuming transportation time and cost to be negligible, the objective of the study is to minimize the expected total cost considering both the manufacturer and retailer. In the process two aspects are to be defined. Firstly, every time a product is taken up for production, how much of it (production batch size, q) should be produced. Considering a large value of q favors the manufacturer while a small value of q suits the retailers. Secondly, for a given batch size q, at what level of retailer’s inventory (production queuing point), the batch size S of a product be taken up for production by the manufacturer. A higher value of S incurs more holding cost whereas a lower value of S increases the chance of backorder. A tradeoff between the holding and backorder cost must be taken into consideration while choosing an optimal value of S. It may be noted that due to multiple products and single processor, a product ‘taken’ up for production may not get the processor immediately, and may have to wait in a queue. The ‘S’ should factor in the probability of waiting time in the queue.

Guided chemotaxis-based bacterial colony algorithm for three-echelon supply chain optimisation

On the base of the existing research study, a multi-period, multi-product, multi-supplier, single-manufacture, and multi-distributor supply chain model is considered in the paper. In the three-echelon model, a variety of decision-making activities involved in the procurement, production and distribution process are integrated at the operational level, giving rise to the non-deterministic polynomial-time hard computational complexity for model optimisation. For tackling the difficult model, this paper proposes a new optimisation method called guided chemotaxis-based bacterial colony algorithm, characterised by centre learning communication mechanism. More specifically, centre learning communication mechanism, where all the bacteria are enforced to learn towards the centre position of the swarm, is designed for the global exploration ability of algorithm. Chemotaxis, which guides the bacterium to fine-tune the solution in an increasingly favourable fitness landscape, is used to enhance the local exploitation ability of algorithm. Numerical experiments on a variety of simulated scenarios show the effectiveness and efficiency of the proposed algorithm in terms of both quality solution and computational time, by comparing it with some existing state-of-the-art solution approaches.

An integrated model for strategic supply chain design: Formulation and ABC-based solution approach

It presents an integrated model for supply chain design.It considers three stages and their interactions in the model.It develops an ABC-based solution approach.It demonstrates the efficiency of the ABC-based approach. This study develops a mixed integer nonlinear programming (MINLP) model to design supply chains. In view of the limitations of many available strategic supply chain design models, this model involves three major supply chain stages, including procurement, production, and distribution, and their interactions; it takes into account bill of materials constraints for modeling complex supply chain inter-relationships. In addition, in accordance with the fact that companies nowadays develop product families, our model addresses multi-product supply chain design to respond to diverse customer requirements. Recognizing their importance, this study identifies and formulates constraints related to facility pairwise relationships and supplier priority along with the classical constraints from the available literature. To efficiently solve such a highly constrained, large scale MINLP model, we develop an approach based on an artificial bee colony (ABC) algorithm. Bicycle design and production is used to demonstrate the potential of the MINLP model for designing supply chains and the performance of the ABC-based solution approach in solving the model. The proposed model and solution approach can be considered as two fundamental components of an expert system in the broad sense. Thus, this study is expected to stimulate more future research on the development of practical expert systems for designing supply chains.

Impacts of quality and transportation on environmental costs in multi-stage multi-product green supply chain

An increase in environmental pollution and costs of carbon dioxide (CO2) emission and subsequent increase in the supply chain's general costs all have contributed to rising attention toward these issues. Transportation and the quality of the raw materials purchased are among the most important factors affecting the environmental pollution of production chains. This paper introduces a bi-objective multi-stage multi-product mixed integer nonlinear programming (MINLP) model of green supply chain which considers the effect of different vehicles and quality of raw materials on the chain's total costs and carbon dioxide emission. Finally a numerical example explained and solved through e-constraint approach.