Multi-period Supply Chain Network Research Articles

A multi-product and multi-period supply chain network design problem with price-sensitive demand and incremental quantity discount

Demand is an important factor in supply chain network design (SCND). Among the many factors that affect demand, the impact of price cannot be underestimated. This study, for the first time, provides enterprises with direct multi-period pricing and demand decision solutions in SCND by simultaneously considering the impact of price-sensitive demand and incremental quantity discounts on the network. In this way, a mixed-integer nonlinear programming model is established based on the relationships between price and demand functions to maximize the overall profit of the supply chain. Due to the nonlinear characteristics of the model, this study proves the existence of the optimal solution of the problem and the feasibility of implementing the following two algorithms by analyzing the nature of the problem. The first algorithm is based on the second-order cone programming (SOCP) method, and the second algorithm is based on the outer-approximation method. The results of numerical experiments at different scales show that the SOCP method can obtain the optimal solution for small and medium-scale experiments. In contrast, the outer-approximation method can find approximate optimal solutions within a reasonable time for large-scale experiments. The results confirm that considering incremental quantity discount can significantly enhance the profitability of supply chain networks in long-term planning. Finally, some future research directions in the field of SCND are discussed.

Designing a reliable aggregate production planning problem during the disaster period

The purpose of this research is to introduce a Bi-Objective (BO) model for dealing with Aggregate Production Planning (APP) for a multi-product and multi-period Supply Chain Network (SCN) that incorporates multiple suppliers, factories, and demand points. One of the goals of the model is to minimize the total cost of this network during the disaster period. The other goal is to account for probabilistic lead times to maximize the minimum level of producers' reliability during the COVID-19 pandemic. They are done to ameliorate the system's performance and improve the reliability of production plans. Finally, considering that the mentioned problem is NP-hard, a Multi-Objective Imperialist Competitive Algorithm (MOICA) based on Pareto is used to solve the proposed model, and a Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is also utilized to measure the performance of the mentioned algorithm. The generated experimental problems' results demonstrate the proposed algorithm's power in finding Pareto solutions. According to innovation, this is the first paper on these topics considering the conditions of the COVID-19 disaster.

Customer Prioritization Integrated Supply Chain Optimization Model with Outsourcing Strategies.

Pre-COVID-19, most of the supply chains functioned with more capacity than demand. However, COVID-19 changed traditional supply chains' dynamics, resulting in more demand than their production capacity. This article presents a multiobjective and multiperiod supply chain network design along with customer prioritization, keeping in view price discounts and outsourcing strategies to deal with the situation when demand exceeds the production capacity. Initially, a multiperiod, multiobjective supply chain network is designed that incorporates prices discounts, customer prioritization, and outsourcing strategies. The main objectives are profit and prioritization maximization and time minimization. The introduction of the prioritization objective function having customer ranking as a parameter and considering less capacity than demand and outsourcing differentiates this model from the literature. A four-valued neutrosophic multiobjective optimization method is introduced to solve the model developed. To validate the model, a case study of the supply chain of a surgical mask is presented as the real-life application of research. The research findings are useful for the managers to make price discounts and preferred customer prioritization decisions under uncertainty and imbalance between supply and demand. In future, the logic in the proposed model can be used to create web application for optimal decision-making in supply chains.

Multiperiod supply chain network dynamics under investment in sustainability, externality cost, and consumers’ willingness to pay

This paper analyzes the multiperiod effects of a multi-tier supply chain network's economic, social, and environmental decision-making. The network consists of suppliers, manufacturers, and retailers who are multicriteria decision-makers. They are constrained by externality costs in taxation and consumers' preferences and willingness to pay for sustainable products. We develop an optimization model that allows us to investigate the interplay of different decision-makers and to compute the resultant network equilibrium pattern of productions, transactions, inventory levels, prices, and sustainability levels in the network over the multiperiod planning horizon. The numerical study simulates and analyzes the effects of consumers' willingness to pay, externality cost, production capacity, NPV (net present value) discount rate, sustainability investment, and the structure of the supply chain network, on the economic, social, and environmental sustainability.

A Multiperiod Supply Chain Network Optimization Model with Investments in Labor Productivity Enhancements in an Era of COVID-19 and Climate Change

We are living in a very challenging time in history with the COVID-19 pandemic upon us plus the impacts of climate change now being notable with the frequency of various disasters increasing as well as their impacts. Nevertheless, products still must be produced, transported, and consumed in order to sustain humanity, and labor has revealed itself to be a critical resource in supply chain networks. In this paper, we construct the first multiperiod supply chain network model, which captures labor associated with the various supply chain network activities of production, transportation, storage over time, and distribution, and also includes link labor productivity enhancements that allow for investments in enhanced safety and health of the workers. We utilize a net present value (NPV) approach with the optimization model being formulated and solved as a variational inequality problem. We report the complete input and solution results for a series of numerical examples in terms of product flows, labor required, wages, as well as link labor productivity enhancements. We then further illustrate the relevance of the framework by conducting sensitivity analysis. We find that investing in link labor productivity can benefit workers also in terms of higher wages earned and the firm in terms of an increase in the optimal value of its objective function represented by the NPV, provided that consumers are aware of and responsive to such investments. This work adds to the literature on the integration and extension of concepts of operations research and economics in order to provide deeper insights into highly relevant aspects of supply chains during this time of their expanded importance.

A bi-objective production-distribution problem in a supply chain network under grey flexible conditions

One of the main topics discussed in a supply chain is the production-distribution problem. Producing and distributing the products plays a key role in reducing the costs of the chain. To design a supply chain, a network of efficient management and production-distribution decisions is essential. Accordingly, providing an appropriate mathematical model for such problems can be helpful in designing and managing supply chain networks. Mathematical formulations must be drawn close to the real world due to the importance of supply chain networks. This makes those formulations more complicated. In this study, a novel multi-objective formulation is devised for the production-distribution problem of a supply chain that consists of several suppliers, manufacturers, distributors, and different customers. Also, a Mixed Integer Linear Programming (MILP) mathematical model is proposed for designing a multi-objective and multi-period supply chain network. In addition, grey flexible linear programming (GFLP) is done for a multi-objective production-distribution problem in a supply chain network. The network is designed for the first time to cope with the uncertain nature of costs, demands, and capacity parameters. In this regard, due to the NP-hardness and complexity of problems and the necessity of using meta-heuristic algorithms, NSGA-II and Fast PGA algorithm are applied and compared in terms of several criteria that emphasize the quality and diversity of the solutions.

The impacts of retailers' regret aversion on a random multi-period supply chain network

<p style='text-indent:20px;'>Most current studies on the equilibrium decision-makings of a supply chain network (SCN) consider only completely rational retailers who always try to maximize their expected profits under the situations that demands are random. However, many evidences show that a retailer wants to choose the decision-making involving random demand which provides him with minimum regret. In this paper, we consider the impacts of retailers' anticipated regret aversion and experiential regret aversion on the equilibrium decision-makings of a random SCN with multiple production periods. Due to the random demand, the decision-makings of retailers are influenced not only by their anticipated regret, but also by their experiential regret after they have encountered bad or good experiences during past periods. The equilibrium conditions of the model are established. A numerical example is solved to illustrate the benefit of retailers obtained by considering their regret-averse behaviors. Moreover, it is found that retailers should consider their anticipated regret aversion or experiential regret aversion according to different situations of the demand markets.</p>

Hybrid meta-heuristic algorithms for a supply chain network considering different carbon emission regulations using big data characteristics

Big data (BD) approach has significantly impacted on the development and expansion of supply chain network management and design. The available problems in the supply chain network (SCN) include production, distribution, transportation, ordering, and inventory holding problems. These problems under the BD environment are challenging and considerably affect the efficiency of the SCN. The drastic environmental and regulatory changes around the world and the rising concerns about carbon emissions have increased the awareness of customers regarding the carbon footprint of the products they are consuming. This has enforced supply chain managers to change strategies to reframe carbon emissions.. The decisions such as an optimization of the suitable network of the proper lot sizes can play a crucial role in minimizing the whole carbon emissions in the SCN. In this paper, a new integrated production–transportation–ordering–inventory holding problem for SCN is developed. In this regard, a mixed-integer nonlinear programming (MINLP) model in the multi-product, multi-level, and multi-period SCN is formulated based on the minimization of the total costs and the related cost of carbon emissions. The research also uses a chance-constrained programming approach. The proposed model needs a range of real-time parameters from capacities, carbon caps, and costs. These parameters along with the various sizes of BD, namely velocity, variety, and volume, have been illustrated. A lot-sizing policy along with carbon emissions is also provided in the proposed model. One of the important contributions of this paper is the three various carbon regulation policies that include carbon capacity-and-trade, the strict capacity on emission, and the carbon tax on emissions in order to assess the carbon emissions. As there is no benchmark available in the literature, this study contributes toward this aspect by proposing two hybrid novel meta-heuristics (H-1) and (H-2) to optimize the large-scale problems with the complex structure containing BD. Hence, a generated random dataset possessing the necessary parameters of BD, namely velocity, variety, and volume, is provided to validate and solve the suggested model. The parameters of the proposed algorithms are calibrated and controlled using the Taguchi approach. In order to evaluate hybrid algorithms and find optimal solutions, the study uses 15 randomly generated data examples having necessary features of BD and T test significance. Finally, the effectiveness and performance of the presented model are analyzed by a set of sensitivity analyses. The outcome of our study shows that H-2 is of higher efficiency.

Multi-stage, multi-product and multi-period milk supply chain network design: a case of coastal region of Odisha

Due to the complexity of supply chain networks in today’s business environment, it is important to consider several strategic planning decisions along with the classical location-allocation decisions to achieve an integrated system. In this paper, a milk supply chain network design (SCND) problem of coastal region Odisha is considered. The proposed model is focussed on multi-stage, multi-product and multi-period supply chain network design of milk of a dairy industry. The network design includes the strategic decision-making approach of influence area, order quantity, replenishment cycle time, preservation factor and number of proposed distribution centre of milk products. This supply chain network design generic model of the milk products is developed as a mixed integer non-linear programming (MINLP) model. It is solved by using piecewise nonlinear optimization approach for location-allocation decisions of the clusters. The sensitivity analysis is also conducted to check the importance and influence of the model parameters on total supply chain network profit per unit time of the multi-milk product. Through a real-world dairy industrial case of multi products, this proposed SCND generic model is demonstrated and then customized model is developed for the case analysis. It is observed that the total supply chain network profit per unit time for the proposed model is more than that of existing model. Hence the strategic conditions like the service region must be greater than the influence area and imposing preservation effort for the multi-milk product can be a mechanism for revenue growth of the supply chain network design.

A bi-objective production-distribution problem in a supply chain network under grey flexible conditions

One of the main topics discussed in a supply chain is the production-distribution problem. Producing and distributing the products plays a key role in reducing the costs of the chain. To design a supply chain, a network of efficient management and production-distribution decisions is essential. Accordingly, providing an appropriate mathematical model for such problems can be helpful in designing and managing supply chain networks. Mathematical formulations must be drawn close to the real world due to the importance of supply chain networks. This makes those formulations more complicated. In this study, a novel multi-objective formulation is devised for the production-distribution problem of a supply chain that consists of several suppliers, manufacturers, distributors, and different customers. Also, a Mixed Integer Linear Programming (MILP) mathematical model is proposed for designing a multi-objective and multi-period supply chain network. In addition, grey flexible linear programming (GFLP) is done for a multi-objective production-distribution problem in a supply chain network. The network is designed for the first time to cope with the uncertain nature of costs, demands, and capacity parameters. In this regard, due to the NP-hardness and complexity of problems and the necessity of using meta-heuristic algorithms, NSGA-II and Fast PGA algorithm are applied and compared in terms of several criteria that emphasize the quality and diversity of the solutions.

A robust optimisation approach for designing a multi-echelon, multi-product, multi-period supply chain network with outsourcing

A robust optimisation approach for designing a multi-echelon, multi-product, multi-period supply chain network with outsourcing

Multi-stage, multi-product and multi-period milk supply chain network design: a case of coastal region of Odisha

Due to the complexity of supply chain networks in today’s business environment, it is important to consider several strategic planning decisions along with the classical location-allocation decisions to achieve an integrated system. In this paper, a milk supply chain network design (SCND) problem of coastal region Odisha is considered. The proposed model is focussed on multi-stage, multi-product and multi-period supply chain network design of milk of a dairy industry. The network design includes the strategic decision-making approach of influence area, order quantity, replenishment cycle time, preservation factor and number of proposed distribution centre of milk products. This supply chain network design generic model of the milk products is developed as a mixed integer non-linear programming (MINLP) model. It is solved by using piecewise nonlinear optimization approach for location-allocation decisions of the clusters. The sensitivity analysis is also conducted to check the importance and influence of the model parameters on total supply chain network profit per unit time of the multi-milk product. Through a real-world dairy industrial case of multi products, this proposed SCND generic model is demonstrated and then customized model is developed for the case analysis. It is observed that the total supply chain network profit per unit time for the proposed model is more than that of existing model. Hence the strategic conditions like the service region must be greater than the influence area and imposing preservation effort for the multi-milk product can be a mechanism for revenue growth of the supply chain network design.

A Fuzzy Mathematical Programming Model for Sustainable Supply Chain under Competition and Uncertainty Environment

In this paper, a fuzzy mathematical programming model based on the nested model is proposed to design a sustainable multi-product, multi-period supply chain network (including three parts of the procurement, production and distribution) under the competition and uncertainty conditions. Sustainability measures are carried out using previous studies and the supply chain operations reference (SCOR) model is extracted in each of the sustainability dimensions and then localised using the fuzzy Delphi method. In order to determine the relationship between indicators and the importance of each index, DEMATEL method is used and then the obtained fuzzy model is converted into a crisp one. To demonstrate the efficiency of the model, a real example is presented in the refractory industry. Finally, the results are analysed and suggestions are presented.

A robust optimization approach for designing a multi-echelon, multi-product, multi-period supply chain network with outsourcing

This paper addresses the problem of designing an integrated multi-echelon, multi-product, multi-period supply chain network under uncertainty in which products can be outsourced to improve responsiveness and the overall performance. The network consists of production plants, distribution centres and retailers. The demands of retailers, production capacities, and transportation costs as well as costs of opening distribution centres are subject to uncertainty. A deterministic mixed-integer linear programming (MILP) model is developed with the objective of minimising sum of the fixed, transportation, and outsourcing costs. In order to capture the uncertainties, a robust optimisation model is proposed. A set of numerical experiments using nominal and realisation data is investigated and the relative performance of the robust and deterministic models is compared based on the standard deviation and mean of the objective function values. In case of data realisation, results confirm that the proposed robust model outperforms the deterministic counterpart.

Sustainable, multiperiod supply chain network model with freight carrier through reduction in pollution stock

Sustainable supply chain management is a huge issue from both managerial and eco- nomical perspectives. This study presents a multiperiod, multitier, sustainable supply chain with freight carriers network model to address such concerns. The model comprises manufacturers, retailers, and carriers engaged in a dynamic, noncooperative game. It considers the longitudinal accumulation of pollution stock, pollution absorbtion by nature, and mitigation actions. The study examines numerical examples with an analysis of the effect of different tax rates on production, transportation, sales, and levels of pollution stock and mitigation efforts. The outcome presents important strategic reactions of decision makers to tax policies.

A multi-period supply chain network equilibrium model considering retailers’ uncertain demands and dynamic loss-averse behaviors

This study constructs an equilibrium model of a multi-period supply chain network with uncertain demand. In the multi-period equilibrium model, we consider not only retailers’ static loss-averse behaviors, but also their dynamic loss-averse behaviors, in which retailers dynamically adjust their loss-averse parameters according to their gains or losses over the production periods. The equilibrium conditions of the various decision makers and the network are established by the finite-dimensional variational inequality. Finally, numerical examples are solved to show how retailers’ loss-averse behaviors would affect decisions, profits of manufacturers and utilities of retailers at equilibrium when compared with their loss-neutral behaviors.

Robust supply chain network design with multi-products for a company in the food sector

The paper aims to solve a problem faced by a company competing in the snacks market in Turkey. In line with the growth in this market, the company needs to make important decisions over the next few years about the timing and location of a new plant, its initial capacity, the timing and amount of additional capacity to be installed at the new and existing plants, the assignment of demand points to plants and the amount of raw materials to be shipped from suppliers to the plants in each period. The objective is to minimize the total cost of various components. The problem is formulated as a multi-period supply chain network design model with multi products. The resulting mixed-integer linear programming model is solved by the commercial solver CPLEX. This model enables us to carry out all analyses requested by the company in an efficient way. After this deterministic model is solved on the basis of a 9% annual increase in demand, it is extended to a minimax regret model to deal with uncertainty in demand quantities. The results suggest that opening the new plant in the city of İzmir is indeed a robust solution that is unaffected in different scenarios that are based on three distinct demand increase rates. Even though the location of the new plant remains unchanged with respect to scenarios, the optimal robust solution differs from the optimal solution of each scenario in terms of the capacity expansion decisions. After all obtained results had been communicated to the company managers and executives, the new plant construction was started in 2016 very close to the city that the mathematical model had determined. The new plant is expected to start operating in 2018.

A multi-stage stochastic program for supply chain network redesign problem with price-dependent uncertain demands

In this paper, we address a multi-period supply chain network redesign problem in which customer zones have price-dependent stochastic demand for multiple products. A novel multi-stage stochastic program is proposed to simultaneously make tactical decisions including products’ prices and strategic redesign decisions. Existing uncertainty in potential demands of customer zones is modeled through a finite set of scenarios, described in the form of a scenario tree. The scenarios are generated using a Latin Hypercube Sampling method and then a forward scenario construction technique is employed to create a suitable scenario tree. The multi-stage stochastic problem is formulated as a mixed-integer linear programming model and then Benders decomposition algorithm is applied for solving it. Numerical results demonstrate the significance of the stochastic model as well as the good performance of Benders algorithm. The scenario tree construction method is also evaluated in terms of out-of-sample and in-sample stability. Finally, several key managerial and practical insights in terms of pricing issues are highlighted.

A competitive multiperiod supply chain network model with freight carriers and green technology investment option

This paper presents a multiperiod supply chain with freight carriers network model. In this model manufacturers, retailers, and carriers maximize the net present value (NPV) of their investments in ecologically friendly technology. Future production, inventory, transaction, and transportation costs savings are used to help fund investments. The environmental impact of production, inventory, transportation, and consumption of products in the supply chain network are all integrated. The tradeoff between the initial technology investment and its ecological footprint effect is considered for the supply chain planning period. We provide variational inequality formulations of the equilibrium conditions and then propose the modified projection method, along with conditions for convergence. Numerical examples are examined with an analysis of the effects of ecologically friendly technology investments on supply chain network production, transportation, and sales.

Designing a bi-objective multi-echelon robust blood supply chain in a disaster

• A multi-objective robust blood supply chain in a disaster was developed. • Three levels of blood supply chain network were considered: supply, processing, and distribution. • Objectives were to minimize total costs and maximize meeting the blood demand. • A real case study was considered to design a disaster blood supply chain. This paper presents a robust optimization model for designing a bi-objective multi-period supply chain network of blood in a disaster in three echelons, namely supply, processing, and distribution. The network consists of blood donors who donate blood at temporary and permanent blood donation facilities. Blood is collected and sent to blood centers for processing. The healthy blood will be sent to care centers depending on their demand and capacity. The aim of the proposed model is to determine the number and location of facilities and the best strategy to allocate them under three different scenarios, while the goals are to minimize costs and shortages of blood. The proposed model is formulated by a robust optimization approach. The application of the model is investigated using real data, which were collected from Qaemshahr city, Iran. The goal programming method was used to solve the problem. The results show that by expending an acceptable amount of budget, we can get ready for such a disaster situation.