Multiperiod Planning Horizon Research Articles

An integrated blockchain-enabled multi-channel vaccine supply chain network under hybrid uncertainties

The recent pandemic caused by COVID-19 is considered an unparalleled disaster in history. Developing a vaccine distribution network can provide valuable support to supply chain managers. Prioritizing the assigned available vaccines is crucial due to the limited supply at the final stage of the vaccine supply chain. In addition, parameter uncertainty is a common occurrence in a real supply chain, and it is essential to address this uncertainty in planning models. On the other hand, blockchain technology, being at the forefront of technological advancements, has the potential to enhance transparency within supply chains. Hence, in this study, we develop a new mathematical model for designing a COVID-19 vaccine supply chain network. In this regard, a multi-channel network model is designed to minimize total cost and maximize transparency with blockchain technology consideration. This addresses the uncertainty in supply, and a scenario-based multi-stage stochastic programming method is presented to handle the inherent uncertainty in multi-period planning horizons. In addition, fuzzy programming is used to face the uncertain price and quality of vaccines. Vaccine assignment is based on two main policies including age and population-based priority. The proposed model and method are validated and tested using a real-world case study of Iran. The optimum design of the COVID-19 vaccine supply chain is determined, and some comprehensive sensitivity analyses are conducted on the proposed model. Generally, results demonstrate that the multi-stage stochastic programming model meaningfully reduces the objective function value compared to the competitor model. Also, the results show that one of the efficient factors in increasing satisfied demand and decreasing shortage is the price of each type of vaccine and its agreement.

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.

Integrated textile material and production management in a fuzzy environment: A logistics perspective

The purpose of this paper is to study the integrated physical material management (including suppliers’ selection, order allocation, and multi-mode inbound transportation) and multi-site aggregate production planning with direct shipping. A multi-objective programming model is developed to determine the material purchasing plan, transportation modes, and production-related decisions in a (non-overlapped) multi-period tactical planning horizon. An interactive algorithm is developed, based on the interval expected value of fuzzy numbers and satisfaction degree, to obtain compromise solutions. Finally, numerical studies show the usefulness of our proposed framework in the clothing supply chain.

Planning of multi-hub energy system by considering competition issue

Energy hub concept has been emerged as a suitable tool to analyze multi-carrier energy systems. Deregulation and increasing competition in the energy industry have provided a suitable platform for developing the energy systems composed of competing energy hubs. Planning of energy hubs considering the competition between the hubs has not been sufficiently addressed, yet. A model has been proposed in this study for planning of a multi-hub energy system considering the competition between the hubs. The hubs are interconnected via an electric transmission system. While the heat demand for each hub must be supplied by deploying associated technologies, the electricity demand can be fulfilled by investing in technologies or exchanging through the transmission system considering the market price and line loading limits. A linear model has been developed to determine the optimal capacity development of heat and electricity generation technologies for energy hubs in a multi-period planning horizon to meet the heat and electricity demand for the defined load zone. The problem has been formulated and solved using Karush–Kuhn–Tucker (KKT) conditions. Once solved, the optimal capacity development in the hubs is determined as well as the amount and price of electricity interchange between the hubs for the load zones of the planning horizon. The proposed model has been applied to 3-Hub and 5-Hub energy systems. The effect of renewable generation and storage system have also been evaluated. The result have been presented and discussed to evaluate the validity of the results as well as the capabilities of the proposed model. It was observed that, due to the competition between the hubs, the electricity generation capacity in a hub can reach 23% higher that the peak demand of the same hub. The electricity price between the hubs differs by 25% while the difference between the gas price of the hubs is about 5 percent. It has also been observed that inclusion of renewable generation or storage technologies can alter the electricity generation capacity by 63 percent in HUB2.

A branch-and-price method for the vehicle allocation problem

The Vehicle Allocation Problem (VAP) consists of allocating a fleet of vehicles to attend to the expected demand for freight transportation between terminals along a finite multiperiod planning horizon. The objective is to maximize the profits generated for the completed services. The previous deterministic and stochastic approaches used heuristic procedures and approximations for solving large-scale instances of this problem. This paper proposes a Branch-and-Price method which is the first tailored exact solution approach for the VAP. This method provides proven optimal solutions within reasonable computational times, even for large-scale problem instances, and it is based on reformulating a compact Integer Linear Programming model of the VAP through the Dantzig–Wolfe decomposition and using efficient procedures for solving each component of the reformulation. The Primal–Dual Column Generation Method (PDCGM) is used to solve the master problem, while the subproblem is modeled as a Maximum Cost Flow Problem and is solved using the aggregation of the optimal longest paths on Directed Acyclic Graphs (DAG). Finally, we use three branching procedures (branching on a set of arcs, on the original variables and on the demand constraints) to obtain the optimal integer solution of the VAP. Computational experiments with 30 instances from a case study and 200 random realistic-sized instances are presented and analyzed, which show that the method has superior performance with respect to other exact approaches in solving large-scale VAP instances.

Performance evaluation of complex electricity generation systems: A dynamic network-based data envelopment analysis approach

To evaluate the performance of complex electricity generation systems, a new dynamic network-based data envelopment analysis (DNDEA) approach is presented. Past data envelopment analysis (DEA) studies on energy system efficiency have often ignored the dynamics of each process of the system individually. Here a network-based DEA method is built, which considers the interrelationships of the operations to determine the efficacy of the system. For assessing the performance over successive periods, with time-based dependencies between the successive periods, a dynamic DEA (DDEA) model is proposed. In DDEA, a linear combination of the efficiencies in successive periods is used as the complement of the system. The network-based and dynamic features of the created model enable measuring the performance of each sub-system process and the entire system in multi-period planning horizons simultaneously. These features make the DEA model identify changes in system efficiencies so much better than the current approaches. The created model is comprehensively implemented in the Iranian electricity sector using real data. Based on the findings, the efficiencies of power generation and transmission sectors are decreasing while the distribution performance is increasing. The proposed model could be applied to electricity generation systems in other countries as well. • Efficiency of regional electricity companies is estimated using company-level data. • A dynamic network-based data envelopment analysis model is employed. • All generation, transmission and distribution sectors are considered. • Efficiency of generation and transmission sectors were decreased from 2017 to 2019. • Privatizing the distribution sector resulted in a huge increase in its efficiency.

Mathematical modeling for green supply chain considering product recovery capacity and uncertainty for demand.

Competition in today's market is the most important concern of companies and producers in free markets. Buyers are also looking for higher quality and lower prices. Manufacturers should, therefore, reduce production costs and increase budgets for research and product development. On the other hand, the limitation of mineral resources in each country and in the world in general is a very important factor for increasing the price of raw materials which increases the cost of production of a product. In this study, a green aspect of decision-making, concurrent modeling for inventory-routing, and application of maximum entropy (ME) method for overcoming uncertainties of demands are applied to optimize the usage of raw materials and returning of defective products to the production cycle in a closed-looped supply chain under multi-period planning horizon. Also, dynamic modeling is used to balance the inventory level in all stages of the network that leads to optimum usage of the raw materials. For this purpose, the first objective function reduces production, transportation-routing, and inventory costs, and the second objective reduces greenhouse gas emissions through all levels of the network. Finally, this model is solved by using the exact solution method with the help of Gams software as well as the non-dominated sorting genetic algorithm II (NSGAII) and multi-objective particle swarm optimization (MOPSO) algorithm. Sensitivity analysis has been performed on failure rates, greenhouse gas emissions during recycling and production, and the optimistic-pessimistic coefficient of the ME solution method. Solution methods have been compared using several criteria, and the NSGAII method has finally obtained the best result. The results show that the manager should pay more costs in order to prevent backorder demands. Also, collecting the more defective products leads to increasing production amount since the collective products can return to the production line. Finally, it is required for the managers to control products' failure rate to optimize capacity usage in the model.

A mixed-integer model for the implementation of postponement strategies in the globalized green supply chain network

Modern business traits and global-scale logistics operations have urged companies to devise responsive and efficient supply chain networks to fulfill customer demands all- around the world. However, such operations have increased resource consumption and pollution production, causing more environmental damage. To address these issues, postponement strategies are adopted to enable responsive and more environmentally friendly supply chain operations. However, only a few studies on supply chain optimization considering postponement strategies and environmental issues have been conducted. It motivates this study to propose a mixed-integer model of an integrated green supply chain network (GSCN) for both single and multi-period planning horizons that incorporate postponement concept, and modularized products and processes. Using these models, various speculation strategies coupled with postponement strategies can be analyzed in configuring green supply chain system with mass customization principle subjected to various carbon tax and carbon cap policies under a global supply chain environment. Computational examples of a mass customization notebook computer supply chain show that postponing product differentiation reduces excessive production processes. As a result, the configured supply chain is able to comply with strict environmental policies with just a slight cost increase. This justifies postponement strategies application in configuring eco-efficient supply chain operations.

Cotas para el problema de asignación de vehículos

El problema de asignación dinámica de vehículos consiste en asignar una flota de vehículos para atender la demanda prevista por transporte de carga entre terminales, durante un horizonte de tiempo finito y con múltiples periodos, cuyo objetivo es maximizar el lucro generado por los servicios completados. Dada la dispersión geográfica por demanda de servicios de transporte de carga, es común que se acumulen vehículos vacíos en lugares donde no son necesarios o se genere una escasez de vehículos donde son necesitados a lo largo del horizonte de planeación, por tanto, es importante balancear el suministro de vehículos y la demanda por servicios a lo largo del horizonte de planeación. El tamaño de los problemas prácticos enfrentados por transportadores logísticos es considerablemente grande para resolver en tiempos computacionales razonables, especialmente en transporte de carga por carre-tera. Consecuentemente, se recurre a métodos heurísticos para obtener soluciones factibles, pese a que no se tiene certificado de calidad de la solución. Por esta razón, en este trabajo se propone estudiar dos métodos de decomposición, que proporcionan certificados de calidad, para obtener cotas para el PADV. Los métodos utilizados son relajación lagranjeana junto con método de subgradiente de optimización y decomposición de Dantzig-Wolfe junto con generación de columnas. Experimentos compu-tacionales son realizados con instancias realistas, y los resultados de las cotas se muestran promisorios en términos de eficiencia computacional para el segundo método.

Iterated local search and simulated annealing algorithms for the inventory routing problem

AbstractThis paper addresses the inventory routing problem (IRP), which consists in defining the customer visit schedule, the delivery quantities, and the vehicle routing plan to meet the demands of a set of customers over a given time horizon. We consider the variant with a single item, a single supplier, multiple vehicles, and a finite multiperiod planning horizon, minimizing the sum of inventory and travel costs. In addition, we address an alternative objective function that minimizes the logistic ratio, defined as the total travel cost divided by the total quantity delivered to customers. This second objective function, while more realistic in some logistics settings, poses a challenge for integer programming models and exact methods because of its nonlinearity. To our knowledge, no heuristic method has been proposed to address this objective in the IRP variant addressed in this paper. To solve this problem with each of these objective functions, we propose effective metaheuristic algorithms based on iterated local search and simulated annealing. Computational experiments show that these algorithms provide reasonably high‐quality solutions in relatively short running times for both objective functions when compared to other methods for well‐known instances from the literature. Moreover, the algorithms produce new best solutions for some of these instances.

Performance Analysis of Intelligent Robust Facility Layout Design

Design of a robust production facility layout with minimum handling cost (MHC) presents an appropriate approach to tackle facility layout problems in a dynamic volatile environment, in which product demands randomly change in each planning period. The objective of the design is to find the robust facility layout with minimum total material handling cost over the entire multi-period planning horizon. This paper proposes a new mathematical model for designing robust machine layout in the stochastic dynamic environment of manufacturing systems using quadratic assignment problem (QAP) formulation. In this investigation, product demands are assumed to be normally distributed random variables with known expected value, variance, and covariance that randomly change from period to period. The proposed model was verified and validated using randomly generated numerical data and benchmark examples. The effect of dependent product demands and varying interest rate on the total cost function of the proposed model has also been investigated. Sensitivity analysis on the proposed model has been performed. Dynamic programming and simulated annealing optimization algorithms were used in solving the modeled example problems.

Inexact Multistage Stochastic Chance Constrained Programming Model for Water Resources Management under Uncertainties

In order to formulate water allocation schemes under uncertainties in the water resources management systems, an inexact multistage stochastic chance constrained programming (IMSCCP) model is proposed. The model integrates stochastic chance constrained programming, multistage stochastic programming, and inexact stochastic programming within a general optimization framework to handle the uncertainties occurring in both constraints and objective. These uncertainties are expressed as probability distributions, interval with multiply distributed stochastic boundaries, dynamic features of the long-term water allocation plans, and so on. Compared with the existing inexact multistage stochastic programming, the IMSCCP can be used to assess more system risks and handle more complicated uncertainties in water resources management systems. The IMSCCP model is applied to a hypothetical case study of water resources management. In order to construct an approximate solution for the model, a hybrid algorithm, which incorporates stochastic simulation, back propagation neural network, and genetic algorithm, is proposed. The results show that the optimal value represents the maximal net system benefit achieved with a given confidence level under chance constraints, and the solutions provide optimal water allocation schemes to multiple users over a multiperiod planning horizon.

Research on Decentralized Supply Chain with Channel-Wide Profit Maximization

This study explores the problem of optimally dynamic joint decisions: replenishment quantity, retail price and depletion time, in a vertically decentralized single-retailer and single-supplier supply chain over a dynamic multi-period planning horizon, subject to multivariate demand function and deteriorating goods with shortages allowed and with no consideration of fixed costs. This research uses a calculus-based formulation coupled with dynamic programming techniques to solve the channel-wide profit maximization under price-only contract and consignment contract respectively. The analysis reveals that the consignment contract can significantly achieve higher channel-wide profit than the price-only contract for the dynamic decentralized channel.

Integrated Bioenergy Supply Chain Network Planning Problem

We consider planning and design of an extended supply chain for bioenergy networks (i.e., networks for multibiomass as well as biofuel logistics) in an integrated fashion while simultaneously addressing strategic and tactical decisions pertaining to location, production, inventory, and distribution in a multiperiod planning horizon setting. In our modeling, we also explicitly incorporate realistic operational parameters, including biomass deterioration rates and transportation economies of scale. For an efficient solution of our model, we suggest a Benders decomposition–based algorithm that can handle realistic size problems for design and analysis purposes. We implement the approach in a particular way using callback functions, in which the master problem is solved only once; we also develop surrogate constraints for enhanced lower bounds to obtain improved convergence especially for large instances. We provide computational results that demonstrate the efficiency of the solution approach on a wide-ranging set of problem instances. Furthermore, we develop a realistic case using data pertaining to the state of Texas and conduct an extensive analysis on the effects of varying input parameters on the design outcomes for a bioenergy supply chain network.

Dimensionamento e alocação dinâmica de veículos no transporte rodoviário de cargas completas entre terminais

Resumo Este artigo trata do Problema da Alocação Dinâmica de Veículos (PADV) no transporte rodoviário de cargas completas entre terminais, incluindo o dimensionamento da frota adicional necessária para o atendimento de demandas em um horizonte de planejamento multi-períodos e finito. O PADV consiste em definir “movimentos” de uma frota de veículos que realiza viagens entre terminais geograficamente dispersos que interagem entre si. Estes movimentos podem ser: veículos carregados com carga completa, vazios para reposicionamento, ou mantidos em um terminal de um período para outro como provisão para o atendimento de demandas futuras. A ênfase é dada na caracterização do problema em situações reais, na modelagem matemática do problema por meio de programação linear inteira e na solução deste utilizando um pacote comercial de otimização. Os experimentos computacionais realizados indicam que essa abordagem pode ser útil para a solução de problemas encontrados no dia a dia de uma empresa transportadora de carga parcelada no Brasil.

Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management

This paper presents a new mathematical model for integrating the virtual dynamic cellular manufacturing system into supply chain management with an extensive coverage of important manufacturing features. The considered model regards multi-plants and facility locations, multi-market allocation, multi-period planning horizons with demand and part-mix variation, machine and labor time-capacity, labor assignment, training and purchasing or selling of new machines for an increased level of plant capacity. The main constraints are market demand satisfaction in each period, machine and labor availability, production volume for each plant and the amounts allocated to each market. To validate and verify the proposed model is explained in terms of an industrial case from a typical equipment manufacturer. Some of the hard constraints of the proposed model are relaxed in order to obtain a lower bound on the objective function value. In fact, the number of machines and workers allocated to each cell are restricted to yield feasible solutions and tight upper bounds on the objective values for medium size instances in a shorter time. The relaxed model yields tight lower bounds for medium instances in a reasonable computational time. Furthermore, a Benders decomposition is developed for solving the upper bounding model.

Allocation of marketing budgets to customer acquisition and retention spending based on decision calculus

Purpose – The purpose of this paper is to allocate marketing budgets in complex environments, where data are scarce and management judgment is available. In this research, marketing budgets are allocated, to maximize customer equity as a long-term profitability measure. Design/methodology/approach – The researchers provide a model for allocation of marketing budgets based on both decision calculus and econometric models and combine it with the concept of Markov chain model to cope with data scarcity. Dynamic programming is used to find the optimal solution. Findings – The authors examine the model in telecommunication industry. Applicability of the model is supported by an illustrative example. To allocate marketing budgets, researchers consider three strategies for each period: do nothing, retention-focused strategy and acquisition-focused strategy. The results show the applicability and effectiveness of the model to find the best strategy. Research limitations/implications – As the suggested approach is based on management judgment, it is useful in situations, as the authors have experts or experienced managers to achieve reliable data. In situations which the authors do not have access to experienced managers, the results may be unreliable. Practical implications – The suggested approach is useful in situations of data scarcity, where experienced managers are accessible. The researchers have focused on telecommunication industry cases; however, the model is useful in other industries like the insurance industry. Originality/value – The main contribution of the research lies in the suggestion of a new approach to allocate marketing budgets in data scarcity situations in multi-period planning horizons. The researchers use both decision calculus and econometric tools to find the transition matrices of marketing plans.

Buyer–supplier relationship and optimisation model in a dynamic collaborative network with shortages allowed

To remain competitive, enterprises must build and manage product/service customisation and dynamic collaborative networks to respond to market needs in a flexible manner with competitive price and high product/service quality. This study deals with the emerging research problem of optimally dynamic combined decisions: retail price, stock depletion time/service level (SL) and replenishment schedule/quantity in a decentralised two-echelon perishable product collaborative network comprising a single supplier and a single retailer (buyer) over a finite multi-period planning horizon. Analytical solutions are derived using calculus with dynamic programming under two different trading policies, namely retailer-managed inventory with price-only (RMIPO) mode and vendor-managed inventory with consignment contract (VMICC) mode. In both models, shortages are allowed and are fully backlogged. The validity of the proposed approach is demonstrated using the case of a simple supply chain comprising a regional seafood supplier and a local branch store of a national retail chain. The results show that the VMICC policy yields lower retail price, larger replenishment quantity, higher SL and greater channel-wide profit than the RMIPO policy and achieves a win-win situation for both parties in the supply chain. Additionally, consumers benefit from lower retail price and higher SL in the VMICC policy.

Optimal Management of Wind Energy with Storage: Structural Implications for Policy and Market Design

It is well known that the generation resource uncertainty induced by significant wind capacity raises concerns about grid security, price stability, and revenue adequacy. One of the most promising solutions is the use of utility-scale energy storage, although the question of general implementation of this strategy remains unanswered. This paper uses a simplified model to show that simple rules exist that govern the decision to generate or store energy from a hybrid wind-storage system. The heuristics developed consider the combination of storage efficiency, electricity price, and shortfall penalty and wind forecast characteristics to guide the decision of whether to bid energy into the electricity market or not. Specifically, this paper develops the optimal strategy for use of a simplified system of an energy storage unit with a wind generator. The solution is analyzed using a dynamic programming formulation in a simplified framework over a multiperiod planning horizon. The analysis of the solution under all regimes yields insightful structural solutions regarding the conditions under which the wind generator should bid into the energy market and when it should not. The results also provide insight into the specific implications of forecast accuracy and market design on the need for storage. This analysis allows additional conclusions to be drawn about the value of various storage technologies based on their capacity and efficiency characteristics. However, the most important contribution of this work is the understanding of the importance of market penalties in encouraging participants to either improve forecasting ability or, perhaps more realistically, contract storage to mitigate shortfall risk. Improving both forecasting accuracy and storage capabilities results in value reduction for both.

The Closed-Loop Supply Chain Network Equilibrium with Products Lifetime and Carbon Emission Constraints in Multiperiod Planning Horizon

This paper studies a closed-loop supply chain network equilibrium problem in multiperiod planning horizons with consideration of product lifetime and carbon emission constraints. The closed-loop supply chain network consists of suppliers tier, manufacturer tier, retailers tier, and demand markets tier, in which the manufacturers collect used products from the demand markets directly. Product lifetime is introduced to denote the maximum times of manufacturing and remanufacturing, and the relation between adjacent periods is described by inventory transfer. By variational inequalities and complementary theory, the optimal behaviors of all the players are modeled, and, in turn, the governing closed-loop supply chain network equilibrium model is established. The model is solved by modified project contraction algorithm with fixed step. Optimal equilibrium results are computed and analyzed through numerical examples. The impacts of collection rate, remanufacturing conversion rate, product lifetime, and carbon emission cap on equilibrium states are analyzed. Finally, several managerial insights are given to provide decision support for entrepreneurs and government official along with some inspirations for future research.