Multi-period Supply Chain 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.

Multi-echelon and multi-period supply chain management network design considering different importance for customers management using a novel meta-heuristic algorithm

Supply chain management is an integrated approach to planning and controlling materials and information from suppliers and flows to customers. Given the strategic planning of distribution networks, decisions about it must be optimized. Among the needs for optimization in the distribution network are facility location decisions and inventory control decisions. In this paper, an integrated location-allocation model with inventory control decisions is presented by considering the importance of customers. The proposed model is proposed for a multi-echelon and multi- period supply chain, in which the demand is considered as an uncertain parameter. The main innovation of this research is to consider the distinction between customers because customers with different purchasing volumes in conditions of demand uncertainty have a different level of importance for the supply chain. Moreover, a novel meta-heuristic algorithm as Seeker Evolutionary Algorithm (SEA) is applied to solve the proposed model. The results of comparing SEA with genetic algorithm and GAMS software show that both in small and large dimensions, SEA provides high-quality solutions, and its speed of operation is at an acceptable level.

Construction of Equilibria in Strategic Stackelberg Games in Multi-Period Supply Chain Contracts

Almost every supplier faces uncertain and time-varying demand. E-commerce and online shopping have given suppliers unprecedented access to data on customers’ behavior, which sheds light on demand uncertainty. The main purpose of this research project is to provide an analytic tool for decentralized supply channel members to devise optimal long-term (multi-period) supply, pricing, and timing strategies while catering to stochastic demand in a diverse set of market scenarios. Despite its ubiquity in potential applications, the time-dependent channel optimization problem in its general form has received limited attention in the literature due to its complexity and the highly nested structure of its ensuing equilibrium problems. However, there are many scenarios where a single-period channel optimization solution may turn out to be myopic as it does not consider the after-effects of current pricing on future demand. To remedy this typical shortcoming, using general memory functions, we include the strategic customers’ cognitive bias toward pricing history in the supply channel equilibrium problem. In the form of two constructive theorems, we provide explicit solution algorithms for the ensuing Nash–Stackelberg equilibrium problems. In particular, we prove that our recursive solution algorithm can find equilibria in the multi-periodic variation of many standard supply channel contracts such as wholesale, buyback, and revenue-sharing contracts.

A Project Scheduling Game Equilibrium Problem Based on Dynamic Resource Supply

In a resource-constrained project scheduling problem, most studies ignore that resource supply is a separate optimization problem, which is not in line with the actual situation. In this study, the project scheduling problem and the resource supply problem are regarded as a dynamic game system, with interactive influences and constraints. This study proposes a Stackelberg dynamic game model based on the engineering supply chain perspective. In this model, the inherent conflicts and complex interactions between the Multi-mode Resource-Constrained Project Scheduling Problem (MRCPSP) and the Multi-Period Supply Chain Problem (MPSCP) are studied to determine the optimal equilibrium strategy. A two-level multi-objective programming method is used to solve the problem. The MRCPSP is the upper-level planning used to optimize project scheduling and activity mode selection to minimize project cost and duration; MPSCP is a lower-level planning method that seeks to make resource transportation decisions at a lower cost. A two-layer hybrid algorithm, consisting of Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), is proposed to determine the optimal equilibrium strategy. Finally, the applicability and effectiveness of the proposed optimization method are evaluated through a case study of a large hydropower construction project, and management suggestions for related departments are provided.

A multi-period closed-loop supply chain network design with circular route planning

A multi-period closed-loop supply chain network design with circular route planning

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.

Multi-echelon, Multi-period Supply Chain Master Planning in the Food Process Industry: A Sustainability Concept

Multi-echelon, Multi-period Supply Chain Master Planning in the Food Process Industry: A Sustainability Concept

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 fuzzy quantitative model for assessing the performance of pharmaceutical supply chain under uncertainty

PurposeThis study aims to investigate a reliability-level demand-oriented pharmaceutical supply chain design with maximal anticipated demand coverage. Different hospitals with the particular reliability value associated with the various pharmaceutical items (PIs) are considered. An inter-connected multi-period supply chain comprising manufacturers, distribution centers, hospitals and patients is assumed for the smooth flow of health-care items, enhancing supply chain reliability. A reliability index for PIs is depicted to highlight product preference and facilitate hospitals’ service levels for patients.Design/methodology/approachA mixed-integer multi-objective programming problem that maximizes maximal demand coverage minimizes the total economic costs and pharmaceutical delivery time is depicted under intuitionistic fuzzy uncertainty. Further, a novel interactive neutrosophic programming approach is developed to solve the proposed pharmaceutical supply chain management (PSCM) model. Each objective’s marginal evaluation is elicited by various sorts of membership functions such as linear, exponential and hyperbolic types of membership functions and depicted the truth, indeterminacy and falsity membership degrees under a neutrosophic environment.FindingsThe proposed PSCM model is implemented on a real case study and solved using an interactive neutrosophic programming approach that reveals the proposed methods’ validity and applicability. An ample opportunity to generate the compromise solution is suggested by tuning various parameters. The outcomes are evaluated with practical managerial implications based on the significant findings. Finally, conclusions and future research scope are addressed based on the proposed work.Research limitations/implicationsThe propounded study has some limitations that can be addressed in future research. The discussed PSCM model can be merged with and extended by considering environmental factors such as the health-care waste management system, which is not included in this study. Uncertainty among parameters due to randomness can be incorporated and can be tackled with historical data. Besides, proposed interactive neutrosophic programming approach (INPA), various metaheuristic approaches may be applied to solve the proposed PSCM model as a future research scope.Practical implicationsThe strategy advised is to provide an opportunity to create supply chains and manufacturing within India by helping existing manufacturers to expand, identifying new manufacturers, hand-holding and facilitating, teams of officers, engineers and scientists deployed and import only if necessary to meet timelines. Thus, any pharmaceutical company or organization can adopt the production and distribution management initiatives amongst hospitals to strengthen and enable the pharmaceutical company while fighting fatal diseases during emergencies. Finally, managers or policy-makers can take advantage of the current study and extract fruitful pieces of information and knowledge regarding the optimal production and distribution strategies while making decisions.Originality/valueThis research work manifests the demand-oriented extension of the integrated PSCM design with maximum expected coverage, where different hospitals with pre-determined reliability values for various PIs are taken into consideration. The practical managerial implications are explored that immensely support the managers or practitioners to adopt the production and distribution policies for the PIs to ensure the sustainability in supply chain design.

Developing a multi-item, multi-product, and multi-period supply chain planning optimization model

Objectives: To develop a multi-item, multi-product, and multi-period mathematical model that optimizes supply, production, distribution, and inventory planning for a supply chain network. Methods: Mixed Integer Linear Programming has been used to formulate the proposed model, while Excel and Evolver solvers have been used to solve problems regarding supply chain network (consisting of two suppliers and two retailers) for profit maximization. Findings: The analysis showed that the developed model has the ability to efficiently and effectively solve real-life problems of the multi-item, multi-product, and multiperiod supply chain. Novelty: The model considered multi-item, multi-product, and multi-period. In addition, it considers initial, final, and intermittent inventory in multi-periods. The model is solved using both Excel and Evolver solvers. The model assists organizations involved in the supply chain to design and plan their network efficiently. Keywords: Supply chain; multi-item; multi-products; multi-periods; MILP;Excel; Evolver Solver

Sustainable Design of an Optimal Supply Chain for Furfural Production from Agricultural Wastes

Biochemicals produced from lignocellulosic residues appear to be a feasible solution to replace traditional fossil resources. However, their implementation must overcome some challenges such as biomass seasonality; feedstock selection; harvest selection; potential geographical biorefineries location; and numerous economic, environmental, and social restrictions. This work proposes a multiperiod supply chain model for the use of agricultural wastes toward the production of platform biochemicals, such as furfural. The most abundant of Mexico’s lignocellulosic residues are considered. The demand of furfural was chosen so that it can replace the feedstocks required to produce the terephthalic acid imported to Mexico. Economic, environmental, and social objectives were considered to evaluate the supply chain solution. The economic aspect consists of the maximization of net profit. The environmental impact is the minimization of eco-indicator 99, and the social objective is the maximization of jobs generated. The results show that furfural production for replacing current raw materials in Mexico is feasible. The supply chain solution with the best trade-off consists of a profit of 1 billion USD/year, 19 000 jobs generated/year, and 370 million eco-points/year. Finally, the supply chain model proposed a distributed furfural production scheme, where several small furfural plants are installed and distributed over all of the country.

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.

An efficient solution method for an agri-fresh food supply chain: hybridization of Lagrangian relaxation and genetic algorithm.

In the traditional agri-fresh food supply chain (AFSC), geographically dispersed small farmers transport their products individually to the market for sale. This leads to a higher transportation cost, which is the primary cause of farmers' low profitability. This paper formulates a traditional product movement problem in AFSC. First, the aggregate product movement model is combined with the vehicle routing model to redesign an existing AFSC (the ETKA Company; the most extensive domestic agri-fresh food supply chain in Iran) based on the available data. For the four-echelon, multi-period supply chain under investigation, a mixed integer linear programming (MILP) model is developed for the location-inventory-routing problem of perishable products via considering the clustering of farmers to minimize the total distribution cost. Considering the complexity of the problem, an efficient and effective "matheuristic" is introduced based on hybridizing the Lagrangian relaxation and genetic algorithm (GA). The solution obtained by the proposed "matheuristic" algorithm is robust and efficient in comparison with an exact solver, GA, and the Lagrangian relaxation approach individually. The comparison analysis reveals that the location-inventory-routing model is efficient, leading to a reduction in total distribution cost by 33% compared to the existing supply chain. Finally, the findings encourage further development and application of the proposed "matheuristic" to solve other complicated location-inventory-routing problems heuristically.

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>

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.

The principal-agent problem in supply chain management – the simulation based framework

Abstract This research deals with a phenomenon well-known in socio-economic studies and referred to as the Agency Theory: the principal-agent problem. The agent is designated to act on behalf of the company owner, i.e., the principal, in the domain of supply chain management in the face of a supplier’s default uncertainty. Each of the players is gain-oriented, but their objective functions and the degree of risk-bearing may significantly differ, leading to an agent’s decisions not being optimal in terms of the principal’s outcome. This article proposes a multi-period supply chain simulation model that can be used to perform a supply chain optimization and comparison between the agent and the principal. The proposed framework allows for differentiating the model parametrization depending on the industry, in particular the consequences of the inability to deliver the end product, costs of keeping safety stocks, or the uncertainty regarding the suppliers’ delivery failure. As players’ objective functions, we consider expected profit-based indicators and measures taking the inter-period variance into account. We find that the agent’s actions may diverge from the principal’s optimum if the agent’s incentive system is not selected correctly. We also propose a solution that unifies the goals of the players. The recent COVID-19 pandemic amplifies the importance of such research. Many companies had to limit production capacities due to global lockdowns and, per the JIT production strategy, the prior safety stock levels were low.

A coordinated scheduling problem for the supply chain in a flexible job shop machine environment

In this study, a new coordinated scheduling problem is proposed for the multi-stage supply chain network. A multi-product and multi-period supply chain structure has been developed, including a factory, warehouses, and customers. Furthermore, the flexible job shop scheduling problem is integrated into the manufacturing part of the supply chain network to make the structure more comprehensive. In the proposed problem, each product includes a sequence of operations and is processed on a set of multi-functional machines at the factory to produce the final product. Final products are delivered to the warehouses to meet customers’ demands. If the demands of customers are not fulfilled, the shortage in the form of backorder may occur at any period. The problem is expressed as a bi-objective mixed-integer linear programming (MILP) model. The first objective function is to minimize the total supply chain costs. On the other hand, the second objective function aims to minimize the makespan in all periods. A numerical example is presented to evaluate the performance of the proposed MILP model. Five multi-objective decision-making (MODM) methods, namely weighted sum, goal programming, goal attainment, LP metric, and max–min, are used to provide different alternative solutions to the decision-makers. The performance of the methods is evaluated according to both objective function values and CPU time criteria. In order to select the best solution technique, the displaced ideal solution method is applied. The results reveal that the weighted sum method is the best among all MODM methods.

Impacts of put option contract and supply chain structure in a multi-period supply chain with uncertain demand

This paper builds the multi-period optimization models that incorporate put option contract and two supply chain structures to determine the production decision for a supplier and the ordering decision for a manufacturer in a two-stage supply chain. This paper applies the method of dynamic programming to derive the structures of optimal policies and provides an approximate algorithm to evaluate the myopic policies. This paper also conducts numerical examples to illustrate the impacts of put option contract, supply chain structure and demand risk on the members’ decisions and total profits as well as the channel’s total profit. The results indicate that put option contract can motivate to increase the channel’s service level and reduce the manufacturer’s inventory risk under two supply chain structures, when compared to the case without put option contract. In the manufacturer-led structure, the channel always benefits from put option contract, the supplier benefits from put option contract with a high option price and a low exercise price, while the manufacturer benefits from put option contract with a low option price and a high exercise price. In the supplier-led structure, the channel and the manufacturer always benefit from put option contract, while the supplier benefits from put option contract with a high option price and a low exercise price. With put option contract, the supplier is more profitable in the manufacturer-led structure than in the supplier-led structure, while the manufacturer and the channel are more profitable in the supplier-led structure than in the manufacturer-led structure. Without and with put option contract, the optimal total profits of two members and the channel will first decrease and then increase in the demand risk. Finally, this paper identifies the explicit conditions under which the multi-period supply chain can be coordinatedviaput option contract under two supply chain structures. With a coordinating contract, the supplier and the manufacturer are better off compared to the case without put option contract.