In this research. a novel two-stage stochastic model is developed to find the optimal locations of the potential manufacturing facilities at the first stage, and to determine the optimal production levels, inventory levels, and quantities of raw materials and finished goods shipped among the members of the supply chain network at the second stage. The main feature of this research is that some suppliers are unreliable, and each unreliable supplier's lifetime is assumed to be an exponentially distributed random variable. However, once the supplier breaks down or loses its ability to supply raw materials, it can be repaired. The length of time the supplier is out of service or does not operate is assumed to be another exponentially distributed random variable. The transitions between the two states of available when the supplier normally operates and unavailable when it is out of service follow a continuous-time Markov chain Demands at markets arc also random variables following normal distributions. The goal is to minimize the sum of first stage construction costs and the expected second stage production, inventory and shipping costs over the planning horizon while meeting service levels at the markets. Copyright (c) 2025 The Authors.

A Markov decision process (MDP) is an appropriate mathematical framework for analysis and modeling a large class of sequential decision-making problems. Real-world applications necessitate the evaluation of the value of a decision according to several conflicting objectives. This paper presents an extended epsilon-constraint method for a multiobjective finite-horizon MDP. This study integrates the epsilon-constraint method with the K-best policies algorithm to find the nondominated deterministic Markovian policies on the Pareto-optimal frontier. The proposed algorithm is evaluated on biobjective maintenance scheduling and machine running speed selection problems, and its performance is compared with a classic approach in the literature (weighted-sum, WS, method). Satisfying results show that the proposed algorithm obtains a good-quality Pareto frontier and has advantages over the WS method.

Increasing competition among various companies has led supply chain managers to devise ways to reduce costs and production times. An important branch of the supply chain, namely the pharmaceutical supply chain network, which plays a significant role in people's lives, is considered in this paper. When it comes to human life, time and accuracy are the most important factors. In this paper, a multi-objective stochastic model is developed to reduce the time of delivering drugs to patients and minimize operating costs of the supply chain, considering congestion in production centers and scheduling jobs in flexible flow shop systems. Reducing greenhouse gas emissions is also addressed in this research. Two multi-objective methods, LP-metric and goal attainment, are used to solve the proposed multi-objective model. Finally, to illustrate the performance of the proposed model, several numerical test problems from small to a large extent are solved with a detailed sensitivity analysis. Through analyzing the computational results, confliction among objective functions is analyzed. Moreover, it is concluded that LP-metric outperforms the goal attainment approach profoundly by comparing two solution approaches.

In this paper, we develop a multi-objective two-stage stochastic programming model, which takes into account the selection of warehouse and retailer sites and the decision about production levels, inventory levels, and shipping quantities among the entities of the supply chain network. The first objective function is to maximize the chain’s total profit over multiple periods, and the second objective function is to minimize the total travel times for unsatisfied customers, whose demands must be met by retailers which are established in other markets, to maximize the chain’s responsiveness. Demands, selling prices and productions times at manufacturing sites are all considered as uncertain parameters. The two objective functions are in conflict with each other, and we use ε-constraint method to generate a set of Pareto optimal solutions for the proposed multi-objective two-stage stochastic programming problem.

Although the literature of the supply chain is teemed with the analysis of the bullwhip effect, few studies regarding the impact of the bullwhip effect or demand distortion on the supply chain profit have been done. Hence, we introduce the concept of Distance to Loss (DL), which is a function of the retailer’s selling price, the manufacturer’s wholesaler price, the end item’s salvage value, the retailer’s expected demand and the retailer’s variance of demand. This concept can perfectly model both stock-out loss and overstocking loss emanated by the bullwhip effect and combines both the newsvendor model and credit risk concepts. Our findings are based on an experimental design and are profoundly in line with previous research. In particular, our model indicates that variations in demand parameters, retailer’s selling price and manufacturer’s wholesaler price impinge on the retailer’s DL, whereas a slight increase in the salvage value negligibly affect the retailer’s DL.

In this paper, we aim to develop optimal production plans in industrial townships modeled as hub location–allocation problems (HLAP) taking congestion into account. In the proposed model, hub nodes are considered as industrial townships where manufacturing plants and a central distribution warehouse are located, and two objectives are targeted. The first is to minimize the total costs, which includes the cost of hub deployment, factories and warehouses, transportation, and so forth. The second is to minimize the total elapsed time of products in manufacturing plants and warehouses modeled as queues. Due to the ambiguity in estimating the model’s parameters, they are considered as fuzzy parameters to make model closer to reality. The fuzzy model is then converted into an equivalent crisp model by combining the expected value (EV) and the fuzzy chance constrained programming (FCCP) approaches. Subsequently, the bi-objective crisp model is converted into a single aggregated objective model. In order to validate the proposed model, six numerical examples are solved, and the sensitivity of the proposed model with regard to changes in model’s parameters is investigated.

Type 2 diabetes has an increasing prevalence and high cost of treatment. The goal of type 2 diabetes treatment is to control patients' blood glucose level by pharmacological interventions and to prevent adverse disease-related complications. Therefore, it is important to optimize the medication treatment plans for type 2 diabetes patients to enhance the quality of their lives and to decrease the economic burden of this chronic disease. Since the treatment of type 2 diabetes relies on medication, it is vital to consider adverse drug reactions. Adverse drug reaction is undesired harmful reactions that may result from some certain medications. Therefore, a Markov decision process is developed in this article to model the medication treatment of type 2 diabetes, considering the possibility of adverse drug reaction occurring adverse drug reaction. The optimal policy of the proposed Markov decision process model is compared with clinical guidelines and existing models in the literature. Moreover, a sensitivity analysis is conducted to address the manner in which model behavior depends on model parameterization and then therapeutic insights are obtained based on the results. The satisfying results show that the model has the capability to offer an optimal treatment policy with an acceptable expected quality of life by utilizing fewer medications and provide significant implications in endocrinology and metabolism applications.

In this paper, a new hub location-allocation model is developed considering congestion and production scheduling. This model assumes that manufacturing and distributing goods, including raw materials and semi-finished or finished goods, take place in hubs only (such as industrial township). The main objective of this study is to minimize the total costs and to minimize the sum of waiting times for processing goods in factories and warehouses. In order to solve the bi-objective model, goal attainment and LP metric techniques are combined to develop a more effective multi-objective technique. Due to the exponential complexity of the proposed approach as well as the nonlinearity of the mathematical model, a number of small and medium-sized problems are solved to demonstrate the effectiveness of the solution methodology.

Medication selection for Type 2 Diabetes (T2D) is a challenging medical decision-making problem involving multiple medications that can be prescribed to control the patient’s blood glucose. The wide range of hyperglycemia lowering agents with varying effects and various side effects makes the decision quite difficult. This paper presents computer-aided medical decision support using a fuzzy Multi-Criteria Decision-Making (MCDM) model that hybridizes a Step-wise Weight Assessment Ratio Analysis (SWARA) method with a modification of Fuzzy Multi-Objective Optimization on the basis of a Ratio Analysis plus the full multiplicative form (FMULTIMOORA) method for pharmacological therapy selection of T2D. It makes the use of SWARA for obtaining the relative significance of every selected criterion by soliciting experts’ opinions and FMULTIMOORA method for evaluation of each alternative according to all criteria based on a published clinical guideline. In this paper, an extended reference point approach is considered in the proposed hybrid MCDM model that resolves the classic reference point limitations and improves the FMULTIMOORA ranking procedure. Computational results indicate that Metformin is confirmed as the first-line medication and Sulfonylurea as the second-line add-on therapy. The Glucagon-like peptide-1 receptor agonist, Dipeptidyl peptidase-4 inhibitor, and Insulin are placed 3rd, 4th, and 5th, respectively. A sensitivity analysis is conducted to validate the model performance by comparing its result with studies in the literature, other fuzzy MCDM techniques and an interval MULTIMOORA method based on an observational dataset. The close correspondence between the final rankings of anti-diabetic agents resulted from the proposed hybrid model and other methodologies provide significant implications for endocrinologists to refer.

In recent years, comprehensive researches have provided ample support for the supply chains in the coordinated decision-making framework. However, the issue of closed-loop supply chain coordination considering various transportation modes has not yet been addressed in the literature. In this paper, a two-echelon closed-loop supply chain consisting of a manufacturer and a retailer is investigated in which the manufacturer acts as a Stackelberg leader and the retailer plays follower role. All transportation activities between the channel members are carried out via two transportation types including the economic and green modes. First, the proposed problem is examined under the decentralized and centralized settings. Then, a mathematical modeling is developed to coordinate the decisions related to retail price, collection effort, and ratio of transportation mode selection. Finally, some numerical examples are applied with the aim of analyzing the performance of decentralized, centralized, and coordinated decision-making structures. The results reveal that not only the Pareto optimal solution is achievable for both channel members but also the coordination scheme has sufficient efficiency to reach the best solution up to the centralized setting.

In this research, we develop a stochastic programming approach for multi-period supply chain design problems under uncertainty. The supply chain design problem involves making location and allocation decisions to support the required flows in a supply chain. It is assumed that the locations of facilities (manufacturing sites, warehouses and/or retailers) are determined at the strategic level, while selection of suppliers, production levels at manufacturing sites, inventory levels at warehouses, transportation modes and shipping quantities among the entities of the supply chain network over the planning horizon are all determined at the tactical level. Demands, processing, transportation and productions times at manufacturing sites are all considered as uncertain parameters following different distributions. To develop a robust model, an additional objective function is added into the model, which is the variance of the net present value of all cash flows.

Introduction: Type 2 diabetes (T2D) imposes high expenses on societies, due to its effects on individual and social functions of patients. Adverse complications of this disease can be prevented through controlling patient's blood sugar level. The purpose of this study was to optimize the medication treatment of type 2 diabetes. Methods: In this applied survey, Markov decision process (MDP) was used to model the scheduling and sequencing of T2D medication treatments. In order to have a model close to reality, expense issues, time value of money (TVM) and inflation were considered and it was tried to plan a cost-effective treatment program. Since anti-diabetic drugs cause hypoglycemia in elderly patients, a hypoglycemia preventive approach was applied on the proposed model and its effect was analyzed. The function of proposed model and efficiency of the obtained optimal policy were compared with clinical guidelines. Moreover, in order to address the model behavior, sensitivity analysis on parameters related to treatment costs was also conducted. Results: The proposed model showed better performance in glycemic control compared to clinical guidelines. Treatment cost parameters affected treatment program. Conclusion: In general, optimizing the medication treatment of T2D not only can improve patients' life period with quality, but also can decline high costs imposed on societies’ healthcare systems.

Aim: The objective of this paper is to design nutrient-adequate, varied and cost-efficient diets for diabetes patients. Methods: A new multi-objective mixed integer linear programming model under uncertainty is developed to design diet plans for diabetes patients. Findings: The analysis is conducted on the population of 30 years old men and women in 24.99 and 18.5 body mass index, 1.50, 1.65 and 1.80 (m) height categorized in 4 physical activity levels (sedentary, low, active and very active). The objectives of the model are the minimization of the total amount of saturated fat, sugar and cholesterol and the total cost of the diet plans. The constraints of the model are fulfilling the body's nutrient requirements and the diversity control of each patient’s diet. In order to get closer to the real world, fuzzy parameters are considered in the model. To solve the model, a new hybrid solution methodology (Jimenez and epsilon-constraint method) is used to offer the optimal Pareto of non-dominated solutions. Each optimal Pareto of the model consists of diet plans that each patient can choose the proper food based on the taste, availability and cost. Conclusion: Mathematical modeling of diet planning and study of its optimal solutions can be considered as a decision support tool for the professionals to design the most proper diet plans.

This paper proposes a time-computing model using the Graphical Evaluation and Review Technique (GERT) to analyse concurrent New Product Development (NPD) processes. The research presented here differs from previous work carried out on concurrent engineering. First, we conceptualise a concurrent NPD process using the GERT scheduling technique and derive a method of modelling the information and communication complexities within the process. Second, we extend previous research carried out on concurrent engineering and incorporate it within our model. Finally, we present an alternative method of analysing concurrent NPD process for both researchers and project managers alike. The GERT model developed in this paper was successfully employed at two NPD firms located in Ireland and Iran. (C) 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.

This chapter develops a Markovian multi-objective mathematical programming model for the resource allocation problem in dynamic PERT networks with a finite capacity of concurrent projects. It is assumed that new projects are generated according to a Poisson process and activity durations are independent random variables with exponential distributions. This system is represented as a queueing network with finite concurrent projects, where each activity of a project is operated at a dedicated service station with one server located in a node of the network. In this investigation, not only activity durations, but also operating costs of service stations per period are all considered as independent random variables. This problem is formulated as a multi-objective model using continuous-time Markov processes with three conflicting objectives to optimally control the resources allocated to service stations. It is impossible to solve this problem optimally in a reasonable time, and consequently we apply a particle swarm optimization (PSO) method to solve this multi-objective continuous-time problem using a goal attainment technique. Finally, to show the effectiveness of the proposed PSO, we compare the results of a discrete-time approximation of the original optimal control problem with the results obtained by the proposed PSO.

A hub location problem appears in a variety of applications involving airline systems, cargo delivery systems and telecommunication network design. The plants known as hubs serve client nodes involving hub and spoke nodes. To act optimally plants work through time horizon. Thus, opening, reopening and active modes as well as their operational cost are accounted for. We have a single objective function that minimises the total expected cost. Additionally, to come close more and more to reality, we consider a stochastic environment, in which a scenario-based type is considered and dedicated a specific probability. The experimental results illustrate the impact of the stochastic environment compared to the deterministic one. A stochastic mathematical model yields a less amount of the objective function value compared with the deterministic one. Finally, a wide sensitivity analysis is performed to recognise the impact of the main parameters on the final solutions.

In this paper, a novel multi-objective mathematical model is developed to solve a capacitated single-allocation hub location problem with a supply chain overview. Three mathematical models with various objective functions are developed. The objective functions are to minimize: (a) total transportation and installation costs, (b) weighted sum of service times in the hubs to produce and transfer commodities and the tardiness and earliness times of the flows including raw materials and finished goods, and (c) total greenhouse gas emitted by transportation modes and plants located in the hubs. To come closer to reality, some of the parameters of the proposed mathematical model are regarded as uncertain parameters, and a robust approach is used to solve the given problem. Furthermore, two methods, namely fuzzy multi-objective goal programming (FMOGP) and the Torabi and Hassini's (TH) method are used to solve the multi-objective mathematical model. Finally, the concluding part presents the comparison of the obtained results. (C) 2015 Elsevier B.V. All rights reserved.

A multi-objective stochastic programming model is developed for supply chain design under uncertainty using an interactive approach. This is a comprehensive model, which includes both the strategic and tactical levels. The uncertainty regarding demands, supplies, processing and transportation costs is captured by generating discrete scenarios with given probabilities of occurrences. The objective functions involved are the expected total cost (min), the variance of the total costs (min) to get a robust design, and the probability of not meeting a certain budget (min). Then, an interactive multi-objective technique with explicit trade-off information given named surrogate worth trade-off (SWT) method is used to solve the multi-objective model.

This article models a multi-stage assembly system with finite capacity as an open queueing network using continuous-time Markov process. We also propose a multi-objective model with three conflicting objectives to optimally control the service rates, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem.