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This paper investigates a problem in a reverse logistics (RLs) network to decide whether to dispose of unsold goods in primary stores or re-commercialize them in outlet centers. By deducting the costs associated with each policy from its revenue, this study aims to maximize the profit from managing unsold goods.

A new mixed-integer linear programming model has been developed to address the problem, which considers the selling prices of products in primary and secondary stores and the costs of transportation, cross-docking and returning unwanted items. As a result of uncertain nature of the cost and time parameters, gray numbers are used to deal with it. In addition, an innovative uncertain solution approach for gray programming problems is presented that considers objective function satisfaction level as an indicator of optimism.

According to the results, higher costs, including transportation, cross-docking and return costs, make sending goods to outlet centers unprofitable and more goods are disposed of in primary stores. Prices in primary and secondary stores heavily influence the number of discarded goods. Higher prices in primary stores result in more disposed of goods, while higher prices in secondary stores result in fewer. As a result of the proposed method, the objective function satisfaction level can be viewed as a measure of optimism.

An integral contribution of this study is developing a new mixed-integer linear programming model for selecting the appropriate goods for re-commercialization and choosing the best outlet center based on the products' price and total profit. Another novelty of the proposed model is considering the matching percentage of boxes with secondary stores’ desired product lists and the probability of returning goods due to non-compliance with delivery dates. Moreover, a new uncertain solution approach is developed to solve mathematical programming problems with gray parameters.

The present work seeks to determine the optimal delivery schedule of equipment at a project site in the backdrop of limited storage space, at a minimum cost, and without disturbing the overall project schedule. In addition, the optimized delivery schedule helps in minimizing the fluctuating requirements of space at the project site across the entire project lifespan.

The study is carried out at a Steel plant operating in a constrained space but undergoing a production capacity expansion. The problem motivated us to explore the possibility of postponing the delivery dates of certain equipment closer to the erection dates without compromising on the project schedule. Given the versatility of linear programming models in dealing with such schedule optimization problems, the authors formulated the above problem as a Zero-One Integer Linear Programming problem.

The model is implemented for all the new equipment arriving for two major units – the Hot Strip Mill (HSM) and the Blast Furnace (BF). It generates an optimized delivery schedule by delaying the delivery of some equipment by a certain number of periods, without compromising the overall project schedule and at a minimum storage cost. The average space utilization increases by 25.85 and 14.79% in HSM and BF units respectively. The fluctuations in space requirements are reduced substantially in both units.

The study shows a timeline in the form of a Gantt chart for the delivery of equipment, storage of equipment across different periods, and the number of periods for which the delivery of certain equipment needs to be postponed. The study uses linearly increasing storage costs with the increase in the number of periods for storage of the equipment in the temporary shed.

1. Determined the optimal delivery schedule of the equipment in a project environment in the backdrop of limited storage space in the project site.

2. Formulated the above problem as a Zero-One Integer Linear Programming (ILP) problem.

3. The average space utilization has increased by 25.85 and 14.79% in HSM and BF units respectively.

4. The optimized delivery schedule helps in reducing the fluctuations in space requirements substantially across the entire lifespan of the project.

5. The timeline of delivery of equipment, storage of equipment across different periods and periods of postponement of the equipment are shown in the form of a Gantt Chart.

Determined the optimal delivery schedule of the equipment in a project environment in the backdrop of limited storage space in the project site.

Formulated the above problem as a Zero-One Integer Linear Programming (ILP) problem.

The average space utilization has increased by 25.85 and 14.79% in HSM and BF units respectively.

The optimized delivery schedule helps in reducing the fluctuations in space requirements substantially across the entire lifespan of the project.

The timeline of delivery of equipment, storage of equipment across different periods and periods of postponement of the equipment are shown in the form of a Gantt Chart.

Supply chain risk management can effectively reduce the loss of retailers. In this regard, retailers need to consider the competition risks of competitors in addition to the disruption risks. This paper designs a resilient retail supply chain network for perishable foods under the dynamic competition to maximize retailer's profits.

A two-stage mixed-integer non-linear model is presented for designing the supply chain network. In the first stage, an equilibrium model that considers the characteristics of perishable foods is developed. In the second stage, a mixed integer non-linear programming model is presented to deal with the strategic decisions. Finally, an efficient memetic algorithm is designed to deal with large-scale problems.

The optimal the selection of suppliers, distribution centers and the order allocation are found among the supply chain entities. Considering the perishability of agri-food products, the equilibrium retail price and selling quantity are determined. Through a numerical example, the optimal inventory period under different maximum shelf life and the impact of three resilient strategies on retailer's profit, selling price and selling quantity are analyzed.

As for future research, the research can be extended in a number of directions. First, this paper studies the retail supply chain network design problem under competition among retailers. It can be an interesting direction to consider retailers competing with suppliers. Second, the authors can try to linearize the non-linear model and solve the large-scale integer programming problem by exact algorithm. Finally, the freshness of perishable foods gradually declines linearly to zero as the maximum shelf life approaches, and it would be a meaningful attempt to consider the freshness of perishable foods declines exponentially.

This paper innovatively designs the resilient supply chain network for perishable foods under dynamic competition. The retailer's dynamic competition and resilient strategies are considered simultaneously when designing supply chain network for perishable foods. In addition, this paper gives insights into how to obtain the optimal inventory period and compare the retailer's resilient strategies.

Uncertainty in data, whether in real-valued or integer-valued data, may result in infeasible optimal solutions or unreliable efficiency scores and ranking of decision-making units. To handle the uncertainty in integer-valued factors in data envelopment analysis (DEA) models, this study aims to propose a robust DEA model which is applicable in the presence of such factors.

This research focuses on the application of fuzzy interpretation of efficiency to a mixed-integer DEA (MIDEA) model. The robust optimization approach is used to address the uncertain integer-valued parameters in the proposed MIDEA model.

In this study, the authors proposed an MIDEA model without any equality constraint to avoid the arise problem by such constraints in the construction of the robust counterpart of the conventional MIDEA models. We have studied the characteristics and conditions for constructing the uncertainty set with uncertain integer-valued parameters and a robust MIDEA model is proposed under a combined box-polyhedral uncertainty set. The applicability of the developed models is shown in a case study of Malaysian public universities.

This study develops an MIDEA model equivalent to the conventional MIDEA model excluding any equality constraint which is crucial in robust approach to avoid restricted feasible region or infeasible solutions. This study proposes a robust DEA approach which is applicable in cases with uncertain integer-valued parameters, unlike previous studies in robust DEA field where uncertain parameters are generally assumed to be only real-valued.

To operate with high efficiency and minimise the risks of power failures, power systems require careful monitoring. The availability of real-time data is crucial for assessing the performance of the grid and assisting operators in gauging the present security of the grid. Traditional supervisory control and data acquisition (SCADA)-based systems actually employed provides steady-state measurement values which are the calculation premise of State Estimation. More often, however, the power grid operates under dynamic state and SCADA measurements can lead to erroneous and inaccurate calculation results. The introduction of the phasor measurement unit (PMU) which provides real-time synchronised voltage and current phasors with very high accuracy is universally recognised as an important aspect of delivering a secure and sustainable power system. PMUs are a relatively new technology and because of their high procurement and installation costs, it is imperative to develop appropriate methodologies to determine the minimum number of PMUs as well as their strategic placements to guarantee full observability of a power system. Thus, the problem of the optimal PMU placement (OPP) is formulated as an optimisation problem subject to various constraints to minimise the number of PMUs while ensuring complete observability of the grid. In this chapter, integer linear programming (ILP), genetic algorithm (GA) and non-linear programming (NLP) constrained models of the OPP problem are presented. A new methodology is proposed to incorporate several constraints using the NLP. The optimisation methods have been written in Matlab software and verified on the standard Institute of Electrical and Electronics Engineers (IEEE) 14-bus test system to authenticate their effectiveness. This chapter targets United Nations Sustainable Development Goal 7.

This study proposes strategies for vaccine center allocation for coronavirus disease (COVID) vaccine by determining the number of vaccination stations required for the vaccination drive, location of vaccination station, assignment of demand group to vaccination station, allocation of the scarce medical professional teams to station and number of optimal days a vaccination station to be functional in a week.

The authors propose a mixed-integer nonlinear programming model. However, to handle nonlinearity, the authors devise a heuristic and then propose a two-stage mixed-integer linear programming (MILP) formulation to optimize the allocation of vaccination centers or stations to demand groups in the first stage and the allocation of vaccination centers to cold storage links in the second stage. The first stage optimizes the cost and average distance traveled by people to reach the vaccination center, whereas the second stage optimizes the vaccine’s holding and storage and transportation cost by efficiently allocating cold storage links to the centers.

The model is studied for the real-world case of Chandigarh, India. The results obtained validate that the proposed approach can immensely help government agencies and policymaking body for a successful vaccination drive. The model tries to find a tradeoff between loss due to underutilized medical teams and the distance traveled by a demand group to get the vaccination.

To the best of our knowledge, there are hardly any studies on a vaccination program at such a scale due to sudden outbreaks such as Covid-19.

This paper aims to minimize the mean-risk cost of sustainable and resilient supplier selection, order allocation and production scheduling (SS,OA&PS) problem under uncertainty of disruptions. The authors use conditional value at risk (CVaR) as a risk measure in optimizing the combined objective function of the total expected value and CVaR cost. A sustainable supply chain can create significant competitive advantages for companies through social justice, human rights and environmental progress. To control disruptions, the authors applied (proactive and reactive) resilient strategies. In this study, the authors combine resilience and social responsibility issues that lead to synergy in supply chain activities.

The present paper proposes a risk-averse two-stage mixed-integer stochastic programming model for sustainable and resilient SS,OA&PS problem under supply disruptions. In this decision-making process, determining the primary supplier portfolio according to the minimum sustainable-resilient score establishes the first-stage decisions. The recourse or second-stage decisions are: determining the amount of order allocation and scheduling of parts by each supplier, determining the reactive risk management strategies, determining the amount of order allocation and scheduling by each of reaction strategies and determining the number of products and scheduling of products on the planning time horizon. Uncertain parameters of this study are the start time of disruption, remaining capacity rate of suppliers and lead times associated with each reactive strategy.

In this paper, several numerical examples along with different sensitivity analyses (on risk parameters, minimum sustainable-resilience score of suppliers and shortage costs) were presented to evaluate the applicability of the proposed model. The results showed that the two-stage risk-averse stochastic mixed-integer programming model for designing the SS,OA&PS problem by considering economic and social aspects and resilience strategies is an effective and flexible tool and leads to optimal decisions with the least cost. In addition, the managerial insights obtained from this study are extracted and stated in Section 4.6.

This work proposes a risk-averse stochastic programming approach for a new multi-product sustainable and resilient SS,OA&PS problem. The planning horizon includes three periods before the disruption, during the disruption period and the recovery period. Other contributions of this work are: selecting the main supply portfolio based on the minimum score of sustainable-resilient criteria of suppliers, allocating and scheduling suppliers orders before and after disruptions, considering the balance constraint in receiving parts and using proactive and reactive risk management strategies simultaneously. Also, the scheduling of reactive strategies in different investment modes is applied to this problem.

Distribution network design involves a set of strategic decisions in supply chains because of their long-term impacts on the total logistics cost and environment. To incorporate a trade-off between financial and environmental aspects of these decisions, this paper aims to determine an optimal location, among candidate locations, of a new logistics center, its capacity, as well as optimal network flows for an existing distribution network, while concurrently minimizing the total logistics cost and gas emission. In addition, uncertainty in transportation and warehousing costs are considered.

The problem is formulated as a fuzzy multiobjective mathematical model. The effectiveness of this model is demonstrated using an industrial case study. The problem instance is a four-echelon distribution network with 22 products and a planning horizon of 20 periods. The model is solved by using the min–max and augmented ε-constraint methods with CPLEX as the solver. In addition to illustrating model’s applicability, the effect of choosing a new warehouse in the model is investigated through a scenario analysis.

For the applicability of the model, the results indicate that the augmented ε-constraint approach provides a set of Pareto solutions, which represents the ideal trade-off between the total logistics cost and gas emission. Through a case study problem instance, the augmented ε-constraint approach is recommended for similar network design problems. From a scenario analysis, when the operational cost of the new warehouse is within a specific fraction of the warehousing cost of third-party warehouses, the solution with the new warehouse outperforms that without the new warehouse with respective to financial and environmental objectives.

The proposed model is an effective decision support tool for management, who would like to assess the impact of network planning decisions on the performance of their supply chains with respect to both financial and environmental aspects under uncertainty.

This paper aims to focus on a medical goods distribution problem and pharmacological waste collection by plug-in hybrid vehicles with some real-world restrictions. In this research, considering alternative energy sources and simultaneous pickup and delivery led to a decrease in greenhouse gas emissions and distribution costs, respectively.

Here, this problem has been modeled as mixed-integer linear programming with the traveling and energy consumption costs objective function. The GAMS was used for model-solving in small-size instances. Because the problem in this research is an NP-hard problem and solving real-size problems in a reasonable time is impossible, in this study, the artificial bee colony algorithm is used.

Then, the algorithm results are compared with a simulated annealing algorithm that recently was proposed in the literature. Finally, the results obtained from the exact solution and metaheuristic algorithms are compared, analyzed and reported. The results showed that the artificial bee colony algorithm has a good performance.

In this paper, medical goods distribution with pharmacological waste collection is studied. The paper was focused on plug-in hybrid vehicles with simultaneous pickup and delivery. The problem was modeled with environmental criteria. The traveling and energy consumption costs are considered as an objective function.

The supply chain (SC) of the fast-moving consumer goods (FMCG) sector in India witnessed a significant change soon after introducing the Goods and Services Tax (GST). With the initiation of this tax, companies started moving from individual state-wise warehouses to consolidation warehouses model to save costs. This paper proposes a model that frames a mathematical formulation to optimize the distribution network in the downstream SC by considering the complexities of multi-product lines, multi-transport modes and consolidated warehouses.

The model is designed as mixed-integer linear programming (MILP), and an algorithm is developed that works on the feedback loop mechanism. It optimizes the transportation and warehouses rental costs simultaneously with impact analysis.

Total cost is primarily influenced by the critical factor transportation price rather than the warehouse rent. The choice of warehouses at prime locations was a trade-off between a lower distribution cost and higher rent tariffs.

The study enables FMCG firms to plan their downstream SC efficiently and to be in line with the recent trend of consolidation of warehouses. The study will help SC managers solve complexities such as multi-product categories, truck selection and consolidation warehouse selection problems and find the optimum value for each.

The issues addressed in the proposed work are transporting products with different sizes and weights, selecting consolidated warehouses, selecting suitable vehicles for transportation and optimizing distance in the distribution network by considering consolidated warehouses.