Single machine scheduling with uncertain release times

A robust optimization framework for energy management of CCHP users with integrated demand response in electricity market

In order to overcome the drawback of the conventional signal timing optimization, a robust optimization algorithm for signal control parameters based on Tabu search-artificial bee colony algorithm is proposed under unsaturated flow condition. Based on the analysis of the characteristics of traffic signal control, a robust optimization model of signal control parameters is constructed by considering the minimum the average delay and the mean square error of average delay. As a consequence, the formation process of the initial solution to the bee colony is improved and the robust optimization model is solved by using the Tabu search-artificial bee colony algorithm. The proposed robust optimization model is validated by using an intersection in Zhangye City of China. The simulation results have shown that the robust optimization model and the algorithm are feasible and practicable. This robust model and algorithm can effectively deal with the volatility of traffic flow and reduce traffic delays.

This paper considers facility location, inventory pre‐positioning and vehicle routing as strategic and operational decisions corresponding to preparedness and response phases in disaster relief logistics planning. For balancing surpluses and shortages, an effective lateral transshipment strategy is proposed to evenly distribute the relief resources between warehouses after the disaster occurs. To handle ambiguity in the probability distribution of demand, we develop a risk‐averse two‐stage distributionally robust optimization (DRO) model for the disaster relief logistics planning problem, which specifies the worst‐case mean‐conditional value‐at‐risk (CVaR) as a risk measure. For computationally tractability, we transform the robust counterpart into its equivalent linear mixed‐integer programming model under the discrepancy‐based ambiguity set centered at the nominal (empirical) distributions on the observed demand from the historical data. We verify the effectiveness of the proposed DRO model and the value of lateral transshipment strategy by an illustrative small‐scale example. The numerical results show that the proposed DRO model has advantage on avoiding over‐conservative solutions compared to the classic robust optimization model. We also illustrate the applicability of the proposed DRO model by a real‐world case study of hurricanes in the southeastern United States. The computational results demonstrate that the proposed DRO model has superior out‐of‐sample performance and can mitigate the adverse effects of Optimizers' Curse compared with the traditional stochastic programming model.

The economic and low‐carbon operation strategy of multi‐energy microgrids (MEM) has become an important research topic in smart grids. The operation of MEM is affected by uncertain factors from renewable energy and internal load. To handle uncertainties from both source and load sides, the authors propose a novel worst‐case‐and‐probability uncertainty sets and a novel worst‐expectation min‐max‐max‐min two‐stage four‐level robust optimisation (RO) model considering stepped carbon trading for MEM. This four‐level RO model is a more generalised model compared with the traditional two‐stage RO and distributionally robust optimisation based models. First, the unsolvable original four‐level model is decoupled into a master problem and a sub‐problem (SP). Second, Karush–Kuhn–Tucker condition is applied to convert SP into a solvable problem. Third, column and constraint generation (C&CG) algorithm is employed to solve the reformulated four‐level RO. Finally, the effectiveness of the proposed model and solution method is verified by case studies. The results indicate that the convergence behaviour of this solution method is excellent. The MEM operator can select appropriate robustness factors and comprehensive norms to control its conservatism level. Besides, MEM could reduce carbon emissions by participating in carbon trading and installing carbon capture devices.

Energy-efficient bi-objective single-machine scheduling with power-down mechanism

An effective closed-loop supply chain (CLSC) is increasingly important for corporate sustainable development, where used products are returned, remanufactured and/or recycled. Optimized planning of CLSC network is required and is influenced by uncertainties of recovery. So, this study seeks to establish a robust optimal model for CLSC network, considering both uncertainties in quantity and quality of returned products. After the general framework of CLSC is discussed, the measurements for uncertain quantity and quality of returned products are formulated mathematically, respectively as a number of discrete scenarios and Quality Index. A mixed integral linear programming (MILP) model for a CLSC network design is established and then translated into a robust optimization model based on regret value, to determine facilities’ locations and quantity of flows between facilities in the network. A numerical example is given, and the simulation results show that the operation strategies of the CLSC are relatively stable under different recycling scenarios. Therefore, the optimization model for CLSC network has good robustness.

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

In recent years, frequent occurrence of extreme weather events has caused great losses to the power system. Meanwhile, the high penetration of renewable energy has brought new challenges to the safe operation of the system. Coordination of various measures against different stages of disaster can effectively reduce the overall loss and enhance system's resilience. This paper proposed a methodology to coordinate preventive and emergency dispatch stages based on the defender–attacker–defender model, in which various dispatching measures are modelled as defenders, whereas the extreme weather event and wind power's uncertainty are modelled as attackers. Specifically, a two‐stage three‐layer robust optimal dispatching model is established, in which conventional generator's output, wind farm's grid‐connected planning, and load shedding are taken as the main dispatching measures. To solve this model, the column and constraint generation algorithm is used to transform the three‐layer optimization model into a mixed integer linear problem . The effectiveness of the proposed model is verified in the modified IEEE RTS‐79 test system, and the results show that the coordination of preventive and emergency dispatch can effectively reduce the load outage cost under extreme weather, thus enhancing the ability of power system to cope with extreme scenarios.

In real-world decision-making, uncertainty plays a crucial role, especially when dealing with complex, multi-objective optimization problems. Traditional linear programming (LP) models often have the assumption that the data is precise and deterministic. However, this ‎assumption is often not realistic for many applications, as imprecision will always be present. This paper presents a fuzzy solution to ‎Z-Z-number-based multi-objective linear programming (ZMOLP) models. Z-numbers can combine fuzzy logic and Z-numbers to manage ‎uncertainty in (multi-objective) decision dilemmas. A Z-number consists of two parts: a fuzzy number for the uncertainty in the ‎data and a reliability score that indicates the degree of confidence in the data. The two aspects of Z-numbers make them ef‎fective for modeling imprecise data in multi-objective positioning. The effectiveness and overall computational efficiency of different ‎fuzzy membership functions (triangular, trapezoidal, Gaussian, etc.) were also explored to understand their impact on optimal solu‎tions. Z-numbers, through fuzzy numbers, provide a flexible and adaptable decision-making solution far superior to traditional methods ‎for managing imprecision that leads to a better representation of uncertainty related to objectives and constraints. To demonstrate the viability of Z-number-based approaches, practical applications were employed to illustrate their usage in healthcare decision-making and ‎engineering optimization‎.

Unpredictable disruptive events significantly increase the difficulty of the management of automobile supply chains. In this paper, we propose an automobile production planning problem with component chips substitution in a finite planning horizon. The shortage of one chip can be compensated by another chip of the same type with a higher‐end feature at an additional cost. Therefore, the automobile manufacturer can divert the on‐hand inventory of chips to product lines that are more profitable in the event of shortages caused by supply chain disruptions. To cope with this, we propose a max‐min robust optimization model that captures the uncertain supplies of chips. We show that the robust model has a mixed‐integer programming equivalence that can be solved by a commercial IP solver directly. We compare the max‐min robust model with the corresponding deterministic and two‐stage stochastic models for the same problem through extensive numerical experiments. The computational results show that the max‐min robust model outperforms the other two models in terms of the average and worst‐case profits.

The various robust linear programming models investigated so far in the literature essentially appear to be based either on what is referred to as rowwise uncertainty models or on columnwise uncertainty models (these basically assume that the rows, or the columns, of the constraint matrix are subject to changes within a well-specified uncertainty set). In this chapter, we discuss a special case of columnwise uncertainty, namely the subclass of robust linear programming (LP) models with uncertainty limited to the right hand side (RHS) only (this subclass does not appear to have been significantly investigated so far). In this context we introduce the concept of a ‘two-stage robust LP model’ as opposed to the standard case (which might be referred to as a ‘single-stage robust LP model’) and we address the question of whether LP duality can be used to convert a LP problem with RHS uncertainty into a robust LP problem with uncertainty on the objective function. We show how to derive both statements of (a) the dual to the robust model and (b) the robust version of the dual. The resulting expressions of the objective function to be optimized in both cases, appear to be clearly distinct. Moreover, from a complexity point of view, one appears to be efficiently solvable (it reduces to a convex optimization problem), whereas the other, as a nonconvex optimization problem, is expected to be computationally difficult in the general case. As an application of the two-stage robust LP model introduced here, we next investigate the PERT (program evaluation and review technique) scheduling problem, considering two possible natural ways of specifying the uncertainty set for the task durations: the case where the uncertainty set is a scaled ball with respect to the L ∞ norm; the case where the uncertainty set is a scaled Hamming ball of bounded radius (which, though leading to a quite different model, bears some resemblance to the well-known Bertsimas–Sim approach to robustness). We show that in both cases the resulting robust optimization problem can be efficiently solved in polynomial time.

Under intense industry competition, decision makers must ensure that products demanded by consumers can be quickly produced with minimum production cost. However, because uncertainties are unavoidable and inevitably affect decision makers, numerous studies have discussed how to control uncertainties or minimize their effects. Multiple uncertainties that interact simultaneously may cause a combined effect in actual systems. Therefore, this study presents a robust optimization model with two uncertainties, extending the method of robust optimization with one uncertainty. To demonstrate the applicability of the proposed model with two uncertainties, this study uses the supplier selection problem with component purchase quantity allocation in supply chain management as an analysis case. This considers the reliability of production and transportation and develops a multi-objective robust optimization model with two uncertainties. In addition, a nondominated sorting genetic algorithm is proposed for solving the proposed multi-objective robust optimization model. The relationship between price of robustness and budget parameters is explored by considering the robust optimization model with production and transportation uncertainties proposed in this study. Finally, there is a comparative analysis between the results for price of robustness in the proposed two-uncertainty model and in the one-uncertainty model.

A robust dynamic scheduling approach based on release time series forecasting for the steelmaking-continuous casting production

A constant development of gas utilization in domestic households, industry, and power plants has slowly transformed gaseous petrol into a noteworthy wellspring of energy. Supply and transportation planning of liquefied natural gas (LNG) need a great attention from the management of the supply chain to provide a significant development of gas trading. Therefore, this paper addresses a robust mixed-integer linear programming model for LNG sales planning over a given time horizon aiming to minimize the costs of the vendor. Since the parameter of the manufacturer supply has an uncertain nature in the real world, and this parameter is regarded to be interval-based uncertain. To validate the model, various illustrative examples are solved using CPLEX solver of GAMS software under different uncertainty levels. Furthermore, a novel metaheuristic algorithm, namely cuckoo optimization algorithm (COA), is designed to solve the problem efficiently. The obtained comparison results demonstrate that the proposed COA can generate high-quality solutions. Furthermore, the comparison results of the deterministic and robust models are evaluated, and sensitivity analyses are performed on the main parameters to provide the concluding remarks and managerial insights of the research. Finally, a comparison evaluation is done between the total vendor profit and the robustness cost to find the optimal robustness level.

PurposeThis study aims to research the influence of non-probabilistic design variables on interval robust optimization of electric multiple units (EMU) brake module, therefore obtain the reasonable of design variables of the EMU brake module.Design/methodology/approachA robust optimization model of the EMU brake module based on interval analysis is established. This model also considers the dimension tolerance of design variables, and it uses symmetric tolerance to describe the uncertainty of design variables. The interval order relation and possibility degree of interval number are employed to deal with the uncertainty of objective function and constraint condition, respectively. On this basis, a multiobjective robust optimization model in view of interval analysis is established and applied to the robust optimization of the EMU brake module.FindingsCompared with the traditional method and the method proposed in the reference, the maximum stress fluctuation of the EMU brake module structure is smaller after using the method proposed in this paper, which indicates that the robustness of the maximum stress of the structure has been improved. In addition, the weight and strength of the structure meet the design requirements. It shows that this method and model introduced in this research have certain feasibility.Originality/valueThis study is the first attempt to apply the robust optimization model based on interval analysis to the optimization of EMU structure and obtain the optimal solution set that meets the design requirements. Therefore, this study provides an idea for nonprobabilistic robust optimization of the EMU structure.