Scheduling Step-Deteriorating Jobs on Parallel Machines by Mixed Integer Programming

Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.

A mixed integer linear programming approach for municipal solid waste management

ＡｍｉｘｅｄｉｎｔｅｇｅｒｌｉｎｅａｒｐｒｏｇｒａｍｍｉｎｇａｐｐｒｏａｃｈｆｏｒｍｕｎｉｃｉｐａｌｓｏｌｉｄｗａｓｔｅｍａｎａｇｅｍｅｎｔＧｏｒｄｏｎＧｕｏＨｅＨｕａｎｇＥｎｖｉｒｏｎｍｅｎｔａｌＳｙｓｔｅｍｓＥｎｇｉｎｅｅｒｉｎｇ，Ｕｎｉｖｅｒ...

Combining Geographic Information Systems for Transportation and Mixed Integer Linear Programming in Facility Location-Allocation Problems

In this study, we aimed to assess the solution quality for location-allocation problems from facilities generated by the software TransCAD®?, a Geographic Information System for Transportation (GIS-T). Such facilities were obtained after using two routines together: Facility Location and Transportation Problem, when compared with optimal solutions from exact mathematical models, based on Mixed Integer Linear Programming (MILP), developed externally for the GIS. The models were applied to three simulations: the first one proposes opening factories and customer allocation in the state of Sao Paulo, Brazil;the second involves a wholesaler and a study of location and allocation of distribution centres for retail customers;and the third one involves the location of day-care centers and allocation of demand (0 - 3 years old children). The results showed that when considering facility capacity, the MILP optimising model presents results up to 37% better than the GIS and proposes different locations to open new facilities.

Closed-loop scheduling optimization strategy based on particle swarm optimization with niche technology and soft sensor method of attributes-applied to gasoline blending process

Gasoline blending scheduling optimization can bring significant economic and efficient benefits to refineries.However,the optimization model is complex and difficult to build,which is a typical mixed integer nonlinear programming(MINLP)problem.Considering the large scale of the MINLP model,in order to improve the efficiency of the solution,the mixed integer linear programming-nonlinear programming(MILP-NLP)strategy is used to solve the problem.This paper uses the linear blending rules plus the blending effect correction to build the gasoline blending model,and a relaxed MILP model is constructed on this basis.The particle swarm optimization algorithm with niche technology(NPSO)is proposed to optimize the solution,and the high-precision soft-sensor method is used to calculate the deviation of gasoline attributes,the blending effect is dynamically corrected to ensure the accuracy of the blending effect and optimization results,thus forming a prediction-verification-reprediction closed-loop scheduling optimization strategy suitable for engineering applications.The optimization result of the MILP model provides a good initial point.By fixing the integer variables to the MILPoptimal value,the approximate MINLP optimal solution can be obtained through a NLP solution.The above solution strategy has been successfully applied to the actual gasoline production case of a refinery(3.5 million tons per year),and the results show that the strategy is effective and feasible.The optimization results based on the closed-loop scheduling optimization strategy have higher reliability.Compared with the standard particle swarm optimization algorithm,NPSO algorithm improves the optimization ability and efficiency to a certain extent,effectively reduces the blending cost while ensuring the convergence speed.

MLD-MPC Approach for Three-Tank Hybrid Benchmark Problem

The present paper aims at validating a Model Predictive Control(MPC),based on the Mixed Logical Dynamical(MLD)model,for Hybrid Dynamic Systems(HDSs)that explicitly involve continuous dynamics and discrete events.The proposed benchmark system is a three-tank process,which is a typical case study of HDSs.The MLD-MPC controller is applied to the level control of the considered tank system.The study is initially focused on the MLD approach that allows consideration of the interacting continuous dynamics with discrete events and includes the operating constraints.This feature of MLD modeling is very advantageous when an MPC controller synthesis for the HDSs is designed.Once the MLD model of the system is well-posed,then the MPC law synthesis can be developed based on the Mixed Integer Programming(MIP)optimization problem.For solving this MIP problem,a Branch and Bound(B&B)algorithm is proposed to determine the optimal control inputs.Then,a comparative study is carried out to illustrate the effectiveness of the proposed hybrid controller for the HDSs compared to the standard MPC approach.Performances results show that the MLD-MPC approach outperforms the standardMPCone that doesn’t consider the hybrid aspect of the system.The paper also shows a behavioral test of the MLDMPC controller against disturbances deemed as liquid leaks from the system.The results are very satisfactory and show that the tracking error is minimal less than 0.1%in nominal conditions and less than 0.6%in the presence of disturbances.Such results confirm the success of the MLD-MPC approach for the control of the HDSs.

Randomized MILP framework for Securing Virtual Machines from Malware Attacks

Cloud computing involves remote server deployments with public net-work infrastructures that allow clients to access computational resources.Virtual Machines(VMs)are supplied on requests and launched without interactions from service providers.Intruders can target these servers and establish malicious con-nections on VMs for carrying out attacks on other clustered VMs.The existing system has issues with execution time and false-positive rates.Hence,the overall system performance is degraded considerably.The proposed approach is designed to eliminate Cross-VM side attacks and VM escape and hide the server’s position so that the opponent cannot track the target server beyond a certain point.Every request is passed from source to destination via one broadcast domain to confuse the opponent and avoid them from tracking the server’s position.Allocation of SECURITY Resources accepts a safety game in a simple format as input andfinds the best coverage vector for the opponent using a Stackelberg Equilibrium(SSE)technique.A Mixed Integer Linear Programming(MILP)framework is used in the algorithm.The VM challenge is reduced by afirewall-based controlling mechanism combining behavior-based detection and signature-based virus detection.The pro-posed method is focused on detecting malware attacks effectively and providing better security for the VMs.Finally,the experimental results indicate that the pro-posed security method is efficient.It consumes minimum execution time,better false positive rate,accuracy,and memory usage than the conventional approach.

Optimal integration of solar home systems and appliance scheduling for residential homes under severe national load shedding

In developing countries like South Africa,users experienced more than 1030 hours of load shedding outages in just the first half of 2023 due to inadequate power supply from the national grid.Residential homes that cannot afford to take actions to mitigate the challenges of load shedding are severely inconvenienced as they have to reschedule their demand involuntarily.This study presents optimal strategies to guide households in determining suitable scheduling and sizing solutions for solar home systems to mitigate the inconvenience experienced by residents due to load shedding.To start with,we predict the load shedding stages that are used as input for the optimal strategies by using the K-Nearest Neighbour(KNN)algorithm.Based on an accurate forecast of the future load shedding patterns,we formulate the residents’inconvenience and the loss of power supply probability during load shedding as the objective function.When solving the multi-objective optimisation problem,four different strategies to fight against load shedding are identified,namely(1)optimal home appliance scheduling(HAS)under load shedding;(2)optimal HAS supported by solar panels;(3)optimal HAS supported by batteries,and(4)optimal HAS supported by the solar home system with both solar panels and batteries.Among these strategies,appliance scheduling with an optimally sized 9.6 kWh battery and a 2.74 kWp panel array of five 550 Wp panels,eliminates the loss of power supply probability and reduces the inconvenience by 92%when tested under the South African load shedding cases in 2023.

A NEW GLOBAL OPTIMIZATION ALGORITHM FOR MIXED-INTEGER QUADRATICALLY CONSTRAINED QUADRATIC FRACTIONAL PROGRAMMING PROBLEM

The mixed-integer quadratically constrained quadratic fractional programming(MIQCQFP)problem often appears in various fields such as engineering practice,management science and network communication.However,most of the solutions to such problems are often designed for their unique circumstances.This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP.We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming(EIGBFP)problem with integer variables.Secondly,we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively,and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator.After that,combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure,an efficient algorithm for solving MIQCQFP globally is proposed.Finally,a series of test problems are given to illustrate the effectiveness,feasibility and other performance of this algorithm.

Accelerated solution of the transmission maintenance schedule problem:a Bayesian optimization approach

To maximize the maintenance willingness of the owner of transmission lines,this study presents a transmission maintenance scheduling model that considers the energy constraints of the power system and the security constraints of on-site maintenance operations.Considering the computational complexity of the mixed integer programming(MIP)problem,a machine learning(ML)approach is presented to solve the transmission maintenance scheduling model efficiently.The value of the branching score factor value is optimized by Bayesian optimization(BO)in the proposed algorithm,which plays an important role in the size of the branch-and-bound search tree in the solution process.The test case in a modified version of the IEEE 30-bus system shows that the proposed algorithm can not only reach the optimal solution but also improve the computational efficiency.

Evaluation of the impact of commodity price change on mine plan of underground mining

Fluctuations in commodity prices should influence mining operations to continually update and adjust their mine plans in order to capture additional value under new market conditions. One of the adjustments is the change in production sequencing. This paper seeks to present a method for quantifying the net present value(NPV) that may be directly attributed to the change in commodity prices. The evaluation is conducted across ten copper price scenarios. Discrete event simulation combined with mixed integer programming was used to attain a viable production strategy and to generate optimal mine plans. The analysis indicates that an increase in prices results in an increased in the NPV from$96.57M to $755.65M. In an environment where mining operations must be striving to gain as much value as possible from the rights to exploit a finite resource, it is not appropriate to keep operating under the same mine plan if commodity prices alter during the course of operations.

Multi-period mine planning with multi-process routes

This paper attempts to optimize optimal capacities, block routing and mine sequencing problems in a mining system. The solution approach is based on a heuristics and the mixed integer programming (MIP). Unlike previous sequential solution approaches, the problems are herein solved at the same time. Furthermore, the proposed approach guarantees practical solutions because it considers ore material distribution within orebody. The paper has two main contributions: (a) the proposed approach generates production rates in a manner that the capacities are satisfied; (b) the proposed approach does not use pre-defined marginal cut-off grades. Thus, idle capacity problem is eliminated and different scheduling combinations are allowed. To see the performance of the approach proposed, a case study is carried out using a gold data. The schedule generated shows that the approach can determine optimal production rates, block destination and sequencing effectively.

A New Multi-Objective Model to Optimise Rail Transport Scheduler

The sugarcane transport system plays a critical role in the overall performance of Australia’s sugarcane industry. An inefficient sugarcane transport system interrupts the raw sugarcane harvesting process, delays the delivery of sugarcane to the mill, deteriorates the sugar quality, increases the usage of empty bins, and leads to the additional sugarcane production costs. Due to these negative effects, there is an urgent need for an efficient sugarcane transport schedule that should be developed by the rail schedulers. In this study, a multi-objective model using mixed integer programming (MIP) is developed to produce an industry-oriented scheduling optimiser for sugarcane rail transport system. The exact MIP solver (IBM ILOG-CPLEX) is applied to minimise the makespan and the total operating time as multi-objective functions. Moreover, the so-called Siding neighbourhood search (SNS) algorithm is developed and integrated with Sidings Satisfaction Priorities (SSP) and Rail Conflict Elimination (RCE) algorithms to solve the problem in a more efficient way. In implementation, the sugarcane transport system of Kalamia Sugar Mill that is a coastal locality about 1050 km northwest of Brisbane city is investigated as a real case study. Computational experiments indicate that high-quality solutions are obtainable in industry-scale applications.

Flexibility analysis for continuous ibuprofen manufacturing processes

Continuous ibuprofen(a widespread used analgesic drug)manufacturing is full of superiorities and is a fertile field both in industry and academia since it can not only effectively treat rheumatic and other chronic and painful diseases,but also shows great potential in dental diseases.As one of central elements of operability analysis,flexibility analysis is in charge of the quantitative assessment of the capability to guarantee the feasible operation in face of variations on uncertain parameters.In this paper,we focus on the flexibility index calculation for the continuous ibuprofen manufacturing process.We update existing state-of-the-art formulations,which traditionally lead to the max-max-max optimization problem,to approach the calculation of the flexibility index with a favorable manner.Advantages regarding the size of the mathematical model and the computational CPU time of the modified method are examined by four cases.In addition to identifying the flexibility index without any consideration of control variables,we also investigate the effects of different combinations of control variables on the flexibility property to reveal the benefits from taking recourse actions into account.Results from systematic investigations are expected to provide a solid basis for the further control system design and optimal operation of continuous ibuprofen manufacturing.

基于混合整数规划模型的PON与WiMAX融合网络规划(英文)

This article analyzes the characteristics of PON and WiMAX convergence network planning.Based on user coverage ratio,WiMAX channel allocation,cell radius,carrier-to-noise ratio threshold,and bandwidth constraint,we propose a mixed integer programming model solved by a Branch-Band and Heuristic Search method.Finally,the simulation result is given and analyzed.The planning method based on a mixed integer programming model can save 20 percentage of the overall planning cost,compared with the greedy algorithm.The relationship between the convergence network planning cost and frequency usage is also analyzed.The optimized planning result with the lowest cost can be acquired through the best frequency usage.

Component reallocation and system replacement maintenance based on availability and cost in series systems

Component reallocation(CR)is receiving increasing attention in many engineering systems with functionally interchangeable and unbalanced degradation components.This paper studies a CR and system replacement maintenance policy of series repairable systems,which undergoes minimal repairs for each emergency failure of components,and considers constant downtime and cost of minimal repair,CR and system replacement.Two binary mixed integer nonlinear programming models are respectively established to determine the assignment of CR,and the uptime right before CR and system replacement with the objective of minimizing the system average maintenance cost and maximizing the system availability.Further,we derive the optimal uptime right before system replacement with maximization of the system availability,and then give the relationship between the system availability and the component failure rate.Finally,numerical examples show that the CR and system replacement maintenance policy can effectively reduce the system average maintenance cost and improve the system availability,and further give the sensitivity analysis and insights of the CR and system replacement maintenance policy.

Decision-making model for risk management of cascade hydropower stations

In a medium-term electricity market,in order to reduce the risks of price and inflow uncertainties, the cascade hydropower stations may use the options contract with electricity supply companies. A profit-based model for risk management of cascade hydropower stations in the medium-term electricity market is presented. The objective function is profit maximization of cascade hydropower stations. In order to avoid the risks of price and inflow uncertainties, two different risk-aversion constraints: a minimum profit constraint and a minimum conditional value-at-risk, are introduced in the model. In addition, the model takes into account technology constraints of the generating units, which includes reservoir flow balance, reservoir capacity limits, water discharge constraints, etc. The model is formulated as a mixed integer nonlinear programming problem. Because the search space of the solution is very large, a genetic algorithm is used to deal with the problem.

Hybrid Continuous-Time MILP Model for Crude Oil Scheduling under the Influence of High Tides

Vessels,especially very large or ultra large crude carriers(VLCCs or ULCCs),often can only dock and leave the berth during high tide periods to prevent being stranded.Unfortunately,the current crude scheduling models do not take into account tidal conditions,which will seriously affect the feasibility of crude schedule.So we first focus on the docking and leaving operations under the tidal actions,and establish a new hybrid continuous-time mixed integer linear programming(MILP)model which incorporates global event based formulation and unit-specific event based formulation.Upon considering that the multiple blending of crude oil can easily cause the production fluctuating,there are some reasonable assumptions that storage tanks can only store pure crude,and charging tanks just can be refilled after being emptied,which helps us obtain a simple MILP model without composition discrepancy caused by crude blending.Two cases are used to demonstrate the efficacy of proposed scheduling model.The results show that the optimization schedule can minimize the demurrage of the vessels and the number of feeding changeovers of crude oil distillation units(CDUs).

Intelligent Scheduling for High Bulilding Multi-type Cooling System

In modern giant buildings,in order to improve energy utilization efficiency, cooling systems have developed from conventional chillers alone to smart energy net which includes chillers,ice storage,ground-source heat pump,combined cooling heating and power( CCHP) and so on. The reasonable distribution of load is the key to guarantee such system in economical operation.Based on typical multi-type cooling system,economic models of different devices are presented and real-time intelligent economic scheduling with the approach of mixed integer programming is carried out. This algorithm has been applied in a certain building of Shanghai and results of simulation show that it is able to provide guidance on intelligent economic scheduling for multi-type cooling system.

Solving open vehicle problem with time window by hybrid column generation algorithm

This paper addresses the open vehicle routing problem with time window(OVRPTW), where each vehicle does not need to return to the depot after completing the delivery task.The optimization objective is to minimize the total distance. This problem exists widely in real-life logistics distribution process.We propose a hybrid column generation algorithm(HCGA) for the OVRPTW, embedding both exact algorithm and metaheuristic. In HCGA, a label setting algorithm and an intelligent algorithm are designed to select columns from small and large subproblems, respectively. Moreover, a branch strategy is devised to generate the final feasible solution for the OVRPTW. The computational results show that the proposed algorithm has faster speed and can obtain the approximate optimal solution of the problem with 100 customers in a reasonable time.

Stochastic Programming For Order Allocation And Production Planning

Stochastic demand is an important factor that heavily affects production planning.It influences activities such as purchasing,manufacturing,and selling,and quick adaption is required.In production planning,for reasons such as reducing costs and obtaining supplier discounts,many decisions must be made in the initial stage when demand has not been realized.The effects of non-optimal decisions will propagate to later stages,which can lead to losses due to overstocks or out-of-stocks.To find the optimal solutions for the initial and later stage regarding demand realization,this study proposes a stochastic two-stage linear program-ming model for a multi-supplier,multi-material,and multi-product purchasing and production planning process.The objective function is the expected total cost after two stages,and the results include detailed plans for purchasing and production in each demand scenario.Small-scale problems are solved through a deterministic equivalent transformation technique.To solve the problems in the large scale,an algorithm combining metaheuristic and sample average approximation is suggested.This algorithm can be implemented in parallel to utilize the power of the solver.The algorithm based on the observation that if the remaining quantity of materials and number of units of products at the end of the initial stage are given,then the problems of the first and second stages can be decomposed.