A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

Integrated lot sizing and energy-efficient job shop scheduling problem in manufacturing/remanufacturing systems

This paper presents a spreadsheet-based decision support system (DSS) for any parameter optimization problem, in the small- and medium-sized enterprises to help the managers to make better decisions. Microsoft Excel is used as a DSS development platform. The DSS application requires the quality characteristics and the level of parameters affecting the problem. The proposed system considers three multi-criteria decision-making methods: TOPSIS, VIKOR and GRA. These methods are integrated into the Taguchi method to convert the multi-response optimization problem to a single-response problem. The DSS suggests proper Taguchi experimental designs and provides the decision maker with an opportunity to use different metrics and to validate the experimental results. Several issues and an application are provided for illustrative purposes. The proposed DSS is tested on a case study (the performance of the mixed integer programming (MIP) formulation solver) and the results highlight that the system is capable of offering satisfactory outcomes. Using such a quick and flexible DSS might help to reduce the daily workload of the decision makers. The different metrics used for the response variables which results with the different parameter combination. Using the optimal parameter combination of TOPSIS (come to the fore in case MinBest metric used), the MIP formulation solver gives the best integer objective function value of 609 and a GAP value of 1.93%, both of which are less than the values obtained using the other methods. Using the optimal parameter combination of GRA (come to the fore in case OptBest metric used), the MIP formulation gives a best integer objective function value of 632 and a GAP value of 6.52%, both of which are less than the values obtained by using the other methods.

The isolated community evacuation problem with mixed integer programming

An extended robust approach for a cooperative inventory routing problem

A cutting plane algorithm for the site layout planning problem with travel barriers

Scheduling experiments on a nuclear reactor using mixed integer programming

High transportation cost and low service quality are common weaknesses in different logistics networks, especially in food delivery. Due to its perishable features, the quality of the food will deteriorate during the while delivery process. In this paper, a two-stage location–routing–inventory problem with time windows (2S-LRITW) for food products is proposed. The first stage corresponds to a location–routing–inventory problem with time windows and the second stage is the transportation problem with vehicle capacity constraints. The problem is formulated as a mixed integer-programming model. Then a hybrid heuristic is proposed, in which distance-based clustering approach, mutation operation and the relocate exchange method are introduced to improve performance of algorithm. At last, the hybrid heuristic was tested using several cases, including some small instances and a real-life case. The results show that the distance-based clustering approach can efficiently improve the convergence speed. And the IACO and the relocate exchange method can enlarge the search space. As a result, the hybrid heuristic is suitable for solving practical larger scale problem. Furthermore, the results also indicate that customer sequence has great effect on the object due to the energy cost considered.

The aim of this work was to study a distribution and lot-sizing problem that considers costs with transportation to a company warehouse as well as, inventory, production and setup costs. The logistic costs are associated with necessary containers to pack produced items. The company negotiates a long-term contract in which a fixed cost per period is associated with the transportation of the items. On the other hand, a limited number of containers are available with a lower cost than the average cost. If an occasional demand increase occurs, other containers can be utilized; however, their costs are higher. A mathematical model was proposed in the literature and solved using the Lagrangian heuristic. Here, the use of the Lagrangian/surrogate heuristic to solve the problem is evaluated. Moreover, an extension of the literature model is considered adding capacity constraints and allowing backlogging. Computational tests show that Lagrangian/surrogate heuristics are competitive, especially when the capacity constraints are tight.

A memetic algorithm for a multistage capacitated lot-sizing problem

Collaborative routing aided by drones in last-mile delivery (LMD) has been an extensively studied topic in recent years. In this article, a new optimization problem for collaborative routing with a truck and a fleet of drones in LMD is introduced. The problem proposes a new strategy to coordinate a truck and a fleet of drones to serve a given set of customers. The plan is based on identifying the locations where the truck can park and where the drones fly to serve the customers. A procedure to locate these parking lots conveniently is given. For the transportation network, which includes these points, a mixed linear integer programming formulation is provided, which aims to minimize the makespan of serving all the customers. Computational experiments on a set of problem instances were conducted to analyze the model solutions' characteristics and find their computational limits. The experiments showed that the proposed model could significantly improve the results obtained when only the truck delivers. Additionally, we propose a GRASP metaheuristic to solve instances of greater size. Its computational performance was studied when applied to a set of instances with different characteristics. The paper discusses some insights obtained from the computational experimentation and presents future research directions.

Lot-sizing and pricing problems have been addressed quite extensively. Most literature study the problems and develop models from the perspective of operations management. Fewer works can give an operational research model as well as exact solutions methods. In this paper, we investigate a joint lot-sizing and pricing problem with the consideration of capacity constraints and backlogging. We make the decision on production planning over a finite multi-period horizon. The demand of each period is related to the price. Therefore, we first propose a nonlinear mixed integer model with the nonlinear objective function to maximize the total profit. The model cannot be solved by off-the-shelf solver directly. Second-order conic programming (SOCP) technique is applied to transform the model into a specific nonlinear model, which can be solved by CPLEX. We develop a mixed integer second-order program (MI-SOCP) model and finally, we conduct the experiment and give an exact solution. Moreover, we make sensitivity analyses on the two parameters.

Heuristic genetic algorithms for general capacitated lot-sizing problems

A new mixed integer programming formulation is presented for cyclic scheduling in flow lines with parallel machines and finite in-process buffers, where a Minimal Part Set (MPS) in the same proportion as the overall production target is repetitively scheduled. The cycle of parts in an MPS is not determined a priori, but is obtained along with the optimal schedule for all parts. In addition to the cyclic scheduling, a cyclic-batch scheduling mode is introduced, where within the MPS the parts of one type are processed consecutively. Numerical examples are included and some results of computational experiments are reported.

In this study, we investigated the time-varying capacitated lot-sizing problem under a fast-changing production environment, where production factors such as the setup costs, inventory-holding costs, production capacities, or even material prices may be subject to continuous changes during the entire planning horizon. Traditional lot-sizing theorems and algorithms, which often assume a constant production environment, are no longer fit for this situation. We analyzed the time-varying environment of today’s agile enterprises and modeled the time-varying setup costs and the time-varying production capacities. Based on these, we presented two mixed-integer linear programming models for the time-varying capacitated single-level lot-sizing problem and the time-varying capacitated multi-level lot-sizing problem, respectively, with considerations on the impact of time-varying environments and dynamic capacity constraints. New properties of these models were analyzed on the solution’s feasibility and optimality. The solution quality was evaluated in terms of the entropy which indicated that the optimized production system had a lower value than that of the unoptimized one. A number of computational experiments were conducted on well-known benchmark problem instances using the AMPL/CPLEX to verify the proposed models and to test the computational effectiveness and efficiency, which showed that the new models are applicable to the time-varying environment. Two of the benchmark problems were updated with new best-known solutions in the experiments.

The optimal restoration problem lies at the foundation of the evaluation and improvement of resilience in power systems. In this report we present a scalable decomposition algorithm for solving this problem for realistic power systems. The algorithm has been developed in three major research threads, corresponding to the chapters in the present report. Chapter 1 studies mixed-integer programming (MIP) formulations for the requirement that each electrical island that appears after a recon guration must have at least one energized generator. We provide three alternative MIP formulations for this restriction, show their equivalence, and prove that two of them are stronger in terms of their linear programming relaxation than the formulation most commonly used in the power systems literature. Since the time to solve MIPs can vary signi cantly between equivalent formulations, we also present computational experiments on IEEE test systems for the Intentional Controlled Islanding (ICI) and the Black Start Allocation (BSA) problems. We observe that a polynomially separable, exponential in size, strong formulation yields the best performance for the BSA problem and exhibits a comparable performance to a linear in size, weak formulation for the ICI problem. Chapter 2 presents a methodology to generate mixed-integer linear approximations of the AC power ow equations governing lines, transformers (including tap regulators and phase shifters), shunt and series compensators, and consumption responsive to voltage. Our approximations are capable of capturing limitations for power grids under abnormal or uncommon operating conditions where common assumptions used in power ow relaxations may not hold. Particularly, the approximation captures overvoltages under almost no load, which is a major concern when energizing lines after a blackout. The method constructs piecewise linear approximations of the non-linear power ow equations by minimizing the squared approximation error over a subset of the feasible domain. We test the method using a realistic database for the Chilean system (1548 buses, 1114 lines, 564 transformers). The resulting approximations yield root mean square errors in the order of 0.05pu and are successfully applied to solve a transmission switching instance for the Chilean system. Chapter 3 presents our algorithm for optimal restoration. The algorithm works by partitioning the problem into a master problem and a slave problem. The master problem optimizes over energization sequences of generators, buses and branches, for the entire restoration horizon, while respecting the energization requiments studied in Chapter 1. The slave problem veri es that there exist power ow solutions supporting the energization sequences proposed by the master problem, adding cuts to the master if an infeasible sequence is detected.