Heuristic genetic algorithms for general capacitated lot-sizing problems

A Simple Heuristic Algorithm Based on Segmentation to Solve Multilevel Lot-sizing Problems

The aim of this work is to propose a solution approach for a capacitated lot sizing and scheduling real problem with parallel machines and shared buffers, arising in a packaging company producing yoghurt. The problem has been formulated as a hybrid Continuous Set-up and Capacitated Lot Sizing Problem (CSLP–CLSP). A new effective two stage optimisation heuristic based on the decomposition of the problem into a lot sizing problem and a scheduling problem has been developed. An assignment of mixture to buffers is made in the first stage, and therefore the corresponding orders are scheduled on the production lines by performing a local search. Computational tests have been performed on the real data provided by the company. The heuristic exhibits near-optimal solutions, all obtained in a very short computational time.

In this paper, we consider a serial supply chain (SC) operating with deterministic and known customer demands and costs of review or orders, holding, and backlog at every installation over a finite planning horizon. We present an evaluation of two order policies: Periodic-review order-up-to S policy (i.e., (T, S) policy), and (s, S) policy. We first present a mathematical programming model to determine optimal re-order point and base-stock for every member in the SC. By virtue of the computational complexity associated with the mathematical model, we present genetic algorithms (GAs) to determine the order policy parameters, s and S for every stage. We compare the performances of GAs (for obtaining installation s and S) with the mathematical model for the periodic-review order-up-to (T, S) policy that obtains in its class optimal review periods and order-up-to levels. It is observed that the (s, S) policy emerges to be mostly better than the (T, S) policy.

Capital replacement models with finite planning horizons can be used to model replacement policies in complex operational contexts. They may also be used to investigate the cost consequences of technological change. This paper reviews the application of these models in various such contexts. We also compare fixed planning horizon models with variable planning horizon models. As technological change, and hence the requirement of users and customers, often drives replacement decisions rather than cost optimality, the modelling focuses not only on obtaining optimal policies, but also on determining the increased cost of sub-optimal policies. The role of penalty cost formulations is also discussed. These ideas are illustrated using a number of case histories from medicine and transport.

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

In this paper, a mathematical model is established for the three-dimensional packing problem. This model is a multi-objective optimization problem which considers two factors: volume utilization ratio and load utilization ratio. This paper uses heuristic algorithm to design on the basis of the actual experience of packing. At the same time, combining genetic algorithm and heuristic algorithm, a three-dimensional hybrid genetic heuristic algorithm (3D-HGH) is proposed. This algorithm improves the performance of heuristic algorithm and improves the utilization ratio. The results of three-dimensional visualization of loading are obtained by simulation experiments.

Meta-heuristics for dynamic lot sizing: A review and comparison of solution approaches

We address the effect of uncertainty on a manufacturer’s dynamic production and pricing decisions over a finite planning horizon. The demand for products, which depends on their price, is characterized by two stochastic processes: potential demand and customer price sensitivity. An optimal policy for coordinating production and pricing is a time-dependent feedback rule with respect to the state of the manufacturer’s inventories. We show that when the volatility of customer sensitivity to the product price is negligible, the optimal policy can be obtained analytically. Moreover, our simulations demonstrate that the volatility of stochastic customer price sensitivity does not have a strong effect on the manufacturer’s expected profit. Therefore, the solution derived for the case of customer price sensitivity with zero volatility can serve as a good approximation heuristic for the optimal policy if the true volatility of customer price sensitivity is within 40 % of its mean and the volatility of potential demand is within 25 % of its mean. Moreover, under these conditions, a simplified, time-independent control rule deteriorates expected profits by only 1.5 %.

Ratchet consumption over finite and infinite planning horizons

A relax-and-fix Pareto-based algorithm for a bi-objective vaccine distribution network considering a mix-and-match strategy in pandemics

This paper deals with the configuration of a wireless network with the aim of minimizing the overall cost of both operation and network installation. The trade-off between the operation cost and the installation cost is the key consideration when designing cellular telecommunication networks, and can save costs and improve the performance of the network. In this paper, we propose an integrated framework for selecting Mobile Switching Center (MSC) among the candidate MSCs and assigning Base Stations (BSs) to the selected MSCs with the objective function of minimizing the cost of MSC setup, BS to MSC cabling, as well as the cost of handover. Capacity constraint for the selected MSC is also considered in the problem. The problem is expressed in an integer programming model and the Lagrangian relaxation method is proposed to solve the problem by dualizing some constraints. The Lagrangian relaxed problem is decomposed into subproblems that can be resolved optimally. The Lagrangian heuristic algorithm is suggested to find feasible solutions to the original problem. Computational experiments are performed to test the effectiveness and efficiency of the proposed heuristic algorithm. In the experiments, Lagrangian bounds on the optimal solution are used to show the effectiveness of the algorithm. The results of the proposed algorithm are also compared with those of some conventional meta-heuristics, Tabu search (TS) and Genetic algorithm (GA). The computational experiments show that the performance of the proposed heuristics is satisfactory in both the speed and the quality of the solution generated.

Inventory issues are often a major concern as they significantly impact operating costs. Lot sizing is one of the key decisions in managing inventory. However, in a real context, the demand for each item is often uncertain. It is supplied from the same supplier, requiring product orders to be placed in the same period. In addition, limited vehicle capacity and transportation costs are important factors to consider in making multi-item lot sizing decisions. The purpose of this study is to propose a new inventory model multi-item lot sizing model involving transportation cost and capacity constraints under stochastic demand. The decision variables involved in the model are each item's ordering cycle and safety factor with the objective function of minimizing the total inventory cost. To optimize the inventory model, this study also offers the advanced procedure of the Aquila Algorithm. This study also presents sensitivity analysis to the appropriate policy for optimizing the multi-item lot-sizing inventory problem involving transportation cost and capacity constraint under stochastic demand.

The problem of scheduling jobs on parallel machines to minimize total tardiness is NP problem. The properties of p // T macr problem were discussed. Base on the properties, the decoding function block decoding algorithm (BDA) of Genetic Algorithm (GA) was designed. Between the encoding space and the solution space, the element numbers of the encoding space are not necessary large than elements of the solution space, It only necessary that at least one element in encoding space corresponds an optimal solution by the decoding function. The encoding space of this paper is n-list space which element is a permutation of n elements. It is proved that at least one optimal solution is corresponded to a permutation of encoding space by the BDA. By the computational experiments, The performance of GA is best than four Heuristic Algorithms (WI,DS,TPI,KPM).

This paper proposes a loss minimum reconfiguration method by Tabu Search for open loop radial distribution system with distributed generators. The problem is to find the optimal normal open sectionalizing switch positions which minimize the total distribution line losses subjected to the line/transformer capacity constraints and voltage constraint. Generally, the problem is mathematically formulated as a complex combinatorial optimization problem or mixed integer programming problem, and is solved by using mathematical programming method, heuristic algorithm, intelligent method, etc. However, satisfactory algorithm for power companies has not yet been attained both in computational burden and solution accuracy. Thus, in this paper, the authors propose a method to solve the above problem by using Tabu Search (TS) method. Reverse power flow caused by distributed generators can be included in the solution algorithm. TS is one of meta-heuristic algorithms, and sometimes evaluated to be better compared with Genetic Algorithm (GA) or Simulated Annealing (SA) from viewpoints of both computational speed and solution accuracy. In order to evaluate the validity and efficiency of the algorithm, several numerical examples are shown in this paper.

In this paper, a hybrid flow shop scheduling problem with a new approach considering time lags and sequence-dependent setup time in realistic situations is presented. Since few works have been implemented in this field, the necessity of finding better solutions is a motivation to extend heuristic or meta-heuristic algorithms. This type of production system is found in industries such as food processing, chemical, textile, metallurgical, printed circuit board, and automobile manufacturing. A mixed integer linear programming (MILP) model is proposed to minimize the makespan. Since this problem is known as NP-Hard class, a meta-heuristic algorithm, named Genetic Algorithm (GA), and three heuristic algorithms (Johnson, SPTCH and Palmer) are proposed. Numerical experiments of different sizes are implemented to evaluate the performance of presented mathematical programming model and the designed GA in compare to heuristic algorithms and a benchmark algorithm. Computational results indicate that the designed GA can produce near optimal solutions in a short computational time for different size problems.