A local search algorithm for the optimization of the stochastic economic lot scheduling problem

This paper describes a model for the stochastic economic lot scheduling problem (SELSP) and a Local Search heuristic to find close to optimal solutions to this model. The SELSP considers multiple products, which have to be scheduled on a single facility with limited capacity and significant setup times and costs. The demand is modeled as a stationary compound renewal process. The objective is to find a schedule that minimizes the long-run average costs for setups and inventories while satisfying a given fill rate. We use a cyclic scheduling approach in which the individual cycle time of each product is a multiple of some basic period (fundamental cycle).For the deterministic version of the SELSP, efficient heuristics have been developed which guarantee the feasibility of the solution by adding an additional constraint to the problem. In our case this is not sufficient, because for the calculation of the average inventory levels and fill rates we need to develop a schedule with detailed timing of the lots. We present an efficient heuristic for this scheduling problem, which can also be used to check the feasibility of the solution. Thereby, the most time-consuming step (the calculation of average inventory levels and fill rates) is only performed for a limited set of candidates.The algorithm was tested on deterministic benchmark problems from literature and on a large set of stochastic instances. We report on the performance of the heuristic in both cases and try to identify the main factors influencing the objective.     

Two-stage flowshop earliness and tardiness machine scheduling involving a common due window

This paper studies a non-preemptive two-stage flowshop scheduling problem to minimize the earliness and tardiness under the environment of a common due window. The window size and the window location are considered to be given parameters. The just-in-time problem exists naturally and has many practical applications. The problem is shown to be NP-complete in the strong sense. We develop a branch and bound algorithm and a heuristic to solve the problem. We conduct the computational experiments to test the performances of the algorithms. A strong lower bound is derived for the branch and bound algorithm that can efficiently solve 15 jobs problem for about 5 minutes. The heuristic is shown to be efficient and effective, which can solve the problem of 150 jobs for about 20 seconds and provide near-optimal solution. We justify that the heuristic is an excellent solution approach for large problem instances. We also show that four special cases are either polynomial solvable or NP-complete in the ordinary sense.     

Variable neighborhood search heuristic for nonconvex portfolio optimization

Abstract

In this article we consider a portfolio optimization problem under multiple real-world constraints, such as: cardinality constraints, tracking error, active share, and turnover. We propose a heuristic based on variable neighborhood search (VNS) that effectively addresses additional constraints that introduce non-convexities. In the VNS-based heuristic, several neighborhood structures are introduced and fast local search is implemented. We develop a VNS portfolio rebalancing framework (VNS-PRF) with two rebalance strategies. Data sets provided by a financial investment firm are used to evaluate the validity and reliability of the proposed VNS-PRF. Computational experiments and different portfolio performance measures indicate that our approach is able to obtain solutions with competitive quality and can be applied on large-scale data sets.     

Heuristics for operational fixed job scheduling problems with working and spread time constraints

Operational fixed job scheduling problems select a set of jobs having fixed ready and processing times and schedule the selected jobs on parallel machines so as to maximize the total weight. In this study, we consider working time and spread time constrained versions of the operational fixed job scheduling problems. The working time constraints limit the total processing load on each machine. The spread time constraints limit the time between the start of the first job and the finish of the last job on each machine. For the working time constrained problem, we present a filtered beam search algorithm that evaluates the promising nodes of the branch and bound tree. For the spread time constrained problem we propose a two phase algorithm that defines the promising sets for the first jobs and finds a solution for each promising set. The results of our computational tests reveal that our heuristic algorithms perform very well in terms of both solution quality and time.     

The maximum capture per unit cost location problem

This paper considers the problem of siting p new facilities of an entering firm to a competitive market so as to maximize the market share captured from competitors per unit cost. We first formulate the problem as a mixed 0-1 fractional programming model, in which we incorporate the fixed cost and transportation cost. The model can deal with the case where some demand nodes have two or more possible closest servers. We then re-formulate the problem as a 0-1 mixed integer linear program. We use a one-opt heuristic algorithm based on the Teitz-Bart method to obtain feasible solutions and compare them with the optimal solutions obtained by a branch-and-bound algorithm. We conduct computational experiments to evaluate the two algorithms. The results show that both algorithms can solve the model efficiently and the model is integer-friendly. We discuss other computational results and provide managerial insights.     

A note on constructive heuristics for the flowshop problem with blocking

This paper analyzes the minimization of the makespan criterion for the flowshop problem with blocking. In this environment, there are no buffers between successive machines, and therefore intermediate queues of jobs waiting in the system for their next operations are not allowed. As the problem is NP-hard, a constructive heuristic that explores specific characteristics of the problem is developed. The small computational effort of such strategy, which is valuable in practical applications, is one of the reasons that motivated this study. The performance of a combination of the proposed method with existing ones is examined through a comparative study. The new methods outperform the NEH algorithm, currently the best constructive heuristic for this problem, in problems with up to 500 jobs and 20 machines.     

Order acceptance and scheduling in a two-machine flowshop

We study the order acceptance and scheduling problem in a two-machine flowshop. The firm receives a pool of orders before a planning period, each of which is characterized by revenue, processing times on machines 1 and 2, a due date, and a tardiness penalty. The firm seeks to decide on the orders to accept and schedule the accepted orders so as to maximize the total net revenue. We formulate the problem as mixed-integer linear programming models, and develop a heuristic and a branch-and-bound (B&B) algorithm based on some derived dominance rules and relaxation techniques. We assess the performance of the B&B algorithm and the heuristic via computational experiments. The computational results show that the B&B algorithm can solve problem instances with up to 20 jobs within a reasonable time while the heuristic is efficient in approximately solving large instances of the problem.     

Interlocking of information systems for international supply and demand chains management

This paper is concerned with coordination aspects of supply chain management and, in particular, investigates setup coordination between two and three stages of a supply chain. The problem arises from a real application in the production chain of a kitchen furniture plant. In different stages of the plant, items are grouped according to different attributes. A setup is required in a stage when the new batch has a different level of attribute from the previous one. Two objectives are considered, i.e., minimizing the total number of setups and minimizing the maximum number of setups of the stages. The problem is to determine a sequence of batches in search for Pareto-optimal solutions with respect to the two objectives. Several metaheuristics, including genetic algorithm, simulated annealing, and iterated local search (ILS) have been proposed for the two-stage problem. In this paper, we develop a constructive heuristic, which combines a least flexibility first principle and a greedy search, for the two- and three-stage problems. Computational results show that the proposed heuristic performs significantly better than the genetic algorithm and simulated annealing. Although the proposed heuristic is inferior to the ILS, which employs two constructive initial solution heuristic, for the two-stage problem, it can be easily extended to the three-stage problem.     

Particle swarm optimization with cocktail decoding method for hybrid flow shop scheduling problems with multiprocessor tasks

This paper addresses the problem of multiprocessor task-scheduling in a hybrid flow shop (HFS) problem to minimize the makespan. Due to the complex nature of an HFS problem, it is decomposed into the following two sequential decision problems: determining the job permutation in stage 1, followed by a decoding method to assign jobs into each machine in subsequent stages when designing a heuristic algorithm. The decoding method plays a pivotal role for improving the solution quality of any algorithm for the HFS problem. However, the majority of existing algorithms ignores the problem and is only concerned with the first decision problem. This study emphasizes the importance of the decoding method via a small test, and searches for a number of solid decoding methods that can be incorporated into the cocktail decoding method. Then, this study develops a particle swarm optimization (PSO) algorithm that can be combined with the cocktail decoding method. In the PSO, a variety of job sequences are generated using the PSO procedure in stage 1, and the cocktail decoding method is used to assign the jobs to machines in sequential stages. Moreover, a modified lower bound is introduced. Computational results show that the proposed lower bound is competitive, and with the help of the cocktail decoding method, the proposed PSO, and even the adoption of a standard PSO framework, significantly outperforms the majority of existing algorithms in terms of quality of solutions, especially for large problems.     

Non-permutation flowshop scheduling in a supply chain with sequence-dependent setup times

In this paper, we consider a flowshop scheduling problem with sequence-dependent setup times and a bicriteria objective to minimize the work-in-process inventory for the producer and to maximize the customers' service level. The use of a bicriteria objective is motivated by the fact that successful companies in today's environment not only try to minimize their own cost but also try to fulfill their customers' need. Two main approaches, permutation and non-permutation schedules, are considered in finding the optimal schedule for a flowshop. In permutation schedules the sequence of jobs remains the same on all machines whereas in non-permutation schedule, jobs can have different sequence on different machines. A linear mathematical model for solving the non-permutation flowshop is developed to comply with all of the operational constraints commonly encountered in the industry, including dynamic machine availabilities, dynamic job releases, and the possibility of jobs skipping one or more machines, should their operational requirements deem that it was necessary. As the model is shown to be NP-hard, a metasearch heuristic, employing a newly developed concept known as the Tabu search with embedded progressive perturbation (TSEPP) is developed to solve, in particular, industry-size problems efficiently. The effectiveness and efficiency of the search algorithm are assessed by comparing the search algorithmic solutions with that of the optimal solutions obtained from CPLEX in solvable small problem instances.     

A DC programming heuristic applied to the logistics network design problem

This paper proposes a new heuristic method for the logistics network design and planning problem based on linear relaxation and DC (difference of convex functions) programming. We consider a multi-period, multi-echelon, multi-commodity and multi-product problem defined as a large scale mixed integer linear programming (MILP) model. The method is experimented on data sets of various size. The numerical results validate the efficiency of the heuristic for instances with up to several dozens facilities, 18 products and 270 retailers.     

A tabu search algorithm for the relocation problem in a warehousing system

Relocation of items in a warehousing system is usually used when the handling machines become the bottleneck. This paper addresses the optimization problem of relocation in a warehouse with dynamic operating policy. An integer linear programming formulation is proposed. A two-stage heuristic method is developed to generate an initial solution. A tabu search algorithm is proposed to improve the solution. Two relocation policies are studied and their performances are compared.     

An efficient heuristic for medium-term planning in shampoo production

This paper presents a single machine problem which occurs in shampoo production at medium-term planning phase. The considered production plant is linked to subsidiary companies which are themselves linked to final customers. The aim is to answer subsidiary companies requests by keeping their stocks in a window defined by their safety stock and maximum inventory levels. After an introduction, we present a formal definition of the problem. Next, we present a two-phase heuristic algorithm: the first phase is based on a greedy algorithm and the second phase on the Goldberg and Tarjan algorithm for the minimum cost flow problem. Experimental testings close to industrial instances show that the heuristic performs very efficiently.     

Resource management in software as a service using the knapsack problem model

This paper proposes a resource allocation model for “Software as a Service” systems that maximizes the service provider's revenues and the resource utilization under a heavy load. Employing the elasticity of virtualized infrastructures, the proposed model dictates that system resources must be fully exploited by incoming jobs, even if they do not satisfy their requirements completely. This yields a higher Service Level Agreement violation probability, which is mitigated by the assignment of more resources when these become available. The problem is deduced to the Fractional Knapsack problem and the heuristic solution is implemented in the frame of a SOA environment.     

Ship routing problem with berthing time clash avoidance constraints

We consider a ship routing problem in which multiple vessels have to perform pickups and deliveries of cargoes at various locations. The loading and unloading time of cargoes at pickup and delivery locations is significant, and at each of these locations we need to assign a time slot to each vessel to perform the loading/unloading task so as to avoid time clashes. This problem is motivated by the operations of feeder vessels and company-owned cargo terminals, where the shipping company wishes to coordinate the routing and the berthing time of its vessels. We develop a heuristic algorithm for the problem using set partitioning formulation and column generation techniques. The effectiveness of the heuristic is tested via extensive computational experiments.     

Stochastic single-source capacitated facility location model with service level requirements

A stochastic version of single-source capacitated facility location problem is considered. A set of capacitated facilities is to be selected to provide service to demand points with stochastic demand at the minimal total cost. The facilities have service level requirements modeled by chance constraints. For Poisson demand, the problem is proved equivalent to a known solvable deterministic problem. For Normally distributed demand, it is equivalent to a deterministic mixed integer non-linear programming problem. A hybrid heuristic of Lagrangean relaxation with a single-customer-multi-exchange heuristic is embedded within a branch-and-bound framework to find upper and lower bounds for this problem. From test instances created from benchmark problems (10–20 facilities and 50 demand nodes) and real-life data on the deterministic problem, the gap between the bounds is within 6.5% with an average of 2.5%.     

Determination of an order-up-to policy in the stochastic economic lot scheduling model

We consider a production–inventory problem with compound renewal item demand. The model consists of stockpoints, one for each item, controlled according to (R,S)-policies and one machine which replenishes them. The replenishment orders are produced with a fixed rate on the machine with significant setup times and costs, which are stochastic and sequence dependent. The time between the release and the production of the replenishment order is called the waiting time. We develop analytical approximations for the first two moments of this waiting time, the order-up-to levels and the average physical inventory levels for all stockpoints, given the target fill rates. These analytical approximations allows for a quick evaluation of the waiting time which is important when optimization of the system is considered.     

Inventory control in a two-level supply chain with risk pooling effect

We consider an inventory control problem in a supply chain consisting of a single supplier, with a central distribution center (CDC) and multiple regional warehouses, and multiple retailers. We focus on the problem of selecting warehouses to be used among a set of candidate warehouses, assigning each retailer to one of the selected warehouses and determining replenishment plans for the warehouses and the retailers. For the problem with the objective of minimizing the sum of warehouse operation costs, inventory holding costs at the warehouses and the retailers, and transportation costs from the CDC to warehouses as well as from warehouses to retailers, we present a non-linear mixed integer programming model and develop a heuristic algorithm based on Lagrangian relaxation and subgradient optimization methods. A series of computational experiments on randomly generated test problems shows that the heuristic algorithm gives relatively good solutions in a reasonable computation time.     

Scheduling a single batch processing machine with arbitrary job sizes and incompatible job families

Motivated by a bottleneck operation in a multi-layer ceramic capacitor production line, we study a scheduling problem of batch processing machine in which a number of jobs are processed simultaneously as a batch. The performance measures considered include makespan, total completion time, and total weighted completion time. We first present a new simple integer programming formulation for the problem, and using this formulation, one can easily find optimal solutions for small problems. However, since the problem is NP-hard and the size of a real problem is very large, we propose a number of heuristic algorithms and design a hybrid genetic algorithm to solve practical big-size problems in a reasonable computational time. To verify performance of the algorithms, we compare them with lower bounds for the problems. From the results of these computational experiments the heuristic algorithms including the genetic algorithm show different performances for the three problems.     

Multiple part-type scheduling in flexible robotic cells

This paper considers the scheduling problem arising in two-machine manufacturing cells which repeatedly produce a set of multiple part-types, and where transportation of the parts between the machines is performed by a robot. The cycle time of the cell depends on the robot move sequence as well as the processing times of the parts on the machines. For highly flexible CNC machines, the processing times can be adjusted. To this end, this study tries to find the robot move sequence as well as the processing times of the parts on each machine that jointly minimize the cycle time. The problem of determining the best cycle in a 2-machine cell is first modeled as a traveling salesman problem. Then, an efficient 2-stage heuristic algorithm is constructed and compared with the most common heuristic approach of longest processing time (LPT).