Multi-item production routing problem with backordering: a MILP approach

The aim of this paper is to present mixed integer linear programming formulations for the production routing problem with backordering (PRP-B) and a new hybrid heuristic to solve the problem. The PRP-B is considered in the context of a supply chain consisting of a production facility with limited production and storage capacities and geographically dispersed points of sale with limited storage capacities. The PRP-B integrates multiple item lot sizing decisions and vehicle routing decisions to the points of sale, where backordering of end customer demands is allowed at a penalty. Two integrated mixed integer programming models are formulated and a solution procedure consisting of a relax-and-fix heuristic combined with a local search algorithm is proposed. The numerical results show that this hybrid heuristic outperforms a state-of-the-art MIP commercial solver, in terms of solution quality and CPU times.     

Dynamic allocation of communicating tasks in computational grids

This paper studies task allocation in computational grids operating in a dynamic and uncertain environment. Computational grids consist of loosely coupled heterogeneous resources or agents with finite buffer capacities. These grids are primarily used to process large-scale applications consisting of several interdependent tasks. The task allocation problem is modeled as an infinite horizon Markov decision process, with the resource service times and the task arrivals following general probability distributions. We explicitly consider the communication cost between agents incurred in coordinating the execution of interdependent tasks. We show that a stationary optimal policy exists for this task allocation problem. Furthermore, we develop an action elimination procedure for reducing the complexity of computational methods in finding the optimal policy. We also present a real-time heuristic policy based on certain structural properties of the problem. Finally, computational results are presented that compare the performance of the heuristic policy with respect to other approaches for allocating tasks in the grid. Results from this paper are also applicable to the task allocation problem in manufacturing and service areas such as distributed design, project management and supplier coalitions.     

SHAPE: A construction algorithm for area placement evaluation

A construction algorithm for the plant layout problem is presented. The problem is formulated as a generalized assignment problem with the objective of minimizing total movement costs. The solution algorithm is a heuristic that utilizes an analogy to the special case of locating one item within a warehouse repetitively for placing and constructing departments. The procedure is sensitive to the departmental areas and approaches the problem as one of area placement. The algorithm provides a large degree of regularity in departmental shape and overall layout outline without having to pre-specify any particular shape. The compact and simple computational nature of the algorithm makes it suitable for adaption to an interactive microcomputer environment.     

Analysis of serial production lines: characterisation study and a new heuristic procedure for optimal buffer allocation

Buffer allocation in serial production lines is one of the important design issues, and hence it has been studied extensively in the literature. In this paper, we analyse the problem to characterise the optimal buffer allocation; specifically, we study the cases with single and multiple bottleneck stations under various experimental conditions. In addition, we develop an efficient heuristic procedure to allocate buffers in serial production lines to maximise throughput. The results of the computational experiments indicate that the proposed algorithm is very efficient in terms of both solution quality and CPU time requirements. Moreover, the characterisation study yields interesting findings that may lead to important practical implications. A comprehensive bibliography is also provided in the paper.     

Improved imperialist competitive algorithms for rebalancing multi-objective two-sided assembly lines with space and resource constraints

In this paper, a mathematical model and an improved imperial competition algorithm (IICA) are proposed to solve the multi-objective two-sided assembly line rebalancing problem with space and resource restrictions (MTALRBP-SR). The aim is to find lines’ rebalance with the trade-off between efficiency, rebalancing cost and smoothing after reconfiguration. IICA utilises a new initialisation heuristic procedure based on classic heuristic rules to generate feasible initial solutions. A novel heuristic assimilation method is developed to vigorously conduct local search. In addition, a group-based decoding heuristic procedure is developed to fulfil the final task reassignment with the additional restrictions. To investigate the performance of the proposed algorithm, it is first tested on MTALRBP of benchmark problems and compared with some existing algorithms such as genetic algorithm, variable neighbourhood search algorithm, discrete artificial bee colony algorithm, and two iterated greedy algorithms. Next, the efficiency of the proposed IICA for solving MTALRBP-SR is revealed by comparison with a non-dominated sorting genetic algorithm (NSGA-II) and two versions of original ICA. Computational results and comparisons show the efficiency and effectiveness of IICA. Furthermore, a real-world case study is conducted to validate the proposed algorithm.     

ABC β–a heuristic for dynamic capacitated lot sizing with random demand under a fill rate constraint

This paper deals with the dynamic multi-item capacitated lot-sizing problem (CLSP) with random demand over a finite discrete time horizon. Unfilled demands are backordered. It is assumed that a fill rate constraint is in effect. We propose a heuristic solution procedure called ABC _β that extends the A/B/C heuristic introduced by Maes and Van Wassenhove for the deterministic CLSP to the case of random demands.     

Parallelized sequential value correction procedure for the one-dimensional cutting stock problem with multiple stock lengths

A heuristic approach with parallel computation is presented for the one-dimensional cutting stock problem with multiple stock lengths. The algorithm is based on the sequential heuristic procedure that generates each pattern to produce some items and repeats until all the required items are fulfilled. A recursion is used to solve the bounded knapsack problem heuristically in the pattern generation process to reduce running time. The item values are adjusted after the generation of each pattern using a value correction formula. The computational results show that the algorithm is more effective than a recently published evolutionary heuristic in improving solution quality, and can reduce computational time because of the efficient parallel implementation.     

Joint optimization of maintenance,buffers and machines in manufacturing lines

This article considers a series manufacturing line composed of several machines separated by intermediate buffers of finite capacity. The goal is to find the optimal number of preventive maintenance actions performed on each machine, the optimal selection of machines and the optimal buffer allocation plan that minimize the total system cost, while providing the desired system throughput level. The mean times between failures of all machines are assumed to increase when applying periodic preventive maintenance. To estimate the production line throughput, a decomposition method is used. The decision variables in the formulated optimal design problem are buffer levels, types of machines and times between preventive maintenance actions. Three heuristic approaches are developed to solve the formulated combinatorial optimization problem. The first heuristic consists of a genetic algorithm, the second is based on the nonlinear threshold accepting metaheuristic and the third is an ant colony system. The proposed heuristics are compared and their efficiency is shown through several numerical examples. It is found that the nonlinear threshold accepting algorithm outperforms the genetic algorithm and ant colony system, while the genetic algorithm provides better results than the ant colony system for longer manufacturing lines.     

A beam search-based algorithm and evaluation of scheduling approaches for flexible manufacturing systems

This paper presents a new algorithm for the flexible manufacturing system (FMS) scheduling problem. The proposed algorithm is a heuristic based on filtered beam search. It considers finite buffer capacity, routing and sequence flexibilities and generates machine and automated guided vehicle (AGV) schedules for a given scheduling period. A new deadlock resolution mechanism is also developed as an integral part of the proposed algorithm. The performance of the algorithm is compared with several machine and AGV dispatching rules using mean flow time, mean tardiness and makespan criteria. It is also used to examine the effects of scheduling factors (i.e., machine and AGV load levels, routing and sequence flexibilities, etc.) on the system performance. The results indicate that the proposed scheduling algorithm yields considerable improvements in system performance over dispatching rules under a wide variety of experimental conditions.     

Model for cost estimation in a finite-capacity environment

Cost estimation is a practical problem that has attracted the attention of many researchers. Past research has focused mainly on cost estimation in an unlimited capacity environment. This paper presents a mixed-integer-programming model (MIP) for estimating cost under finite capacity. It proposes an iterative heuristic model based on a marginal analysis where the total cost without the new order is subtracted from the total cost with the new order. The proposed heuristic's efficiency and effectiveness are examined with respect to the optimal solution for small instances of the problem and compared with a partial enumeration solution for larger problem instances. Lower bounds obtained from the partial Branch-and-Bound procedure are also used for comparison. A computational study is performed to test how different factors affect the advantage of using the proposed heuristic over a conventional method for cost estimation.     

A Heuristic Algorithm for the Multi-Item Lot-Sizing Problem with Capacity Constraints

A heuristic algorithm is presented for solving the scheduling of several items in parallel under capacity constraints with setup and carrying costs. The method is based upon finding a lower bound solution for these costs, securing the feasibility of the solution, and improving the feasible solution so obtained until no further improvements can be made. Comparison of the performance of the proposed heuristic algorithm to that of an exact mixed-integer programming model showed that best solution costs found by the heuristic deviated on an average by 1% from the optimal values, while the computing time was on an average 1/140 of that required by the exact method.     

An efficient algorithm for analysis of nonlinear heat transfer with phase changes

A new, simple and effective finite element procedure is presented for the practical solution of heat transfer conditions with phase changes. In this method, a fixed finite element mesh is employed, and a relatively coarse finite element mesh and large time step can be used in the incremental solution. The results of various numerical studies using the algorithm are presented that demonstrate the effectiveness of the procedure.     

Performance evaluation of production lines with finite buffer capacity producing two different products

This paper presents an approximate analytical method for the performance evaluation of a production line with finite buffer capacity, multiple failure modes and multiple part types. This paper presents a solution to a class of problems where flexible machines take different parts to process from distinct dedicated input buffers and deposit produced parts into distinct dedicated output buffers with finite capacity. This paper considers the case of two part types processed on the line, but the method can be extended to the case of n part types. Also, the solution is developed for deterministic processing times of the machines which are all identical and are assumed to be scaled to unity. The approach however is amenable of extension to the case of inhomogeneous deterministic processing times. The proposed method is based on the approximate evaluation of the performance of the k-machine line by the evaluation of 2(k-1) two-machine lines. An algorithm inspired by the DDX algorithm has been developed and the validation of the method has been carried out by means of testing and comparison with simulation. Correspondence to: T. Tolio     

External partner selection using tabu search heuristics in distributed manufacturing

With every passing month, a number of new virtual enterprises emerge on the internet. Many companies have responded to the idea of distributed manufacturing in which the value adding activities comprising a finished product are dispersed geographically in a remote place. This study suggests an idea for selecting partners in a distributed manufacturing environment, which enables machining companies to share their capacities. A mathematical model is constructed to show how to minimize the sum of the operation and transportation costs based on alternative process plans considering several kinds of operation characteristics in the real world. Four heuristic algorithms are developed to get an optimal or near-optimal solution using tabu search since the model is proven NP-hard. Example problems are tested to illustrate their procedure and performance.     

Adaptive radial basis function–generated finite differences method for contact problems

This paper proposes an original adaptive refinement framework using radial basis function–generated finite differences method. Node distributions are generated with a Poisson disc sampling–based algorithm from a given continuous density function, which is altered during the refinement process based on the error indicator. All elements of the proposed adaptive strategy rely only on meshless concepts, which leads to great flexibility and generality of the solution procedure. The proposed framework is tested on four gradually more complex contact problems. First, a disc under pressure is considered and the computed stress field is compared to the closed-form solution of the problem to assess the behaviour of the algorithm and the influence of free parameters. Second, a Hertzian contact problem is studied to analyse the proposed algorithm with an ad hoc error indicator and to test both refinement and derefinement. A contact problem, typical for fretting fatigue, with no known closed-form solution is considered and solved next. It is demonstrated that the proposed methodology produces results comparable with finite element method without the need for manual refinement or any human intervention. In the last case, generality of the proposed approach is demonstrated by solving a three-dimensional Boussinesq's problem.     

Optimal design of flexible production lines with unreliable machines and infinite buffers

Despite the increasing use of automated manufacturing systems, combining flexible technology, only a few models for designing such systems are available. This paper presents a model for the determination of the profit-maximizing configuration of workstations (both machine types and number) along a flexible production line with unreliable machines and infinite buffers. A mixed integer programming formulation of the problem is introduced and an optimal solution algorithm is developed. For large scale problems a heuristic procedure is presented.     

A heuristic procedure for the automobile assembly-line sequencing problem considering multiple product options

Mixed-model assembly nowadays is a common practice in the automobile industry. In an automobile assembly plant, many car options often need to be considered in sequencing an assembly line, for example, the multiple sequencing objectives that consider a pattern, blocking, spacing, and smoothing of options. A general heuristic procedure is developed in this paper for sequencing automobile assembly lines considering multiple options. The procedure obtains an initial sequence by an enhanced constructive procedure, swaps orders for the most deteriorating category of objectives, and performs re-sequencing attempting to improve the swapped sequence. The heuristic procedure was shown to frequently improve the initial sequences by swapping and re-sequencing when swapping opportunities exist. A further improvement step is also proposed to perform a limited search based on the swapped solution. The limited-search improvement step was shown to be effective in further improving solutions from the heuristic procedure in the computational experimentation. Solutions from the heuristic procedure in conjunction with the limited-search improvement step were compared to those from the simulated annealing procedure for large-size problems and showed relatively positive results.     

PERFORMANCE ANALYSIS OF A TRANSFER LINE WITH UNRELIABLE MACHINES AND FINITE BUFFERS

This paper examines the performance analysis of a transfer line with unreliable machines and finite buffers. All machines have the same processing times. We propose a new decomposition method which decomposes a line into a set of two-machine lines. A set of equations is established to find performance measures such as production rate and average buffer levels. A simple iterative algorithm is then proposed to solve these equations. We also prove that the set of decomposition equations has a unique solution and that die computation algorithm converges to this unique solution. Experimental results show that the computation algorithm leads to a good solution.     

Optimal and heuristic algorithms for the multi-location dynamic transshipment problem with fixed transshipment costs

We consider centrally controlled multi-location systems, which coordinate their replenishment strategies through the use of transshipments. In a dynamic deterministic demand environment the problem is characterized by several locations, each of which has known demand for a single product for each period in a given finite horizon. We consider replenishment, transshipment and inventory holding costs at each location, where the first two have location-dependent fixed, as well as linear components, and the third is linear and identical to all locations. We prove that the resulting dynamic transshipment problem is NP-hard, identify a special structure which is satisfied by an optimal solution and develop, based on this structure, an exponential time algorithm to solve the problem optimally. In addition, we develop a heuristic algorithm, based on partitioning the time horizon, which is capable of solving larger instances than the optimal solution. Our computational tests demonstrate that the heuristic performs extremely well.     

Finite element multigrid solution of Euler flows past installed aero-engines

A finite element based procedure for the solution of the compressible Euler equations on unstructured tetrahedral grids is described. The spatial discretisation is accomplished by means of an approximate variational formulatin, with the explicit addition of a matrix form of artificial viscosity. The solution is advanced in time by means of an explicit multi-stage time stepping procedure. The method is implemented in terms of an edge based representation for the tetrahedral grid. The solution procedure is accelerated by use of a fully unstructured multigrid algorithm. The approach is applied to the simulation of the flow past an installed aero-engine nacelle, at three different free stream conditions. Comparison is made between the numerical predictions and experimental pressure observations.