A heuristic for production scheduling and inventory control in the presence of sequence-dependent setup times

The consideration of sequence-dependent setup times is one of the most difficult aspects of production scheduling problems. This paper reports on the development of a heuristic procedure to address a realistic production and inventory control problem in the presence of sequence-dependent setup times. The problem considers known monthly demands, variable production rates, holding costs, minimum and maximum inventory levels per product, and regular and overtime capacity limits. The problem is formulated as a Mixed-Integer Program (MIP), where subtour elimination constraints are needed to enforce the generation of job sequences in each month. By relaxing the subtour elimination constraints, the MIP formulation can be used to find a lower bound on the optimal solution. CPLEX 3.0 is used to calculate lower bounds for relatively small instances of this production problem, which are then used to assess the merit of a proposed heuristic. The heuristic is based on a simple short-term memory tabu search method that coordinates linear programming and traveling salesperson solvers in the search for optimal or near-optimal production plans.     

The generalised machine layout problem

The Generalised MAchine Layout Problem (GMALP) is a generalisation of the integrated machine and layout problem, which is an extension of the machine layout problem. More specifically, the GMALP is the designing of a facility layout by defining the product mix, selecting the number of machines to be used, assigning these machines to the plant floor, and assigning products to machines such that total profit is maximised. Moreover, the GMALP integrates the quadratic assignment problem with a multicommodity flow problem. Therefore, the GMALP is a computationally intractable problem. Consequently, a mixed-integer nonlinear programming model was developed and used to solve small problem instances. Also, two simple construction algorithms and a tabu search (TS) heuristic were developed for solving large GMALP instances in acceptable computation times. In addition, a test dataset was used to evaluate the performances of the TS heuristic using the different construction algorithms. The results show that the TS heuristic perform slightly better with the second construction algorithm.     

When less is better: Insights from the product mix dilemma from the Theory of Constraints perspective

Perhaps due to its origins in a production scheduling software called Optimised Production Technology (OPT), plus the idea of focusing on system constraints, many believe that the Theory of Constraints (TOC) has a vocation for optimal solutions. Those who assess TOC according to this perspective indicate that it guarantees an optimal solution only in certain circumstances. In opposition to this view and founded on a numeric example of a production mix problem, this paper shows, by means of TOC assumptions, why the TOC should not be compared to methods intended to seek optimal or the best solutions, but rather sufficiently good solutions, possible in non-deterministic environments. Moreover, we extend the range of relevant literature on product mix decision by introducing a heuristic based on the uniquely identified work that aims at achieving feasible solutions according to the TOC point of view. The heuristic proposed is tested on 100 production mix problems and the results are compared with the responses obtained with the use of Integer Linear Programming. The results show that the heuristic gives good results on average, but performance falls sharply in some situations.     

Unrelated parallel machine scheduling with job splitting

Scheduling jobs on unrelated parallel machines is an activity that is very much a part of industrial scheduling. We report a methodology for minimizing the total weighted tardiness of all jobs intended to be processed on unrelated parallel machines in the presence of dynamic job releases and dynamic machine availability. More importantly, the mixed (binary) integer linear programming model formulated for the problem incorporates a couple of “hard” operational constraints to ensure that just-in-time manufacturing practices are followed by controlling the work-in-process and/or finished goods inventories generated by split jobs mandated by a tight due date, a high priority, and/or a high workload. Four different methods based on simple and composite dispatching rules are used to identify an initial solution, which is then used by the tabu-search-based heuristic solution algorithm to ultimately find the best solution. Incorporating the various tabu search features led to the development of six different heuristics that were tested on eight small problem instances to compare the quality of their solutions to the optimal solutions. The results show that the proposed heuristics are capable of obtaining solutions of good quality in a remarkably short computation time with the best performer among them recording a percentage deviation of only 1.18%. A factorial experiment based on a split-plot design is performed to test the performance of the heuristics on problem structures, ranging from nine jobs and three machines to 60 jobs and 15 machines. The results show that the newly developed composite dispatching heuristic, referred to as the modified apparent tardiness cost, is capable of obtaining initial solutions that significantly accelerate the tabu-search-based heuristics to attain the best solution. The use of a long-term memory function is proven to be advantageous in solving all problem structures. In addition, the variable tabu list size is preferred for solving the small problem structure, while the fixed tabu list size is preferred as the problem size grows from small to medium and then large.     

Search heuristics for operation sequencing in process planning

The operation-sequencing problem in process planning is considered to produce a part with the objective of minimizing the sum of machine, setup and tool change costs. In general, the problem has combinatorial characteristics and complex precedence relations, which makes the problem difficult to solve. Six local search heuristics have been developed based on simulated annealing and tabu search to obtain good solutions for practical-sized problems within a reasonable amount of computation time. Application of the algorithms is illustrated using an example part. Also, computational experiments were done on randomly generated problems and the results show that the tabu search-based algorithms are better than the simulated annealing-based algorithms on overall average. In particular, one of the tabu search algorithms suggested here gave optimal solutions for most small-sized test problems within very short computation times.     

Efficient methods for scheduling make-to-order assemblies under resource,assembly area and part availability constraints

We consider the problem of scheduling multiple, large-scale, make-to-order assemblies under resource, assembly area, and part availability constraints. Such problems typically occur in the assembly of high-volume, discrete maketo-order products. Based on a list scheduling procedure proposed by Kolisch in 1999 we introduce three efficient heuristic solution methods. Namely, a biased random sampling method and two tabu search-based large-step optimization methods. The two latter methods differ in the employed neighbourhood. The first one uses a simple API-neighbourhood while the second one uses a more elaborated so-called 'critical neighbourhood' which makes use of problem insight. All three procedures are assessed on a systematically generated set of test instances. The results indicate that especially the large-step optimization method with the critical neighbourhood gives very good results which are significant better than simple single-pass list scheduling procedures.     

Optimizing the multiple constrained resources product mix problem using genetic algorithms

The theory of constraints (TOC) is s a management philosophy for maximizing throughput. Since its introduction, many have criticized it as being inefficient when multiple constrained resources exist. The application of the five steps contained in TOC have been criticized by some researchers on the grounds that the application of five steps of TOC to the product mix decision leads to implicit or unrealizable solutions when multiple resource constraints in a plant exist. This paper views TOC as a management philosophy and a genetic algorithm-based TOC procedure is presented for solving combinatorial problems encountered in practice which cannot be solved using linear-integer programming or similar techniques. For smaller size problems, the results of the proposed procedure are compared with results of optimal methods published in the literature. The results are encouraging and therefore support the use of the proposed approach in an industrial setting.     

Heuristics for minimizing total weighted tardiness in complex job shops

Semi-conductor manufacturing is arguably one of the most complex manufacturing processes in existence today. A semi-conductor wafer fabrication facility is comprised of batching machines, parallel machines, machines with sequence-dependent set-ups, and re-circulating product flow. The individual job release times and due dates combine with the other processing environment characteristics to form a ‘complex’ job shop scheduling problem. We first present a mixed-integer program (MIP) to minimize total weighted tardiness in a complex job shop. Since the problem is NP-hard, we compare a heuristic based on the MIP (MIP heuristic) with both a tuned version of a modified shifting bottleneck heuristic (SB heuristic) and three dispatching rules using random problem instances of a representative model from the literature. While the MIP heuristic typically produces superior schedules for problem instances with a small number of jobs, the SB heuristic consistently outperforms the MIP heuristic for larger problem instances. The SB heuristic's superior performance as compared to additional dispatching rules is also demonstrated for a larger, ‘real world’ dataset from the literature.     

基于瓶颈的产品组合决策方法

产品组合决策关系到企业的效益。本文基于约束理论中确定瓶颈的方法,针对约束理论关于产品组合决策方法在多约束条件下的不可行性,提出了一种同时考虑主约束和最大次约束的启发式方法,分为五个步骤对其进行了详细的说明。文中还通过实例仿真来说明了新方法的可行性及简单、易用性。     

A multi-level heuristic search algorithm for production scheduling

This paper introduces a multi-level heuristic search algorithm for identifying the optimal production schedule considering different levels of manufacturing requirements and constraints. The multi-level heuristic search algorithm generates search nodes at different levels. An upper level search node is composed of lower level search nodes, and evaluated based upon the evaluation of these lower level search nodes using a heuristic function. A production scheduling system was developed based upon the multi-level heuristic search algorithm. In this scheduling system, production requirements and constraints are represented at three different levels: task level, process level, and resource level. A task describes a manufacturing requirement. A process defines a method to achieve the goal of a task. A resource, such as a machine or a person, is a facility for accomplishing a required process. The multi-level heuristic search-based scheduling system was implemented using Smalltalk, an object-oriented programming language. Discussions on scheduling quality and efficiency are addressed at the end of this paper.     

An MILP model and a hybrid evolutionary algorithm for integrated operation optimisation of multi-head surface mounting machines in PCB assembly

This paper focuses on an operation optimisation problem for a class of multi-head surface mounting machines in printed circuit board assembly lines. The problem involves five interrelated sub-problems: assigning nozzle types as well as components to heads, assigning feeders to slots and determining component pickup and placement sequences. According to the depth of making decisions, the sub-problems are first classified into two layers. Based on the classification, a two-stage mixed-integer linear programming (MILP) is developed to describe it and a two-stage problem-solving frame with a hybrid evolutionary algorithm (HEA) is proposed. In the first stage, a constructive heuristic is developed to determine the set of nozzle types assigned to each head and the total number of assembly cycles; in the second stage, constructive heuristics, an evolutionary algorithm with two evolutionary operators and a tabu search (TS) with multiple neighbourhoods are combined to solve all the sub-problems simultaneously, where the results obtained in the first stage are taken as constraints. Computational experiments show that the HEA can obtain good near-optimal solutions for small size instances when compared with an optimal solver, Cplex, and can provide better results when compared with a TS and an EA for actual instances.     

A priority rule-based constructive heuristic and an improvement method for balancing assembly lines with parallel multi-manned workstations

Assembly lines of big-size products such as buses, trucks and helicopters are very different from the lines studied in the literature. These products’ manufacturing processes have a lot of tasks most of which have long task times. Since traditional assembly line models including only one worker in each station (i.e. simple assembly lines) or at most two workers (two-sided assembly lines) may not be suitable for manufacturing these type of products, they need much larger shop floor for a number of stations and long product flow times. In this study, an assembly line balancing problem (ALBP) with parallel multi-manned stations is considered. Following the problem definition, a mixed integer programming formulation is developed. A detailed study of priority rules for simple ALBPs is also presented, and a new efficient constructive heuristic algorithm based on priority rules is proposed. In order to improve solutions found by the constructive heuristic, a genetic algorithm-based solution procedure is also presented. Benchmark instances in the literature are solved by using the proposed mathematical programming formulation. It has been seen that only some of the small-size instances can be solved optimally by this way. So the efficiency of the proposed heuristic method is verified in small-size instances whose optimal solutions are found. For medium- and big-size instances, heuristics’ results and CPU times are demonstrated. A comparative evaluation with a branch and bound algorithm that can be found in the literature is also carried out, and results are presented.     

A robust cell formation approach for varying product demands

In cellular manufacturing environments, manufacturing cells are generally formed based on deterministic product demands. In this paper, we consider a system configuration problem with product demands expressed in a number of probabilistic scenarios. An optimization model integrating cell formation and part allocation is developed to generate a robust system configuration to minimize machine cost and expected inter-cell material handling cost. A two-stage Tabu search based heuristic algorithm is developed to find the optimal or near optimal solutions to the NP-hard problem. Numerical examples show that this model leads to an appropriate compromise between system configuration costs and expected material handling costs to meet the varying product demands. These example problems also show that the proposed algorithm is effective and computationally efficient for small or medium size problems.     

A column generation based heuristic for the capacitated vehicle routing problem with three-dimensional loading constraints

This paper addresses an integrated problem of vehicle routing and three-dimensional loading with additional practical constraints such as stability, fragility and LIFO. A column generation (CG) technique-based heuristic is proposed to handle this problem. To generate new columns in CG technique, first, an elementary shortest path problem is solved to find routes with negative reduced cost. Then an extreme point-based heuristic method is employed to verify feasibility of obtained routes in terms of loading and other constraints. To speed up the CG technique, fast column generation is also performed by applying an efficient heuristic pricing method. The CG technique, tested on the benchmark instances, outperforms the efficient tabu search method developed in the literature in terms of solution quality and computation time.     

Unrelated parallel machine scheduling with setup times and ready times

We consider the problem of scheduling unrelated parallel machines with sequence- and machine-dependent setup times and ready times to minimise total weighted tardiness (TWT). We present a mixed integer programming model that can find optimal solutions for the studied problem. We also propose a heuristic (ATCSR_Rm) and an iterated hybrid metaheuristic (IHM) that can find optimal or nearly optimal solutions for the studied problem within a reasonable time. The proposed IHM begins with effective initial solutions, and then improves the initial solutions iteratively. The IHM integrates the principles of the attraction–repulsion mechanism within electromagnetism-like algorithms with local search. If the search becomes trapped at a local optimum, an elite search procedure is developed to help the search escape. We have compared our proposed IHM with two existing metaheuristics, tabu search (TS) and ant colony optimisation (ACO). Computational results show that the proposed IHM outperforms TS and ACO in terms of TWT for problem instances of all sizes.     

New Tabu search heuristics for the dynamic facility layout problem

A manufacturing facility is a dynamic system that constantly evolves due to changes such as changes in product demands, product designs, or replacement of production equipment. As a result, the dynamic facility layout problem (DFLP) considers these changes and is defined as the problem of assigning departments to locations during a multi-period planning horizon such that the sum of the material handling and re-arrangement costs is minimised. In this paper, three tabu search (TS) heuristics are presented for this problem. The first heuristic is a simple TS heuristic. The second heuristic adds diversification and intensification strategies to the first, and the third heuristic is a probabilistic TS heuristic. To test the performances of the heuristics, two sets of test problems from the literature are used in the analysis. The results show that the second heuristic out-performs the other proposed heuristics and the heuristics available in the literature.     

An improved branch and bound procedure for scheduling a flow line manufacturing cell

This paper presents a new branch and bound procedure for scheduling a flow-line manufacturing cell. This procedure and an existing procedure are tested on several problem sets with varying numbers of families, jobs and machines, and varying setup time distributions. The results show that the new procedure solves small problems dramatically faster than the existing procedure. Three heuristic procedures, based on the new branch and bound procedure, are developed. These heuristic procedures as well as a tabu search procedure are tested on problem sets with larger problem sizes. The results show that one of the new procedures generates solutions with improved makespans compared to the tabu search procedure.     

Flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints

The purpose of this research is to solve flexible job-shop scheduling problems with ‘AND’/‘OR’ precedence constraints in the operations. We first formulate the problem as a Mixed-Integer Linear Program (MILP). The MILP can be used to compute optimal solutions for small-sized problems. We also developed a heuristic algorithm that can obtain a good solution for the problem regardless of its size. Moreover, we have developed a representation and schedule builder that always produces a legal and feasible solution for the problem, and developed genetic and tabu search algorithms based on the proposed schedule builder. The results of the computational experiments show that the developed meta-heuristics are very effective.     

Three perspectives for solving the job grouping problem

The production efficiency of printed circuit board (PCB) assembly depends strongly on the organization of the component placement jobs. This is characteristic, especially in a high-mix low-volume production environment. The present study discusses the problem of arranging the jobs of one machine into groups in such a way that the job change costs will be minimized when the costs depend on the number of the job groups. This problem is motivated by the practical case where the group utilizes a common machine set-up and the number of set-up occasions is the dominating factor in the production line optimization. The problem is well known and its large instances are hard to solve to optimality. We show how real-life problem instances can be solved by three different methods: efficient heuristics, 0/1-programming, and constraint programming. The first two of these are standard approaches in the field, whereas the application of constraint programming is new for the job grouping problem. The heuristic approach turns out to be efficient: algorithms are fast and produce optimal or nearly optimal groupings. 0/1-programming is capable of finding optimal solutions to small problem instances and it therefore serves as a benchmark to approximative methods. The constraint approach solves moderately large problem instances to optimality and it has the great advantage that changing the problem formulation is relatively easy one can add new constraints or modify the details of the existing ones flexibly.     

Initial allocation compensation algorithm for redundancy allocation: The scanning heuristic

The tiny feature size in current semiconductor integrated circuits naturally requires redundancy strategies to improve manufacturing yield and operating reliability. To find an optimal redundancy architecture that provides maximum yield and reliability is a trade-off problem. In the reliability optimization field, this type of problem is generally called a redundancy allocation problem. In this paper, we propose a new iterative algorithm, the scanning heuristic, to solve the redundancy allocation problem. The solution quality of conventional iterative heuristics is highly dependent on the initial starting point of the algorithm employed. To overcome this weakness, the scanning heuristic systematically divides the original solution space into several small bounded solution spaces. The local optimum in each divided solution space then becomes a candidate for the final solution. The experimental results demonstrate that the proposed heuristic, and subsequently some combinations of heuristics, are superior to existing heuristics in terms of solution quality.