A Critical Review of Machine Loading Problem in Flexible Manufacturing System

Production planning is the foremost task for manufacturing firms to deal with, especially adopting Flexible Manufacturing System (FMS) as the manufacturing strategy for production seeking an optimal balance between productivity-flexibility requirements. Production planning in FMS provides a solution to problems regarding part type selection: machine grouping, production ratio, resource allocation and loading problem. These problems need to be solved optimally for maximum utilization of resources. Optimal solution to these problems has been a focus of attention in production and manufacturing, industrial and academic research since a number of decades. Evolution of new optimization techniques, software, technology, machines and computer languages provides the scope of a better optimal solution to the existing problems. Thus there remains a need of research to solve the problem with latest tools and techniques for higher optimal use of available resources. As an objective, the researchers need to reduce the computational time and cost, complexity of the problem, solution approach viz. general or customized, better user friendly communication with machine, higher freedom to select the desired objective(s) type(s) for optimal solution to the problem. As an approach to the solution to the problem, a researcher first needs to go for an exhaustive literature review, where the researcher needs to find the research gaps, compare and analyze the tools and techniques used, number of objectives considered for optimization and need, and scope of research for the research problem. The present study is a review paper analyzing the research gaps, approach and techniques used, scope of new optimization techniques or any other research, objectives considered and validation approaches for loading problems of production planning in FMS.


Introduction
Manufacturing is the pilot element within the overall enterprise.Possible manufacturing outputs of the firm to meet pre-determined corporate level goals should be known to remain in competition at global market.Manufacturing strategy writes the script to calculate possible manufacturing outputs.Existence of the manufacturing strategy guides daily decisions and activities with clear understanding of decision-goal relationship of the corporation and provides a vision for the firm to remain aligned with the overall business strategy of the firm.The firms having manufacturing strategies for achieving corporate goals survive for long run.A strategy is also a strong communication tool between different levels of management to bring all operations in line with corporate objectives.Custom manufacturing, continuous manufacturing, intermittent manufacturing, flexible manufacturing, just-in-time manufacturing, lean manufacturing and agile manufacturing are major manufacturing strategies revealed in the literature.
FMS is an automated manufacturing system consisting of computer numerical control (CNC) machines with automated material handling, storage and retrieval system.The aim of FMS is to attain the efficiency of mass production while utilizing the flexibility of job shop simultaneously.FMS is adopted for batch production of mid production volume and mid part variety (flexibility) requirements.Since its evolution, researchers are working for optimality of FMS strategy.FMS is a field of great potential hence a numerous complex planning problems need to be solved.Major complex production planning problems are part type selection: machine grouping, production ratio, resource allocation and loading problem (Stecke, 1983).All the production planning problems need to be optimally solved.The present research is the critical literature review for the loading problem of production planning in FMS.
Tooling individual or group of machine(s) to collectively accomplish all manufacturing operations concurrently for all part type in a batch is termed as loading problem.A solution to the problem specifies the machine(s) to which a job has to be routed in sequence for each of its operation(s) with respective tooling under capacity and technological constraint(s) for all jobs in a batch simultaneously to achieve certain objective(s).Loading is a complex combinational planning problem because a batch of jobs is to be machined simultaneously and each job requires unique set of operations effect on manufacturing cost.
To solve the problem, highly experienced and skilled professionals are required.Without the use of some computational or optimization technique, the solution may or may not be optimal.Thus there arises the need of optimal solution with the help of computational methods using optimization techniques.The paper is a critical review paper analyzing the research gaps, approach and techniques used, scope of new optimization techniques or any other research, objectives considered and validation approaches for loading problems of production planning in FMS.

Literature Review of Loading Problems in FMS
In brief, to solve a problem using optimization techniques and computational analysis, objective(s) are first set, the physical system is modelled using certain technique like mathematical modelling, the solution is then derived under given boundary conditions and constraints to achieve the given objectives, the results are then analysed and the solution approach is then validated.Heuristics has been widely used by the researchers.Table 1 presents the tabulated research review discussing the approach, objectives and results of the loading problems in FMS.Flexible manufacturing is an overall pilot element within an enterprise.Each multinational manufacturing concern has to satisfy business goals to remain in competition with the global market.The manufacturing firm should be aware of the possible manufacturing outputs that will closely match the goals and strategy determined at the corporate level.The existence of a manufacturing strategies guide the daily decisions and activities with clear understanding of how those daily decisions relate to the overall goals of the corporation.The firms having manufacturing strategies for achieving corporate goals survive long.A manufacturing strategy provides a vision to the manufacturing organization for keeping itself aligned with the overall business strategy of the corporation.A strategy is also a strong communication tool between different levels of management to bring all operations in line with corporate objectives.Custom manufacturing, continuous manufacturing, intermittent manufacturing, flexible manufacturing, just-in-time manufacturing, lean manufacturing and agile manufacturing are the major manufacturing strategies which are revealed in literature.
FMS is an automated manufacturing system consisting of numerical control (computer) machines with automated material handling, automated storage and retrieval system.The aim of FMS is to attain the efficiency of Loading means allocation of the operations and required tools to a part types among the set of machine(s), subjected to resource & technological constraints to collectively accomplish all manufacturing operations for each pat type machined concurrently.The allocation of workloads to the existing production facilities for manufacturing products with several constraints in order to perform production activities according to the production plan established, it is essential to adjust the workload for each of the facilities and workers in each time period so they are not assigned work exceeding the given capacity.A solution to this problem specifies the tools which must be loaded in each machine tool magazine and the machine(s) to which a part can be routed for each of its operations before production begins.A variety of products are manufactured simultaneously in FMS, where each part requires potentially unique set of operations, and loading problem is declared as a combinational problem by Kathryn E. Stecke [2] which is highly complex, time-consuming and tedious in nature & requires highly experienced process planners.
Machine loading is one of the most critical production planning problems of FMS.It concerns with the time spend by the job(s) on machine(s) and the manufacturing cost.Manufacturing cost is the sum of fixed and variable costs.Variable cost varies with the level of production output.As output increases, variable cost increases.Once invested, we can't play around the fixed cost; hence to reduce the manufacturing cost, researcher has to minimize the variable cost while maximizing the output.This is done by developing and optimizing a virtual model of manufacturing by some conventional or non-conventional technique for certain number of objectives with their individual weightage accordingly.A researcher has to solve the manufacturing model to minimize the time spent by the job on machine, number of tool used, and movements of tool and job.FMS is a group technology concept hence all the operations on the group jobs are required to be completed at once keeping in view that no machine should be idle or overloaded at any instance of time.Thus the optimized solution of the machine loading problem for certain objectives under technological and capacity constraints is required.The solution to the machine loading problem is to minimize the manufacturing cost as a whole.
Increasing part varieties with raised productivity is necessary to be in competition and to maintain the demand of the product, which is possible by continuous research and optimized solutions to each of the production planning problem.This paper presents a research review of the optimization techniques and the objectives for which the machine loading problem in FMS has been solved, and scope of the research in the field.
Before presenting literature review, an introduction to the optimization techniques and their classification seems necessary to be discussed here for better understanding of the subject.Optimization is the approach for ideal solution.Accuracy of the solution depends on the approach, modeling, computational time and capacity, and nature of the problem.Optimization is classified into six categories: function, and trial and error, single variable and multiple variables, static and dynamics, continuous and discrete, constrained and unconstrained, and random and minimum seeking.
A functional optimization is for theoretical approach where a mathematical formula describes the objective function.Trial-and-error optimization is for experimental optimization with change in the variables which affect output without knowing much about the process.An optimization can be single variable for one dimensional analysis, and multi variables for multi-dimensional analysis.As the number of variables increases, the complexity of the problem also increases.Static optimization is independent of time and dynamic optimization as a function of time.Discrete optimization has a finite number of variables with all possible values, while continuous optimization has infinite number of variables with all possible values.Values are incorporated in equalities and inequalities to an objective of variable function in constrained optimization while the variables can take any value in unconstrained optimization.Random optimization finds sets of variables by probabilistic calculations while minimal seeking is the traditional optimization algorithms which are generally based on calculus methods and minimizes the function by starting from an initial set of variable values.
These optimization approaches can be further sub-categorized as stochastic programming, integer programming, linear programming, nonlinear programming, bound programming, network programming, least squares methods, global optimization, and non-differential optimization.
Most of the researches are focused on solving the machine loading problem by global optimization algorithms.Global optimization algorithms are generally categorized into two approaches: deterministic and probabilistic.Deterministic are sub-categorized into static space search (1992) [3], branch and bond and algebraic geometry algorithms.Probabilistic is sub-categorized as Monte Carlo algorithms, soft computing and Artificial Intelligence (AI).Monte Carlo algorithms includes two classes, one covers Stochastic (hill climbing) (2002) [4], Random optimization (1963) [5], Simulated Annealing (SA) (1953) [6], Tabu Search (TS) (1989) [7], Parallel tempering, Stochastic tunneling and Direct Monte Carlo Sampling, and second class includes Evolutionary Computation (EC).EC can be performed by Monte Carlo algorithms or soft computing or AI.EC is further classified as Evolutionary Algorithms (EA), Memetic Algorithms (hybrid Algorithms) (1989) [8], Harmonic Search (HS), Swarm Intelligence (SI).EA is sub-classified as Genetic Algorithms (GA) (1962) [9], Learning Classifier System (LCS) (1977) [10], Evolutionary Programming, Evolution Strategy (ES), Genetic Programming (GP) (1958) [11].ES includes Differential Evolution (DE), and GP includes Standard GP, Linear GP and Grammar Guided GP.SI includes Ant Colony Optimization (ACO) (1996) [12] and Particle Swarm Optimization (PSO) (1995) [13].The above discussed classifications scheme will be used for classifying the optimization techniques for solving the machine loading problems of FMS in the paper.Figure 1 shows the evolution of the major optimization techniques along the time axis.

Literature Review of Machine Loading Problems in FMS
An exhaustive research review has been carried out for study of approaches and optimization techniques for machine loading problems in FMS. A. Baveja, A. Jain, A. K. Singh, A. Kumar The tabulated research review discussing the approach, objectives, results and validation approach for machine loading problems in FMS is discussed in Tables 1-3.The literature review is classified into three groups: (1) heuristics; (2) global optimization; and (3) other optimization techniques.
Table 1 presents the review of machine loading problems of FMS based on heuristics approach.The heuristics approach has been significantly used for solving the research problem.Research has gained significant acceleration with the evolution and growth of global optimization techniques.
Table 2 presents the review of machine loading problems in FMS based on global optimization algorithms.Global optimization techniques have been explored rigorously by the researchers.The natural selection techniques have reported good results compared to others.The application of global optimization techniques for solving machine loading problem is increasing with growth of natural optimization techniques.The results reported by natural optimization techniques are more acceptable.Natural optimization techniques, GA and PSO are widely used techniques.
Table 3 presents the review of machine loading problems in FMS based on optimization techniques not falling in the above classification.Since the major focus is on heuristics and global optimization techniques, thus other techniques are grouped in a single table.These techniques have been adopted from time to time for solving the machine loading problem as shown year wise in Table 3.
Optimization techniques and approaches under the classification of global optimization scheme are discussed in Table 2.
Optimization techniques and approaches not falling under the above classifications are discussed in Table 3. Table 4 has been formulated on regressive analysis of Tables 1-3, for the analysis of the loading objectives to be fulfilled while solving the loading problem.It is a year-wise tabulation and analysis of the loading objectives.The table is showing the list of objectives for which the loading problem is solved.The tick mark (√) in the table shows the density for repeatability of the objectives.Abbreviations used in Table 4: 1) Minimizing system unbalance 2) Maximizing throughput 3) Balancing of workload in the system configured of groups composed of machines of equal size 4) Minimizing make span 5) Meeting delivery dates 6) Minimizing manufacturing cost/Minimizing total processing cost/ Minimizing total flexible manufacturing cell cost per unit of production 7) Minimizing tardiness 8) Minimizing production cost 9) Unbalancing the workload per machine for a system of groups of pooled machines of unequal sizes  techniques utilized by researchers for problem formulation and its solution are identified and tabulated in Table 3.
The tick marks (√) shows the density of repetitive occurrence of the optimization techniques and approaches for solving the machine loading problem.
Abbreviations used in Table 5: 1) Genetic Algorithm (GA): GA, Hybrid GA, Constraint based GA, Constraint-chromosome GA, Real coded GA, integrated approach based on GA 2) Heuristic Algorithm (HA): HA, Fast HA, Fuzzy based HA, GA based HA, Hybrid TS and SA based HA, Lagrangian based HA, GA and PSO based Meta-hybrid HA, multi stage programming approach based HA 3) Simulated annealing (SA): SA, Constraints-Based Fast SA, GA based SA, Hybrid GA-SA & SA-TS algorithm 20) Dynamic approach 21) Fuzzy Logic

Conclusion Arrived on Machine Loading Objectives and Optimization Techniques in FMS
Detailed study of the machine loading problem is conducted by the authors.The conclusions of the research throttled are divided into three sections as below.

Conclusion on Machine Loading Objectives
On exhaustive study, twenty eight loading objectives are observed in the reviewed literature.Tick marks (√) in Table 4 are showing the density for repeatability of the machine loading objectives, which concludes that a research with maximum loading objectives is still required for solving the machine problem.Maximizing expected production rate (throughput) & unbalancing the workload per machine for a system of groups of pooled machines of unequal sizes are the two objectives on which most of the researchers have worked.Balancing of workload on machines for a system of groups of pooled machines of equal sizes is the second most researched loading objective.Minimizing make span is the third most researched loading objective.Minimizing job tardiness is fourth loading objective in the order.Minimizing mean job flow time & minimizing production cost are found at fifth position in the order.Loading objectives observed at sixth rank are maximizing profitability, maximizing the assigned workload, maximizing the part types in each batch, maximizing utilization of system, minimizing subcontracting costs and minimizing the total number of cutting tools required.Material handling time, maximizing routing flexibility of the batches, minimizing earliness, minimizing mean lateness, minimizing mean machine idle time, minimizing overall machining cost, minimizing production time, minimizing the effect of breakdowns, minimizing the maximum workload of the machines, minimizing the number of late jobs, minimizing total flexible manufacturing cell cost per unit of production, minimizing total inter-station transfer time, minimizing total processing time, minimizing part movements and minimisation of the total distance travelled by parts during their production are the loading objectives that are least considered.

Conclusion on Optimization Techniques in FMS
The categorized literature review concludes that the researcher's major emphasis and contribution are towards the use and application of global optimization techniques and with natural optimization techniques, too.Heuristic Algorithms is the mostly used optimization technique by researchers, followed by Genetic Algorithms (GA).Mixed Integer Programming (MIP) & Simulated Annealing (SA) approach are the third mostly used optimization techniques.Linear Mathematical Programming (LMP) is next in the queue succeeded by Integer Programming (IP).At sixth level is Particle Swarm Optimization (PSO) approach.The least used optimization techniques are Tabu search, Swarm Optimization Approach, Branch and backtrack procedure, Branch and bound approach, Combined machine loading (CML) algorithms, Dispatching approach, Due-Date Based methods, Dynamic approach, Fuzzy Logic, Global criterion approach, Hierarchical approach, Artificial immune algorithm, Iterative algorithms, Lexicographic approach, Non-linear programming, Queueing network model and Stochastic model.

Conclusion on validation approaches
A few research problems are solved and the results are compared with previous research results.The results are validated by comparing with literature available results.

Methodologies Findings and Interpretations
A problem when solved for a limited or less number of objectives, it is rather a customized solution for a problem.For general solution, the problem needs to be solved for all possible objectives.On extreme analysis of the machine loading problem and objectives, and on discussion with the academicians and industrialists, the authors emphasise to solve the loading problem for maximization of throughput, part types in a batch, routing flexibility, balancing/unbalancing of system and workload, and minimization of make-span, delivery dates (covering late-ness, tardiness and earliness), part movements, subcontracting costs, machine processing time, tool magazine capacity, number of cutting tools required, breakdowns, non-splitting of jobs, time spend by job on machines in one study.Machine loading problem should be solved for general solution to the problem, for maximum number of objectives.All these objectives are having a common goal of optimizing the production and manufacturing costs.
The literature review reports the application of heuristics, global optimization techniques and some other optimization techniques for solving the loading problem for the listed objectives.Among these approaches, the global optimization techniques were more frequently adopted and the results as founded by the researchers were more accurate and acceptable.Based on regressive analysis of the available literature, and skills and concluding remarks, the authors suggest for the use of natural optimization techniques like swarm optimization for further research.The results of swarm optimization were found more reliable and acceptable as compared to GA, and PSO has attractive characteristics.PSO retains knowledge of all previous particles, which is destroyed in GA when the population changes.PSO is a mechanism of constructive cooperation and information-sharing between particles.Due to the simple concept, ease of implementation, and quick convergence, PSO has gained much attention and has been successfully applied to a wide range of applications.

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Minimizing part movements 11) Maximizing part types in each batch 12) Minimizing subcontracting costs 13) Maximizing weighted sum of number of operation to machine assignments 14) Minimizing flow time 15) Minimizing late jobs (number)/ lateness 16) Minimizing machine processing time 17) Minimizing production time 18) Filling the tool magazines as densely as possible 19) Maximizing assigned workload 20) Maximizing routing flexibility of batches 21) Maximizing the sum of operations priorities 22) Minimizing material handling time 23) Minimizing total distance travelled by parts during production 24) Minimizing total number of cutting tools required 25) Minimizing workload of machines 26) Minimizing breakdowns 27) Minimizing earliness After regressive analysis of the loading objectives of various researchers the optimization approaches and

Table 1 .
Review of machine loading problems in FMS based on heuristics approach.

Table 2 .
Review of machine loading problems in FMS based on global optimization algorithms.

Table 3 .
Review of machine loading problems in FMS based on optimization techniques not falling in the above classification.