Integration of part selection, machine loading and machining optimisation decisions for balanced workload in flexible manufacturing system

Article history: Received 1 April 2011 Received in revised form May, 08, 2011 Accepted 08 May 2011 Available online 10 May 2011 This paper demonstrates the importance of incorporating and solving the machining optimisation problem jointly with part selection and machine loading problems in order to avoid unbalanced workload in the FMS. Unbalanced workload renders to ineffective FMS such that some machines on the manufacturing shop floor become more occupied than others. Since CNC machine tools employed in the FMS are rather expensive, it is mostly important to balance the workload so that all machines can be effectively utilised. Therefore, in this study, two mathematical models are presented and solved in efforts to balance the workload and improve the performance of the FMS. A two-stage sequential approach is adopted whereby the first stage deals with the maximum throughput objective while the second stage deals with the minimum production cost objective. The results show that when part selection, machine loading and machining optimisation problems are jointly solved, more practical decisions can be made and a wide range of balanced workload in the FMS can be realised with minimum production cost objective. The results also show that the available machine time and tooling budget have enormous effects on throughput and production cost. © 2011 Growing Science Ltd. All rights reserved


Introduction
Intensive market competition has forced manufacturing industries to focus on flexible manufacturing systems (FMSs).This is because FMSs offer a rapid and timely response to market demands thus helping the manufacturing industries to win competitive advantage.FMSs are highly automated manufacturing systems that consist of a group of processing workstations, usually computernumerical control (CNC) machine tools, interconnected by automated material handling and storage systems altogether interfaced via a central computer.They are designed to combine the flexibility of a low-production-volume job shop and the efficiency of a high-production-volume flow shop to best suit the batch production of mid-volume and mid-variety of products.Job shop and flow shop are two conventional manufacturing systems that are associated with a traditional arrangement of machine tools on a manufacturing shop floor.In a job-shop system, machines are grouped together to perform similar operations for different parts.In a flow-shop system, machines are arranged together to process the parts as they flow from one machine to the next through the sequence of operations.
Although the installation of FMSs requires a greater capital investment, their expected benefits are substantial.The benefits include increased machine utilisation, less machines, reduced floor space, greater responsiveness to changes, reduced inventories, lower manufacturing lead times, and higher labour productivity.In order to justify these benefits, the FMS resources should be well planned and then effectively utilised to meet the production requirements, achieve the operational objectives and yet provide the payback more quickly.Various FMS planning problems have been addressed at different stages of the FMS's life cycle.Stecke (1985) divided the FMS planning problems into five subproblems of part type selection, machine grouping, machine loading, production ratio, and resource allocation.Hwang (1986) found that among the five planning subproblems, part selection and machine loading are the most important in the FMS.However, the decisions of part selection and machine loading problems in the FMSs may not be effective because they often lead to unbalanced workload.As reported by Liang (1994), some planning policies such as maximising throughput may cause extremely unbalance workloads thereby causing bottleneck in some machines involved in the manufacturing process.The source for unbalanced workload decisions in part selection and machine loading problems may be the fact that the values of machining parameters are always predetermined and not optimised during FMS planning process as exhibited in Liang (1994), Yang and Wu (2002), and Choudhary, et al (2006).
The optimisation of machining parameters such as cutting speed, feed rate, and depth of cut is an essential step in achieving high machining efficiency and effective FMS.Ermer and Kromodihardjo (1981) and Manna and Salodkar (2008) optimised machining parameters for single machine problems while Agapiou (1992) optimised machining parameters for a conventional multi-stage machining system for effective machine utilisation.It is however learnt that previous studies on the optimisation of machining parameters mainly relied on either standalone machines or traditional multi-stage manufacturing systems rather than on FMSs.In order to utilise the machines in the FMS more effectively, it is necessary to determine the optimum machining parameters during the production planning stage.It is the purpose of this study to integrate the decisions of part selection, machine loading and machining optimisation problems in an attempt to balance the workload while improving the performance of the FMS.

Mathematical notations
The following mathematical notations are used for providing the theoretical concepts and in formulating the mathematical models for the FMS: (1) Indices The concept of solving part selection, machine loading and machining optimisation problems jointly comes with the need to define the relationship among their entities.In reality, processing time and tooling cost form a major linkage among part selection, machine loading and machining optimisation problems.On one hand, the selected parts for processing in the FMS depend on the available machine time.Similarly, due to higher tooling cost, the number of tools that can be loaded on the tool magazine depends on the available tooling budget.On the other hand, machining parameters, processing time and tooling cost are strongly coupled.For instance, at higher cutting speeds, machining time and the related cost are less but more cutting tools are consumed thus increasing tooling cost.Major components of processing time are machining time and tool replacement time.
Machining time is the actual time required to process a part on a machine described as (Narang and Fischer, 1993): Machining cost is the product of machining time and operating cost rate.Denoting U o as the operating cost rate, the machining cost can be written as: Tool replacement time is the time needed to remove a worn tool from the machine and replace with a new tool.Tooling cost is the cost of purchasing new cutting tools.Both the tool replacement time and tooling cost are functions of the Taylor's tool life equation.The extended tool life equation reported by Lambert and Walvekar (1978) can be written in the following form: The tool life is reached and the tool can be replaced when several parts have been processed on a machine.It follows that the number of parts at each tool replacement is the ratio of tool life in Eq. ( 4) to unit machining time in Eq. (1) expressed as: Substituting Eqs.(2a) and (2b) into Eq.( 5) and rearranging the terms, the tool replacement time and tooling cost distributed to each part can be respectively presented as: M jot is a machining constant which is defined by Wang and Liang (2005) as: The machining constant for milling operations defined by Shnumugam, et al (2002) and Wang and Liang (2005) is: Correspondingly, the tool replacement cost is the product of tool replacement time and operating cost rate and is defined as: Taking the sum of machining time in Eq. ( 1) and tool replacement time in Eq. ( 6), the processing time can be represented as: In similar manner, adding up the machining cost in Eq. ( 3), tool cost in Eq. ( 7), and tool replacement cost in Eq. ( 9), the total production cost can be obtained as: As shown earlier, both processing time and tooling cost make a significant link among part selection, machine loading and machining optimisation problems.Therefore, Eq. ( 7), Eq. ( 10) and Eq. ( 11) are accordingly useful for the formulation of mathematical models in the subsequent sections.Before formulating the models, the main assumptions are defined as follows: (1) The manufacturing parameters are deterministic and static.Breakdowns on machines are not considered and parameters are considered as constant and hence do not change over time.
(2) The depths of cut of part-tool-machine combinations are known and given.
(3) The compatibilities of part-machine and tool-part combinations in the FMS are given.(4) A part type is selected or rejected for processing before the beginning of the production period and remains unchanged during this period.(5) The CNC machining centres are identical and can perform different operations on any part type.
One machining centre can process one operation at a time.(6) Machining, loading and unloading workstations have sufficient input and output buffer spaces.(7) Machining centres, raw materials, parts and tools are simultaneously available in the beginning of the production period.(8) The material handling system, pallets and fixtures are fully available.(9) Setting-up of parts is performed offline and the times required for transferring parts between machining centres are negligible.

Methodology
A theoretical framework in Section 2 provided a relational base of the FMS variables aimed at formulating throughput and production cost models in attempts to integrate the decisions of part selection, machine loading and machining optimisation problems and to achieve balanced workload in the FMS.The model formulation process adopts a two-stage sequential approach as follows.The first stage maximised the throughput of the FMS and the decisions of part selection, machine loading and machining optimisation are simultaneously made.In the second stage, the production cost is minimised while making the decisions of machine loading and machining optimisation but retaining the maximum throughput obtained in the first stage.The two-stage sequential approach was chosen primarily to avoid the complexity of meeting two different objectives concurrently in one aggregate planning problem.
Computational experiments are designed for sensitivity analysis, which involves varying the values of some control factors and examining how the observed results change with variations in control factors.This would help to test out the range of validity of models and data, and also to get more insights of the results and consequently make easier to evaluate and interpret the results.A two-factor full factorial design was adopted with the available machine time and maximum tooling budget as control factors each assigned to 5 levels.Therefore, a total of 5 2 =25 computational experiments were conducted using Extended LINGO 11 software.The two FMS models are formulated in the following subsections:

Maximisation of throughput
The primary objective in the first stage was to maximise the FMS throughput within the boundaries of the operational requirements.The decisions of the integrated part selection, machine loading (operation allocation, part routing and tool assignment) and machining optimisation (cutting speed and feed rate) problem can be obtained when the model is solved.The model for maximising the FMS throughput was formulated by Mgwatu, et al (2009) as follows: 1 The objective function ( 12) maximises the FMS throughput where the level of importance of part types at production quantity Q j can be in terms of dollar or due-date value coefficients u j .If part type j is selected, x j = 1, and 0 if otherwise.Constraint (13) states that the total proportion of a part processed at all alternative machines using all feasible tools should be the same for all operations, either x jotk = 0 or 1.The variable x jotk = 1, if operation o of part j is processed using tool t on machine k, and 0 if otherwise.To ensure that all machines are utilised in the shop floor, constraint ( 14) binds every machine to perform at least one operation on a part.Constraint (15) prevents recirculation of parts on machines and maintains the flexibility of the system.Constraint ( 16) ensures that if a part is allocated to a machine, the required tool y tk should be assigned to that machine.If tool type t is assigned to machine k, y tk = 1, and 0 if otherwise.Constraint (17) restricts the total number tool types needed on tool slots S t not to exceed tool magazine capacity G k .Constraint (18) forces the total processing time at each machine not to exceed the available machine time A k on the shop floor.Constraint (19) assures that the total tooling cost is not beyond the available tooling budget B. Constraints ( 20) and ( 21) give the lower and upper bounds for cutting speed (V L jotk , V U jotk ) and feed rate (F L jotk , F U jotk ) respectively.Constraints ( 22) through ( 24) represent binary restrictions on the decision variables.

Minimisation of production cost
The model in the second stage was formulated to minimise the production cost.The selected parts already obtained in the first phase were maintained and used among other input data in the second stage model.There was an attempt to re-assign the selected parts and reallocate the tools to machines, and also to re-optimise the cutting speed and feed rate for the purpose of exploring the most possible minimum production cost.Once the second stage model is solved, the decisions of machine loading (operation allocation, part routing, tool assignment), machining optimisation (cutting speed and feed rate), and processing times of parts on machines can be made.The formulation of the production cost minimisation model is presented as: min 1 1 ( ) ∑∑∑∑ , ∀k, and Constraint (24), 0 = tk y or 1, ∀(t, k) The objective function (25) minimises the production cost of the selected parts.Constraints ( 26)-( 29) and Constraints ( 33)-( 36) are equivalent to Constraints ( 13)-( 16) and Constraints ( 19)-( 22), respectively.Constraint (30) assigns equal processing time h at all machines to guarantee balanced workload in the FMS.In Constraint (31), the processing times at machines are bound within the available machine time.Constraint (32) specifies the processing time p jk of each part at different machines.

Results and discussions
Both the formulated throughput and production cost models are integer nonlinear programming (INLP) problems and were computed using Extended LINGO 11 software.LINGO is a nonlinear programming software package which has the capability to solve nonlinear programming problems with unlimited number of linear and nonlinear constraints as well as unlimited number of integer, nonlinear and global variables (LINDO Systems Inc., 2008).The computations were conducted using the numerical data summarised in Table 1-Table 5.In the data, the tool-operation and tool-machine compatibilities are pre-specified.Tool life constants were taken from Shnumugam, et al (2002) and Wang and Liang (2005) while the tool costs per edge were obtained from McMaster-Carr Supply Company (2008).Limits of cutting speeds and feed rates were found in Chapman (2002).A set of results for the throughput model including the selected parts, maximum throughput, average workload, number of selected tools for different operations, and the status of the FMS are summarised in Table 6.The results indicate that not all parts and tools were selected for immediate and simultaneous processing on the machines symbolizing that the parts and tools were competing for production resources.The workloads on machines in the FMS were either balanced or unbalanced.
For unbalanced workload, some bottleneck machines were identified while others had slack times.
The reason for unbalanced workload could be that the parts had different processing requirements including the differences in their machining operations, cutting tools, and machining parameters.However, this study has revealed the fact that, when machining parameters are optimised with part selection and machine loading problems for maximum throughput objective, they are likely to adjust themselves within their allowable limits and in some cases they can provide balanced workloads in the FMS.Furthermore, the magazine tool slots in the machines were not fully utilised even when the workloads in the FMS were balanced.Although machine tool manufacturers normally try to equip machining centres with larger tool magazines in order to reduce the impact of the magazine capacity constraint, larger tool magazines result in higher spindle idle times during tool change-over between different operations.However, lower tool magazine usage results in using fewer cutting tools and thus spending lower total tooling cost.In addition, better tool magazine utilisation requires the tool slots to be loaded as densely as possible.Therefore, the tooling cost and the penalty cost due to unused tool slots can be compromised basing on the economical benefits that suit the needs of a particular FMS.Fig. 1 and Fig. 2 give more insights of the results summarised in Table 6 and explore the relationships between tooling budget and throughput, and available machine time and throughput.The observations in these figures show that increasing the tooling budget or available machine time results in increased throughput.(m/min)  More results of three representative sets of available machine time and tooling budget for the throughput model are presented in Table 7.As can be seen from the table, the decisions of part selection, machine loading (tool assignment, operation allocation and part routes) and machining optimisation (cutting speeds and feed rates) were simultaneously made while the throughput was maximised.The optimum cutting speeds and feed rates were achieved within their recommended limits.A set of results for the production cost model are summarised in Table 8 covering the minimum cost of the selected part types, average workload, number of selected tools for different operations, status of the FMS, time savings and tool cost savings.The status of the FMS showed that the workloads were fully balanced for all computational experiments.The values of machining parameters indicate changes where cutting speeds are mostly lower and the feed rates are almost higher for minimum production-cost objective in the second stage than for maximum throughput objective in the first stage.Also, slight tool reassignments and significant part reallocation are observed.It has also been shown that operating machines at higher feed rates within their recommended ranges tend to reduce machining time.It is important to note that the time savings indicated might be caused by reduced machining time, and reassigning of tools and reallocation of parts on machines.These observations designate the fact that by re-allocating parts and re-assigning tools on machines, and re-optimising the machining parameters, there is a great possibility of achieving equal processing times amongst the

Conclusions
In previous studies, the isolation of machining optimisation from the planning of FMSs resulted in unbalanced workload in the FMSs.This study has made an attempt to integrate the decisions of part selection, machine loading and machining optimisation problems for a more balanced workload and therefore effective FMS.Two integrated models have been formulated and solved based on designed computational experiments.The findings illustrate the following two important implications: (i) the maximum throughput objective in the first stage could not guarantee balanced workload in the FMS for the combined part selection, machine loading and machining optimisation problems.Only some cases would demonstrate balanced workloads in this stage; and (ii) the minimum production-cost objective in the second stage guarantees balanced workload in the FMS without affecting the maximum throughput objective in the first stage.With minimised production cost, the bottleneck machines are eliminated and in some cases, the average workloads are decreased.This is a result of re-adjusting the machining parameters such as cutting speeds and feed rates, and also reallocating parts and reassigning tools on machines.The findings also support the applicability of the adopted approach over a wide range of planning period and tooling budget.

Table 4
Upper and lower limits of cutting speeds

Table 5
Upper and lower limits of feed rates

Table 6
General results for maximum throughput model Available

Table 7
Decisions of part selection, machine loading and machining optimisation for maximum throughput model

Table 9
Decisions of machine loading and machining optimisation for minimum production-cost model

Table 10
Decisions of part processing time and part routes for minimum production-cost model Available Time (min)