Literature Review in Project Scheduling Techniques

The Engineering Center

Florida International University

10555 West Flagler Street

Miami, Florida 33174

By

Alex E. Obi-Ugbo

In fulfillment of final Submission for Independent Study

MAY 04, 2016

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ABSTRACT

This paper is a report based on a review of 33 journal articles from as early as 1994 to 2016.

The reviewed research papers were centralized on developing new scheduling methods to

overcome barriers and limitation posed by the traditional scheduling tools, CPM/PERT.

Literature portrayed ongoing research to meet the demands of a dynamic scheduling

environment. The common denominator in all reviewed papers was the need to reduce project

makespan, solve time constraints, resource constraints and solving problems associated with

the job shop.

Keywords: Project Scheduling, Critical Path, Fuzzy Critical Path Time Constrained Project

Scheduling, Resource Constrained Project Scheduling, Job Shop Project Scheduling Problem.

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INTRODUCTION

Project scheduling can be said to be the milestone, activities and deliverables with a

definable, intended start date and finish date. The completion of any project is largely dependent

on how managers are able to schedule activities to ensure timely and successful completion. All

things being equal, scheduling should ensure timely completion of any project; however, it is not

always the case. Managers are confronted with a myriad of constraints which make the process

difficult.

Over the years, various researchers have explored several approaches to ensure effective

scheduling. Up until today, scheduling approaches are a contested terrain as they are not free from

criticism. The Critical Path Method and Bar Charts are the most predominant approaches used in

scheduling. CPM was introduced by DuPont Corporation and Remington Rand Corporation [1].

The approach is based on a mathematical model which determines the sequence of project

activities. CPM lists all the required activities to complete a project, the time required to complete

an activity as well as the dependencies between the activities.

A lot of importance is placed on the critical activities on the longest path. One of the

objectives is to shorten the time spent on the critical path: this is achieved by either pruning critical

path activities, fast tracking or crashing which entails bringing in more resources than planned [1].

CPM techniques were traditionally used in industrial projects and later utilized in completing

construction projects.

Bar charts are a much simpler technique for scheduling; they can be developed by hand or

spreadsheet software. The bar charts are however not mathematical and neither are they based on

any theory. They provide detailed work activities from assumed start to finish. Compared to CPM,

they are much simpler to develop and to interpret. Unlike CPM, they do not have a critical path

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and neither do they show activity dependencies. Project Evaluation and Review Technique

(PERT) focus on creating and controlling project schedules in stochastic environments [2].

Although updated CPM/PERT have proved useful in handling scheduling for various

projects, the methods are still not able to accurately model projects of repetitive nature such as

those in a linear construction. Network-based models cannot provide work continuity for the crew

as well as resources. They are also not able to indicate the rate of progress and actual conditions

of the project. In an attempt to deal with the limitations other models such as Line of Balance

(LOB), The Vertical Production Method (VPM), Linear Scheduling Method (LSM) and Repetitive

Scheduling Method (RSM were developed.

The linear method utilizes graphical models to show the sequence in which project

activities will be constructed. This method is typically used in projects which contain identical

units in which there will be a lot of activity repetition. Examples include horizontal repetition in

the construction of highways and pipelines, vertical repetition in the construction of high-rise

buildings [3]. Its major advantage is that it provides production rate, duration information as well

as future potential bottlenecks. Its major pitfall is that it assumes that production rates are linear as

a result, it is better suited for repetitive projects as opposed to non-repetitive ones [3].

Traditional approaches to scheduling have gone through a myriad of criticisms for reasons

to do with their applicability and reliability. As a result, a lot of research has emerged to deal with

limitations posed by these techniques. Various scholars have proposed better methodologies to

effectively address scheduling problems. Research has also focused on building on the existing

methodologies to better suit them for various environments.

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LITERATURE REVIEW

Developments in scheduling techniques.

Maheswari and Varghese in International Journal of Management [4] focused on reducing

the limitations of CPM/PERT by developing the Dependency Structure Matrix (DSM). The main

objective was to solve the problem of sequence analysis and information exchange. DSM major

advantages include the ability to provide systematic mapping’ among elements, readability as well

as a clear presentation of where interdependence occurs. The model also allows critical path

calculations by presenting the amount of work done for the duration of the activities. DSM does

not only capture workflow but, communication times as well, this is because a lot of information

exchange occurs between activities. Even though DSM is a powerful tool, it also has some

drawbacks. It cannot function on its own as a result; researchers have integrated it with other tools

such as critical path float. Shi and Blomquist criticized this model for failing to estimate activity

time due to an overlap in activities

In an attempt to solve the vagueness of communication time in DSM model,

Shi and Blomquist in Journal of International Management [5], proposed Fuzzy Dependency

Structure Mix. The model is based on the assumption that it is difficult to give a precise time for

some projects. It is, however, better to give fuzzy number or variable rather than a specific time.

Its strength is that it can analyze the critical degree of activities path and duration of a project in

an uncertain environment, with information dependencies between activities. There are however

other factors which may affect information sharing mechanisms such as resource allocation,

organizational structure as well as behaviors of stakeholders; these cannot be addressed in the

proposed method.

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Lin in, Institute of Electrical and Electronics Engineers [6], also proposed another

methodology as a solution to the vagueness problem in CPM. The proposed method uses statistical

data to determine the critical path. The assumption in the method is that, the “fuzzy CPM based

on statistical data is an extension to the crisp CPM”. Statistical data in this method is based on

“confidence, interval estimates”, combined with fuzzy sets based on viewpoints for solving

practical problems in the unknown situation. The major advantage of this approach is that it takes

into account the fact that time variables are vague hence the use of fuzzy numbers. Another major

disadvantage is that; the method may be difficult to employ in the absence of statistical date.

Liberatore, in Transactions on Engineering Management [7] proposed a new methodology

for fuzzy critical path analysis consistent with the extension principle of fuzzy logic. The objective

was to create a method to quantify uncertainties likely to occur in the project. This approach is a

direct generalization of critical path analysis to the fuzzy domains. The main advantage of this

approach is that “the integrated procedure determines the fuzzy set of critical path length and fuzzy

activity critically”. This approach is likely to better assist managers in managing project schedule

as well as uncertainty. Further research should focus on testing the mathematical programming

procedure on other project management programs to find out the number of project networks

which can be solved.

Solutions for Scheduling in Stochastic environments.

PERT is criticized for its lack of calibration and its tendency to underestimate stochastic

Variation [2]. To provide solutions for scheduling in dynamic environments research has focused

on finding multiple critical paths.

Lee and Shi, in Institute of Electrical and Electonics Engineers [8] proposed the Stochastic

Project Scheduling Simulation (SPSS). This method works by integrating CPM, PERT and

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Discrete event simulation (DES). The combination produces a deterministic schedule, probabilistic

schedule as well as simulation-based stochastic schedule. The manager will then compare the three

schedules to estimate the potential risk. Advantages of this method are that it can forecast the

probability of finishing a project at a given duration, compare schedule results as well as test the

significance of differences between different simulations. The problem with this approach is that

project duration may become complicated with the existence of multiple critical paths or close to

critical. There is, therefore, a need for a corresponding t-test.

Trietch and Baker, in International Journal of Project Management [2] contributed to

scheduling research by proposing an approach called PERT 21. Their model was built on the ideas

of (Ash and Pittman, 1994) who constructed the Critical Chain Project Management (CCPM) to

address the issue of stochastic variation: they, however, ignored the fact that projects must

be managed hierarchically. The proposed approach is a combination of the PERT engine 21 and

the DSS. The new engine is based on the assumptions that “stochastically dependent processing

times can be modeled by a lognormal distribution with linear association”, secondly, “historical

data can be used to estimate the necessary parameters” [2]. The advantage of this approach is that it

does not require a lot of input, which makes it easier to use. Another plus is that it can be used in

budgeting. Its ability to provide valid risk analysis means that it can be used to support bidding for

new projects. Although the engine comes with some benefits, its main downfall is its reliance on

history and correlations to assess risk, risk modules are subjective and therefore are not 100%

reliable. The model is also limited in that the engine cannot coordinate multiple projects.

Linear Project Scheduling

Arditi, Sikangwan, and Tokdemir, in Construction Management Economics [9] developed

a method to deal with scheduling of high rise building. They found that the construction of high

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rise buildings, though repetitive in nature were different from other linear projects such as the

construction of pipelines and pavements. They further developed the Line of Balance (LOB) to

accommodate peculiar conditions encountered when constructing high rise buildings. In the

approach, two new concepts were introduced, flexible unit networks, and multi-level LOB. By

coding the new concepts into the scheduling module (Lob plans), results showed excellent benefits

in data preparation, network generation, and network modification. This approach was tested in

different scenarios, including extreme cases and it produced workable schedules. Its pitfall is that

it does not have the capability to handle structures involving steel as well as steel reinforced

concrete structures. The method is highly complex and therefore requires a high degree of

knowledge.

Agrama, in Industrial Engineering and Operations Management International

Conference [10] challenged the strength of the LOB. The author's argument was that, although it

maintains resource continuity for an activity from one unit to another, it has several

disadvantages when used in high rise buildings. These problems include, “variability in

construction work, the diverse direction in activities, skeleton constraint, and presentation

difficulties” [10]. To deal with these problems, a Versatile, Multi Objective Optimization Method

was introduced. This method focuses on non-identical storey building projects. Two models were

developed, one to deal with time parameters, the other to deal with cost parameters. The first

model enables the investigation of the optimal construction plan to establish the tradeoff between

project duration and total work interruptions. The second model objective is to establish the

optimal trade-off between total project cost and total penalty cost for work interruptions. This

model has proved to be robust and consistent. Although it has benefits, there are challenges with

crew synchronization for non-typical repetitive activities.

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Cho, Hong, and Hyun, in Canadian Journal of Civil Engineers [11] proposed a

scheduling model for repetitive construction processes for high rise buildings. This was done by

developing a model which includes LLFP, LLSP, and a linking dummy. The model proposed

differs from other existing models in that, it considers “the flexible job logic of multiple work

task that comprise a construction process, the productivity of construction equipment as well as

labor productivity loss as a result of idle time. This model is believed to meet the demands of

simultaneous or overlapping work tasks involving repetitive construction processes. The model

offers a basis for one to propose a model to minimize idle time to ensure effective use of

construction equipment. The model has several limitations, the model does not have a probability

function and therefore excludes uncertainties which may arise. Important constraints such as

availability of equipment, labor and spaces were not included. This model does not take into

consideration cost factors which are a major issue in linear projects.

Cho, Hong, and Hyun in Journal of Management in Engineering [12] developed another

model, this time taking into consideration cost factors. They developed an integrated schedule

and cost model for the repetitive construction process. This was achieved by, “integrating the

schedule and cost information used in the integration model with resource information inputted

to the project”. The developed model comprises of scheduling model, cost estimation module

and a tradeoff analysis module. The advantage of this model is that it allows managers to

efficiently manage schedule as well as cost. Its major disadvantage is that it cannot be applied to

the entire project, there is a need for the development of a model which covers an entire project.

Jiang and colleagues at the Joint International Conference on Computing and Decision

Making in Civil and Building Engineering [13] contributed a method to deal with the challenges

which may occur during a construction of two or more utility line with different layouts. The main

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objectives were to indicate the interference locations, predict interference times and adjust the

schedule to avoid work space conflicts. This was achieved by modifying the linear scheduling

method to include extraction of data on each utility line from drawings and then listing equations

of each line to be able to compute the intersected points. The benefits of this would include less

construction interruption and delay of construction and cost overruns.

Polat and colleagues in Institute of Electrical and Electronics Engineers [14] proposed a

method for scheduling the construction of Asphalt highway using Line of Balance and Discrete

Event Simulation Techniques. The objective was to find a solution to scheduling problems of both

onsite and offsite operations of a real life Asphalt project. Using the Line of Balance, they

determined the starting date and the ending date. Discrete Event simulation was used to determine

the arrival of trucks that would provide an uninterrupted work flow”. From their study, they found

out that the method fits neatly. The major advantage of this approach is that it takes into

consideration constraints on resources and stochastic features as well as enable the contractor to

achieve an uninterrupted workflow between two different sites.

Constraints in Project Scheduling

In any given project, the possibility of constraints or problems is very likely. Various

research has focused on identifying these problems and providing solutions for them in project

scheduling. Common constraints include resource constraints, time constraints as well as

problems associated with the job shop.

Resource Constrained Project Scheduling Problem.

Resource constrained project scheduling problem is concerned with minimizing make span

at the same time satisfying resource constraints and precedence [15]. Several solutions were

developed to solve the resource constraint problem.

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Nisar, Yamamoto, and Suzuki in Journal of Japan Society of Civil Engineers

[16], proposed the Resource Dependent Critical Path Method (RDCPM). The method, identifies

resource dependencies that exist between activities to be able to determine the critical path, by so

doing, both total floats and free floats are accurately computed. The advantage of this approach is

that it is not necessary to check the entire schedule to establish resource dependencies; it can

provide alternative schedules which can be derived from certain activities in RCS. RDCPM also

provides resource link optimization to reduce the number of resource links. The limitation this

method is its assumption of one resource constraint, in any project, there is always a possibility of

multiple resource constraints. Although the study is expected to solve MRCPSP its limitation is

that it does not give a solution to solving projects with multiple objectives and there is also need

for improvement on the computational effort for solving MRCPSP using the proposed (ACO).

Reyck and Herroelent in Computers and Operations Research [17] researched resource

constrained project scheduling problem with discounted cash flow and generalized precedence

relation (RSPSDC-_GPR). The objective of this approach was to increase the present net value of

the projects. The approach also extends the RCPSP to arbitrary minimal and the maximal time lag

between start and completion of activities The associated conflicts are resolved by using the

concept of minimal delay modes which, is a delay alternative originally developed for the RCPSP.

Vanhoucke and Coelho in Journal of Operational Research, [18] proposed SAT solvers to

deal with the RCPSP with logical constraints. The algorithm is believed to compete with other

multi-mode algorithms in literature with no logical constraints. With this approach, a major

reduction in the project makespan was observed. Most approaches to deal with resource constraints

assume that each activity and its resources are known and fixed. In reality, this may not be the

case. The choice of activities is largely determined by the availability of resources and time

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tradeoff. The other problem which may exist together with resource problem is uncertainty, which

may include weather and other factors that human may not be in control of.

Long and Ohsato, in International Journal of Project Management [19] proposed the

Fuzzy Critical Chain method to address both resources and uncertainty problem. The proposed

solution has three logical iterative stages. In the first stage, the RCPSP with resource and time is

solved to provide a minimum make span deterministic schedule. Using the deterministic schedule,

fuzzy numbers are used to model uncertainty in activity durations, this is achieved by adding an

activity buffer to deal with uncertainty. The last stage focuses on updating the final schedule based

on the penetration level in the project schedule. The advantage of this approach is that it can be

used for scheduling at both planning and execution stages. Its main strength is its ability to reduce

project risk and also makes it possible for managers to negotiate for additional resources. The

shortfall is related to the inefficient method to determine a project buffer size in certain instances

a good example is that of construction projects where one single factor such as weather can have

a bearing on many activities.

A very common problem which is now receiving a lot of attention is the multi-mode

resource constrained cross dock scheduling problem (MRCDSP). Cross docks reduce

transportation cost by utilizing high capacity in bound and out bound vehicles. Cross docks allow

just in time (JIT) production method through sending materials in smalls batches in the right

sequence [20]. The major factors which drive operational cost in the docking industry include,

assigning containers to dock doors as well as assigning containers at the cross dock. If any of these

activities is not properly managed, the result may be excessive travel cost. Time management in

inbound and outbound also allows efficient use of limited resources such as machines and labor.

To be able to solve the problem associated with docking, it is necessary to use a holistic plan which

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goes beyond the scheduling problem and the assignment. Hermel and colleagues in Omega [20]

proposed a methodological framework (MRCDSP) which encompasses the following: container

clustering, dock assignment, workflow scheduling and container scheduling to solve the problem.

The method proved to reduce the total processing time.

Time Constrained Project Scheduling Problem.

Crashing is a popular method used by many industries to meet project deadlines. However,

this process is not free from error. The process involves allocating more resources than planned to

shorten the length of projects. When such an approach is employed, there will be a need to consider

reworking as nonconformance may lead to error [21].

Kim, Kang and Hwang in International Journal of Project Management [21] proposed an

approach to solving the problems which may come as a result of crushing. The main assumption

was that, quality is a major factor in ensuring timely projects, thus, the goal of managers is to

ensure quality. By ensuring quality, time will not be wasted in fixing errors or rework. Attention is

given to the individual activities under the assumption that the time–cost tradeoffs are linear. Under

the proposed PQLC, the direct costs are minimized as nonconformance will always require rework:

as a result, the contractor requirements and specifications are to be identified at the completion of

each activity. The modification will not have a bearing on time expenditure as it is bounded by

crash duration. The rework or modification cost of any activity is also bounded by the cost of

crashing. In this approach, the manager will identify the risk of crash activities which will allow

the prevention of rework by closely monitoring activities which may lead to error.

Although the model has several advantages it also has constraints. Firstly, activities cannot

be reduced by more than the maximum time reduction; secondly, the start time of each activity is

expected to be as great as the finish time of all the immediate predecessors. Projects are expected

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to be finished by the deadline. Another great pitfall of this approach is that the manager is

responsible for limiting the number of nonconformance activities. Although the model has a few

constraints, its strength compared to other modes is in the fact that it considers the activity quality.

Those that do not include the activity quality are too optimistic and may not work in reality. As

discussed above whenever there is no conformance, expected quality cannot be guaranteed.

Mohammadipour and Sadjadi in Computers and Industrial Engineering [22] proposed a

multi-objective mixed integer linear programing for minimizing project extra cost, project total

risk enhancement and project total quality reduction which are liable to time constraints. This was

achieved through the use of goal attainment technique. The assumption in this method is that the

tradeoff between the three would shorten the overall project duration. The results of this model

showed that it could lead to efficient solutions when conflicting objectives are considered

simultaneously, which is an advantage as most approaches only consider a single objective. The

model is very practical and relates to what happens in the real world. There is potential for the

model to be extended, delay penalty and maximal lag could be imposed in future models.

Another approach to dealing with time constraints includes hiring overtime or hiring

Additional resource capacity. This approach is often criticized for being costly. The main

challenge is in determining when and what extra capacity should be employed to be able to meet

deadlines. Another issue is that the approach only utilizes overtime when the project misses its

scheduled deadline. This approach leads to the pile up of cost towards deadline which may go

above cost objectives.

Guldenmond, Hurink, and Paulus, in Journal of Scheduling [23] proposed a method to

schedule jobs with strict deadlines at the same time addressing problems associated with hiring

overtime. They argued that the popular solution to meet the deadline by hiring overtime is not

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always beneficial as it shifts bottlenecks towards the end which may have financial consequences.

To be able to avoid shifting bottlenecks towards the end, they employed a two stage heuristic. In

the first stage, partial schedules are constructed by scheduling a job at a time for “only a fraction

of their duration and then the fraction for which the jobs are scheduled is gradually increased”.

The significance of this approach is that jobs are partially employed into the schedule before

addressing bottlenecks. The approach decreases the deadline project by 10% which in turn means

that less than 10% of the work is done using irregular capacity which is costly. The strength of this

approach is in its flexibility in parameter setting and also the ability to choose where to spend

computational effort.

Job Shop Scheduling Problem.

A job shop is made up of different machines which perform different activities on

operations on a job. Job shops are confronted with a number of constraints. In a job shop, there is

no precedence among different activities of different jobs, operations cannot be interrupted and

each machine can handle one job at a time. In a job shop, the machine sequence is fixed, the major

challenge is determining the sequence which minimizes the make span. [24]. There is a plethora

of research done to solve a variety of problem encountered in job shops scheduling

When machines break down the work is interrupted, this gives rise to a series of

problems. Li and Chen, in Systems Man and Cybernetics [25] paid particular attention to a problem

associated with a machine breaking down followed by the arrival of a new job. To solve this

problem, they constructed a Mathematical model of dynamic job scheduling to minimize make

span. The problem is solved using the Back Propagation Neural Network (BPNN), which makes

it possible to “describe machine break down and the arrival of a new job”. After determining

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whether or not constraints are satisfied and solving constraints, BPNN will now generate a solution

for the JSP. The author does not take not of any limitations of this solution.

Yulianty and Maruf, [26] in the Journal of innovation management and technology

contributed to a flexible job shop scheduling problem. The goal of their approach was to find a

solution to schedule jobs to resources when a disruption occurs as a result of a machine breakdown.

In their approach, they focus on FJSP, controllable processing time, and machine breakdown. They

built a mathematical model which deals with job assignment and processing time of the jobs. In

this scheduling, downtime is predicted and included in the initial schedule to minimize

disturbances. The advantage of this approach is that it reduces tardiness and rescheduling cost.

They did note any disadvantages of this approach.

Kundakci and Kulak [27] in Computer and Industrial Engineering contributed to solving

the job shop scheduling problem by developing Hybrid genetic algorithms for minimizing makes

span. The objective was to solve dynamic job shop scheduling problems which include new arrival,

machine breakdown, and change in processing time. This method combines the KK heuristic +

swap and well know dispatching heuristics+ swap are integrated with a GA algorithm The

method ensures quality JSP solution with regards to quality and CPU time. The method takes into

account dynamic factors thereby providing solutions for large scale problems. Further research

may apply the method to scheduling environments such as parallel machines, flow shops, and open

shop

Jacobs and Lauer, [28] Industrial Management and Data Systems published a paper on

DSS for job shop scheduling. The objective was to come up with a tool to assist managers to

improve decision making for machines. The system is capable of producing sequences through

rules that “incorporate set up-time reduction, shortest processing sequencing” as well as

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downstream requirements and job due dates. The advantage is that it forms an interactive interface

between the human scheduler and the factory system. The system is able to expedite hot jobs and

jobs near due date and it tracks all jobs through the shop real time. No limitations are stated in the

article.

Agarwa, Pattanelk and Kumai, [29] in Journal of Advances in Management Research,

proposed a solution for a flexible job scheduling problem where alternate machines are available

to process the same job. This was achieved by using a multi-objective genetic algorithm approach

in order to minimize make-span and total machining time. The method employed yielded positive

results, the method gives optimum solutions for job allocation to machines to achieve equal

utilization of machine resources. The downfall is that it does not provide solutions in other possible

instances such as more machines, multiple constraints, machine breakdown and inspection to

apply it to real life situations.

Phanden, Jain and Verma [30] in Journal of Manufacturing Technology Management,

proposed a simulation based genetic algorithm to optimize the job shop scheduling problem by

minimizing tardiness and make span. The adopted methodology was implemented on a job shop

consisting of 15 machines. Mean tardiness and make span were used as performance measures.

Three cases were observed. The first one consisting of a randomly selected single process plan,

second one nonrandom considered according to “minimum production criterion and the third one

dealt with MPP for each part. Results showed that the algorithm yields better results only when a

single process plan is used compared to when a randomly selected one is used.

Liang, Li and Qi-Di, [31] in International Symposium Intelligence Control introduced a

new method to deal with JSP based on Hopfield Neutral Networks. The construction method is

improved by including a new computational energy function. The method develops all constraints

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of JSP scheduling problem as well as permutation matrix express. Simulated Annealing algorithm

is applied to avoid Hopfield neural network from converging to local minimum volume. The

method improved the original Hopfield network; its advantage is that the developed one can keep

the steady outputs of neural networks as feasible solutions for JSP. Although the annealing

algorithm works, the local minimum has not been completely resolved.

Gran, Ismail, Ajol and Ibrahim [32] in International Conference on Computer

Communication and Control Technology developed a solution for flexible job scheduling problem

using mixed integer programming model. The objective of developing the model was to minimize

makes span and total Machining time. The model includes 6 different stages. Data collection from

auto part manufacturers, data recording and analysis. Data is screened to ensure that it is useful

and reliable for testing the theory in question’s third stage includes the development of the

mathematical model, followed by identification of mathematical solution approach and finally

solving the solution. The strength of the model is that it can also be applied to different but similar

problems. The major plus of the approach that it is simple and is to put to practice compared to

other methods

In IEEE Explore Yin and Zhao [33] proposed a two step approach to solving the flexible

Job Shop Scheduling Problem (FJSP). With this approach, a Job Scheduling Problem is created by

disputing all operations to the machine to ensure that each operation is performed by a certain

machine. To solve the JSP, a quasi- physic and quasi human algorithm is proposed. This two-step

approach has proved to be effective and efficient. They also found out that the quasi physic and

quasi human algorithm is a new idea that could be used to design effective and efficient algorithm.

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CONCLUSION

The review of literature conducted provided evidence for developments in scheduling methods.

Developments were based on the limitations of the traditional methods such as CPM/PERT.

Proposed methods offered solutions to enable effective scheduling.Vast research focused on

finding solutions of vagueness in Critical path by proposing Fuzzy critical methods. Literature also

showed a trend in scheduling method to not only include one critical path as in the traditional

approach but multiple critical paths. Another issue addressed in literature is scheduling in

stochastic environments which tradition methods excluded. Attention has also been devoted to the

scheduling of linear projects especially those of repetitive nature. In the literature reviewed the

main focus was on ensuring resource continuity as well as managing cost. Literature also showed

that methods have been developed to deal with projects of linear nature. Literature on major

constraints associated with scheduling was also reviewed. The most common constraints include,

resource constraints, time constraints as well as problems associated with the job shop scheduling

There seems to be more research on resource constraints compared to time constraints s problem.

Below is a list of common methods, research objectives and environments explored in literature?

Scheduling Methods identified in literature

Statistical Data

Systematic Algorithms, Genetic Algorithm , Hybrid genetic algorithm, Simulation based

genetic Algorithm and Simulated Annealing Algorithm

Discrete event simulation

Line of Balance,

Mixed integer programing method

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Scheduling issues researched

Solutions for vagueness in CPM

Sequence analysis and Information exchange in CPM and PERT

Solutions for multi utility lines scheduling

Solutions for multi-storey high rise buildings

Scheduling in Stochastic environments

Resource constrained project scheduling

Time constrained project scheduling

Job shop scheduling problems

Scheduling Environments

Manufacturing

Construction

RECOMMENDATION

It is evident from the literature that there is no one perfect scheduling method as every

problem requires a different approach. The goal of managers is to keep abreast of on ongoing

research to find better scheduling methods to suit their needs. Given that most methods have

negatives and positives, project managers should weigh their options and adopt to methods

which give them the best results also taking into consideration cost and quality. There is also

need for researchers to focus on problem encountered when scheduling projects in foreign

countries. This is because of the increase in job outsourcing. Research should focus on foreign

regulations in scheduling. It is clear that scheduling environments are dynamic therefore,

managers should continue to find effective solutions to scheduling.

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Although ther is a lot of research on diverse issues in scheduling, there are still other

aspects or scheduling environments which have received as much attention. Most research

focused on the job itself, little attention is devoted to other external factors which may have a

bearing on project schedules.

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REFERENCES

[1] Vyas R.S. (2013). Scheduling Project Management Using Crashing CPM Network to get

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