Mining Equipment Supplier Selection - Mine Management Questions and Answers Series (7)

Morobe Mining  Joint Venture (MMJV) is developing the Hidden Valley mine and the mine is considering several suppliers of machinery and equipment and continual service at the mine site. From experience and data available, the premier suppliers are Caterpillar, UWM Machinery and Hasting Deering. The manager identified the criterion for selecting the best service providers are based on cost, product quality, productivity and life/durability. The manager develops the following pairwise comparison matrices for each of the three four criteria.

X = CAT,Y= UWM,Z=Hastings Deering.

		Cost			P/Quality				Productivity				Life/Durability
	X	Y	Z		X	Y	Z		X	Y	Z		X	Y	Z
X	1	2	5	X	1	0.25	0.2	X	1	5	4	X	1	0.143	0.2
Y	0.5	1	7	Y	4	1	0.125	Y	0.2	1	3	Y	7	1	0.125
Z	0.2	0.1429	1	Z	5	8	1	Z	0.25	0.333	1	Z	5	8	1

From the above table, the cost matrix shows that supplier  X is “ equally to strongly preferred ” to supplier Z, but supplier Z is “equally to very strongly preferred” to supplier Y. Diagonally, it is equally preferred as it has the value of 1 which indicates one supplier is compared to itself.

The suppliers are prioritized within each criterion. For example, the manager intend to know which is the most preferred supplier, the second, third  within each of the four criteria. Mathematically, it is complex but it only employ approximation method to estimate preference scores. The first step is to sum the values in each column of pairwise comparison matrix as shown below for cost matrix(a).

Step  1	(a)				(b)
		Cost					Cost
Supplier	X	Y	Z		Supplier	X	Y	Z		Row Average
X	1	2	5		X	0.588	0.6364	0.3846		0.5364
Y	0.5	1	7		Y	0.294	0.3182	0.5385		0.3836
Z	0.2	0.1429	1		Z	0.118	0.0455	0.0769		0.08
Sum	1.7	3.143	13						Sum	1

In (a) the cost synthetization is done by adding cost pairwise comparison rating matrix. In (b) each column of cost pairwise comparison rating matrix is divided by the corresponding column sums (i.e. 0.5/1.7 = 0.294). it is also notice that at (b), each column sums to 1. Next, the values in each row are averaged as shown on the right hand side of the table above. Also column sum is 1 for the average values.

Step 2. Compare qualities.

The procedures applied above in cost comparison matrix is applied to the other comparison criterion and only the results (row averages) are tabulated for each supplier as given below. The row averages provide the company with its preferences for each criterion. For example, for the cost criterion, supplier  X is most preferred followed by supplier Y and supplier Z.

Supplier	Cost	P/Quality	Productivity	Life/Durability
X	0.5364	0.0927	0.6597	0.0812
Y	0.3836	0.2008	0.2236	0.2474
Z	0.08	0.7065	0.1167	0.6714
Sum	1	1	1	1

The prioritized decision criteria according to pairwise comparisons are shown below. Note that the corresponding columns are summed.

Criteria	Cost	P/Quality	Productivity	Life/Durability
Cost	1	0.1667	0.25	0.125
p/Quality	6	1	0.1429	0.1111
Productivity	4	7	1	6
Life/Durability	8	9	0.1667	1
Sum	19	17.167	1.5595	7.2361

 The column values of the above table have been divided by the column sums correspondingly and then averaged the rows as shown below.

Criteria	Cost	P/Quality	Productivity	Life/Durability	Row Average
Cost	0.05263	0.0097	0.1603	0.0173	0.05998
P /Quality	0.31579	0.0583	0.0916	0.0154	0.12025
Productivity	0.21053	0.4078	0.6412	0.8292	0.52217
Life/Durability	0.42105	0.5243	0.1069	0.1382	0.2976
Sum					1

The preference vector for the criteria consists of the row averages.

	Criteria
Cost	0.05998
P /Quality	0.12025
Productivity	0.52217
Life/Durability	0.2976

It can be clearly seen that the productivity of machines is the most important criterion with its life/durability the second in decision making. The overall score for each supplier is obtained by multiplying the matrix summarizing MMJV’s preference for each supplier criterion which was developed previously by the preference vector for the four criteria above. This is illustrated  in the table below.

Criteria
Supplier	Cost	P/Quality	Productivity	Life /Durability			Criteria
X	0.5364	0.0927	0.6597	0.0812		Cost	0.05998
Y	0.38359	0.2008	0.2236	0.2474	x	P/Quality	0.12025
Z	0.08001	0.7065	0.1167	0.6714		Productivity	0.52217
						Life/Durability	0.2976

Below are the scores each supplier was rated.

Supplier	Score		Order  of score
X- CAT	0.411952		X- CAT	0.412
Y-UWM	0.237541		Y-UWM	0.3505
Z-Hasting Deering	0.350507		Z-Hasting Deering	0.2375

By seeing the scores above, CAT is the most preferred supplier of machineries for MMJV. MMJV must be confidence in the judgements made in pairwise comparisons if MMJV will rely on the result above. But even if the company doesn’t make its selection based on the analytical hierarchy process (AHP) result, following this process results in identifying appropriate and reliable supplier to meet company’s production needs. Hence, AHP can help identify and prioritize the criteria, and examine strengths and weaknesses of different suppliers.

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Wafi-Golpu Mining Warden Hearing at Wenebele and Bawaga Villages.

The Mining Warden Hearing for Wafi-Golpu Support tenements for SML 10 application commenced on Monday the 2^nd of July 2018 at Wenebele and Bawaga Villages.

The Wenebele village of Yanta clan and Bawaga Village of Hengambu comprising of Elemu Gwagu and Demagu clans and Wonkins Village of Babuaf Clans are the primary landowners of the SML area and together with the LMPs and MEs under application for the Wafi-Golpu Joint Venture.

Yanta clan have four groups while Hengambu has three Landowner groups/clans have turned up during the meeting in numbers and gave their views in regards to the tenement applications.

Firstly, the Community Affaires superintendent of Wafi-Golpu Joint Venture, Mr.David Masani introduced the warden hearing team to the landowners and opened with a word of prayer to commence hearing. Then handed over to chief Mining Warden of Papua New Guinea, Mr, and Andrew to actually proceed into the Mining Warden Hearing.

The Chief Warden , Mr, Andrew Gunua conducted the Mining Warden Hearing  for Mining Easements comprise of ME 91, Me 93, ME 94. He explained the process of application with displays of posters and explained simplified illustrations with the flow chats of how an SML and supporting tenements are granted following due processes.

He further explained the warden hearing procedure and order of hearing.

The Chief Warden then allowed the company representative to explain to the warden hearing parties of the amendment to the orginal applications and the new work plans and David Masani explained exactly the company’s intention for the three amended ME applications.

The Chief Warden after recording the company’s work plan, he allowed the landowners to give their views whether they support the company’s application or object the applications. The people raised few concerns and asked few questions for the benefit of doubts of which the Chief Warden provided response which were of satisfactory to them.

The Chief Warden then closed the meeting upon satisfying all the requirements under the Mining Act 1992 regarding wardens hearing.

Further questions regarding benefits and other agreement meetings were raised after the meeting and the landowners were advised that, there will be a Development Forum of which the Mining Minister will officially open for them to further discuss matters of this regard.

The Project Coordinator Moses Mambu briefly explained the Development Forum to the landowners and the landowners were looking forward to the Development Forum later during the month.

The same procedure was followed at the Bawaga Village and warden hearings for ME 91, me 93 and ME 94 at both venues were successfully completed. These conclude the Mining Warden Hearing for the First Day and the warden hearing team anticipates  to complete the rest of the hearings in the remaining days.



Chief Mining Warden, Mr.Andrew Gunua Explaining the Flow Chat for SML Application Process at Yanta Community Hall

Landowner Acting Deputy President of Yanta, Mr.Johnson Ruben Responded during the Warden Hearing at Wenebele(Yanta Community Hall)

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Wafi-Golpu SML 10, Mining Warden Hearing for Supporting Tenements.

The Wafi-Golpu Joint Venture is a 50/50  joint venture between Newcrest and Harmony Gold to fund and operate the Wafi-Golpu porphyry gold-copper deposit in the Morobe Province of Papua New Guinea.

The Wafi-Golpu Joint Venture has applied for a Special Mining Lease SML10 with the Mineral Resources Authority(MRA), together with supporting Tenements such and Lease for Mining Purposes(LMP) and Mining Easements(ME).

Mining Warden Hearing is one of the requirements under the Mining Act 1992 and is part of application process for lease grant. Thus, part of the hearing for SML 10 were conducted in 2016 .

Due to some technical considerations, part of the feasibility study was ongoing during the submission of SML 10. Thus, some of the support Tenements were lodged with the MRA  later in 2017-2018.

As such, Mining Warden Hearings for the support Tenements will be conducted on the 2nd July 2018 to 5th July 2018.

The Hearings will start at Yanta Community Hall and Hengambu Community Hall on Monday 2/7/18.
Then on Tuesday 3/7/18 Hearing will continue at Babuaf Community Hall.
on Wednesday,4/7/18 Hearing will be at Wampar LLG Hall near Nadzap airport and at Zifasing at 40 Mile.
On Thursday 5/7/18, Hearing will conclude at Lae indoor sports stadium and Wagang Hall.

The awareness of the Tenements were  conducted by the company officers at the affected communities and the landholders of the affected communities are expected to turn up during the fixed dates and time to give their views whether to support or object the applications and their proposed Tenements/facilities.

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Queuing Theory - Mine Management Questions and Answers Series (5)

Part A

1.   What is queuing theory?

In simple terms queuing theory is the study of waiting in lines or queue. Furthermore, Queuing theory is a field of study that deals with Queuing or waiting lines that are analyzed with a set of mathematical formulas. Different queuing models and mathematical models exist to deal with different types of waiting line systems.

2.   What is finite calling population and give an example of it?

Finite calling population is when one knows exactly the population that is in a queue system. E.g. a mine engineer knows the exact number of trucks (i.e. 20) which will be served by a number of shovels (i.e. 2).

Or  finite calling population has a specific , countable number of potential customers that planning is often easy, for example fixed production equipment at mining sites, trucking terminals, trains and airplanes.

3.   What is the expected logic between the arrival and service rates? Why is this important?

The expected logic is that the Arrival Rate must be less than the Service Rate. In other words, the service rate must be greater than the arrival rate. So it is logic to assume that the rate at which services are completed must exceed the arrival rate of customers to increase productivity. This logic is very important because if this is not the case then, the waiting line will continue to grow and there will be no average solution. Hence, it is generally assumed that the service rate must exceed the arrival rate, λ<µ.

4.   What is the difference between the average number of customers in the queue system and average number of customers in the waiting line?

Average number of customers in queue system  is when customers waiting in a single or multiple line to be served in a Bank, dinner at the mess etc. not only people but trucks/machines/ships parts and products queue to be loaded/unloaded and manufacturing operation to be worked on.

Whereas

Average waiting line system comprises of arrivals, servers and waiting line structure. Waiting lines are based on averages of customers or trucks/machines/ships/plane/train arrivals and service times.

5.   Explain the cost relationships between service cost and level of service, and waiting cost and level of service. Explain with an example of each.

Generally the service cost is inversely related to waiting cost. For example, as the level of service is improve by increasing the number of servers, the cost of services will increase whereas waiting cost decreases.

Cost of providing the service is reflected in the cost of servers like loaders/shovels, bank clerk or repair crew in maintenance plant. As the number of servers is increased to reduce service time, service cost rises. The major effect of waiting cost is the loss of business because customers might be tired of waiting and leave, or loss production due to time waste (e.g. in mining) but this loss is temporary.

The curve below shows these relationships.

Part B

1.      Given the information, calculate the operating characteristics and determine if there is any improvement required, including the possibility of increasing number of   mechanics.

Number of customers in the queue is exactly known so this is a finite calling population.

Data; 

Population size N (no. of trucks) = 10 trucks

Number of servers = 1

Arrival rate (λ) per customer = 1/140 = 0.00714 per hour

Service rate (µ) is =1/4.5 = 0.2222 hour

i.     Po =  =  = 0.692162    n=0, 1, 2, 3……….10

Po is the probability of no trucks in the system.

n	0	1	2	3	4	5	6	7	8	9	10
Po	1	0.3213	0.0929	0.0239	0.0054	0.001	0.00017	2.14E-05	2.1E-06	1.3E-07	4E-09
sum(1/sum)	0.692162

ii.      Lq =   == 0.1121 waiting for maintenance.

iii.    L = Lq + (1-Po) = 0.1121 + (1 – 0.692162) = 0.419938 trucks in the queue system.

iv.    Wq =  =    =1.64 hours waiting for repair.

v.      W = Wq +  = 1.64 +  = 6.14 hours’ time in the maintenance workshop.

From the results above, it is seen that the mechanics are busy for about 51% of 12 hour shift each day repairing one machine on the queue system. Out of the 10 haul trucks, an average of 0.42 machines are in the queue for maintenance or4.2 % trucks are broken down waiting for repair or under repair. Each broken down truck is idle which means in 12 hour shift, about two tucks are repaired (12hrs/6.14). Therefore there is no need to increase the number of mechanics. But if the fleet size is increased to 20 or so, then there is a need for couple of mechanics at the workshop. But otherwise, no need.

2.      Given the information, calculate the operating characteristics and recommend if there is anything to be done to improve truck – shovel productivity and reduce queue time.

Data:

λ = 4 trucks per hour (poison distribution)

µ = 3 trucks per hour

s = 2 shovels

sµ = 2*3 = 6, (>λ = 4)

Po = =   = 0.2 This is the probability that

No trucks are in the waiting line or queue.

L =  *Po +  =  *0.2 +  = 2.4, so 2 trucks arrive for loading at the pit.

                    

W =  =   = 0.5 hours or 30 minutes in the queue (waiting and served).

Lq = L -   = 2.4 -   = 1.0667 trucks in queue to be loaded by the two shovels.

Wq =  = 1.0667/4 = 0.267 hours or 16 minutes in the queue.

Pw =  =   = 0.533333

Now, there is 0.533 probability that trucks must wait or queue for loading which means that there is one or two trucks in the open pit queue system to be loaded by the two shovels.

Result Discussion

It can be seen from the results above which shows that the truck – shovel combination productivity is not attractive. There is more truck capacity and less number of shovels causing low truck productivity. The queuing time of 16 minutes for one or two trucks in queue is not attractive. There are 2 trucks entering the pit for loading at any time. By loading only one of the total 2, it consumes 16 minutes of production time where the truck(s) remain idle. It is now a need to reduce queuing time at all cost as it is recommended here. It is also recommended that, one shovel must be added to the existing fleet to increase productivity but keeping the fleet of trucks constant. With this recommendation the following are the results of improvements made in the queue system:

Recommended data: s = 3; λ = 4; µ = 3

Po = 0.254 probability that no trucks in the queue or loading

L = 1.48, so 1 truck enter the pit for loading.

W = 0.25 hour or 15 minutes queue time (average waiting time to load) 

Lq = 0.15 waiting to be served.

Wq = 0.0375 hour or 2.25 minutes waiting in line before one truck is being loaded.

Pw =0.18 probability that one truck must wait for loading or all 4 shovels are busy.

Upon the above recommendation, it is seen that productivity y is improved when one truck’s average queuing time is reduced to 2.25 minutes from 16 minutes. In the future the cost of adding one shovel to existing fleet will be compensated by the higher production which is objective of the mine management.

3.      Given the data, the manager wants to determine the average length of waiting line and average waiting time at counter. If the office space can only accommodate 10 clients, what do you recommend?

Data: λ = 5 rate per hour;   µ = 60/10 = 6 clients per hour.

Now, Lq =   =  = 2.08 clients waiting

Wq =  =  = 0.416 hour or 24.96 minutes waiting in line or queue.

The results above shows that the client service provided by the law firm is not effective as there is almost half an hour consumes while the clients are waiting to be served. Therefore, it is recommended that the constant service time must be reduced 8 minutes and by increasing one server to the exiting but clients arriving rate will be constant as it can’t be controlled. That means the law firm must accommodate two clients at a time with two servers serving the clients at all cost. Upon these changes, the following results are obtained;

Λ = 5 rate per hour;   µ = 60/8 = 7.5 clients per hour.

Lq = 0.667 clients waiting

Wq = 0.133 hours or 7.98 minutes waiting in line or queue.

Now this effective since the waiting line is reduced to 7.98 minutes from 24.96 minutes. It is assumed that there will be no or one client waiting to be served. The cost of the additional server will be covered the more clients paying for the business as they are being served.

Note also that the office capacity to accommodate only ten clients doesn’t mean that all of them are going to be served at the same time but, will sit comfortably waiting to be served. That doesn’t have an effect on the queuing time but queuing time depends on serving time. Therefore, I think the purpose of office capacity to accommodate ten clients is just for the firm’s good reputation and attractiveness of the business.

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