Question 4-Mine Workers' Transport Vehicle Problem

Workplace’s activity: Mine Workers' Transport Vehicle Problem

Question 4    

A mine workers' transport vehicle can carry 36 workers. All workers need to be transported to the mine daily across a 90 minutes periods: 6.30-8.00 in the morning, and 4.00-5.30 in the afternoon. The round trip takes 15 minutes. If 1134 workers need to be transported every day, morning and evening, how many vehicles would be required assuming the mine vehicles are the only option for workers to get to the worksite?

A- Solution

My working on this question includes three steps through two parts: Part 1 is my Planning, and Part 2 is my Action.

PART 1- PLANNING

My aim is to plan a procedure of steps to find out three key features of 
*the total number of round trips needed, 
*the maximum number of trips that a vehicle can transport/operate within 90 minutes, and 
*the minimum number of vehicles which are needed to transport all mine workers to the mine worksite.

These features will be determined through the procedure of three steps as below.
 
Step 1-Finding the total number of round trips needed
In this first session of Step 1, I consider knowing and working out the total number of round trips, also called trips in this activity, which are required/needed to transport all mine workers to the worksite.

Step 2- Finding the maximum number of trips that a vehicle could operate/transport within 90 minutes.
In this second session of Step 2, after knowing the total trips needed from Step 1, I consider knowing and working out the maximum number of trips that a vehicle could transport within 90 minutes.

Step 3- Finding the minimum number of vehicles needed.
In the final session of Step 3, I consider finding out the minimum number of vehicles that is required/needed to achieve all trips (which found at Step 1).

With this planning, my Action concentrating on three steps above will be illustrated in next part.

PART 2- ACTION 
Based on three steps above, in this Part 2, my detailed approach and calculations are as below.

Let's start
Step 1

The total number of trips = 1134 workers ÷ 36 workers per trip = 32 trips.

(Note: 31 trips with full 36 workers, and 1 trip with 18 workers. This may develop further interesting things such as rearrangements of numbers of workers between vehicles).

At this point, I may find real objects representing for 32 trips. For example, I would collect 32 wooden sticks, and put each stick representing one trip. 

Step 2

The maximum number of trips that a vehicle could transport within 90' = 90' ÷ 15' = 6 trips. 
I have set that one stick stands for one trip. So with six trips that a vehicle can operate/transport, it needs six sticks.
In other words, at this stage, I know that for each vehicle, I need six sticks standing for six trips. It means that 6 sticks are the maximum numbers which can be put in one group representing one vehicle.

Step 3

The minimum number of vehicles needed = (1) ÷  (2) =  32 trips ÷ 6 trips = 6 vehicles.

This result is found by putting 32 the wood sticks in groups of 6. 

A reminder here: each group of 6 sticks is to represent one vehicle with the maximum of 6 trips [each stick stands for one trip].

As a result, I need 6 vehicles. Now I can visually realize that the vehicles from #1 to #5 will operate/transport 6 trips, and the vehicle #6 will operate/transport 2 trips only. See the image below.

                                   

Because the last group #6 or the last vehicle #6 has only 2 sticks or 2 trips, therefore, from this point, I can play some games by moving the sticks around, to make new decisions. This allows and opens new options in scheduling to manage the vehicles and their trips. For example, if moving one stick from vehicle #1, one stick from vehicle #2 and put them to vehicle #6, then the numbers of trips operating by the vehicle #1 are now reduced to 5 trips; the numbers of trips operating by vehicle #2  are also reduced to 5 trips; but the numbers of trips operating by the vehicles #6   are now increased to 4 trips;

Further from this point, for example, if in the morning session, the vehicle #3 operated all 6 trips, then in the afternoon session, I would reduce the number of trips for this vehicle. This would create a better working environment in terms of reducing stress levels for both drivers and mine workers.

In conclusion, the minimum of six (6) vehicles would be required assuming the mine vehicles are the only option for workers to get to the worksite.

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My Notes
*These mine workers need time to get on and get off the vehicles. This factor, of loading and unloading workers, is ignored in this activity. In reality, time for loading and unloading needs to be considered.



*I've found that this question is very interesting since it develops more issues to think about, particularly, the management matter. 

B-A collection of peers' feedback

 

This task is also posted on 
*my google site Learning Teaching Adult Numeracy in VET at https://sites.google.com/site/lydiale2016eeb308csu/how-many-they-would-be-required;

and more detailed information can be viewed @
*my Learning and Teaching Blog at http://lydialeeleuts.blogspot.com.au/2016/08/using-sticks-in-solving-numeracy-problem.html