2.1. Cost Calculation for 5 Scrapers

Now let us consider the economics of going for 5 scrapers. So, 5 in the sense you are going to use lesser than what is needed, you are assuming 5 that means you are going to use the number of scrapers lesser than what is needed. So, when the number of scrapers are lesser than the balanced number so obviously scrapers are more critical, but a pusher will have the ideal time. Your pusher will wait for the scraper.

This chunk introduces the scenario of using 5 scrapers for a project. It highlights that using fewer scrapers than necessary creates a condition where scrapers become critical to the workflow. If there are not enough scrapers, the pusher (a machine that pushes the scrapers) will often be idle, waiting for the scrapers to finish their tasks. This imbalance can lead to inefficiencies in production, as the pusher cannot perform its role without the scrapers.

Imagine a restaurant where you have only two chefs (scrapers) but many tables to serve (pushers). If the chefs can only prepare two dishes at a time, many diners will be waiting for their meals while the chefs work slowly. Meanwhile, a waiter (the pusher) is standing idle, unable to serve more diners without the chefs completing their dishes. This situation reflects the inefficiency created by having too few scrapers.

So, now, let us see the productivity in this case of n equal to 5 scrapers...𝑃𝑟𝑜𝑑𝑢𝑐𝑡𝑖𝑜𝑛 (𝑆𝑐𝑟𝑎𝑝𝑒𝑟 𝑐𝑜𝑛𝑡𝑟𝑜𝑙𝑙𝑖𝑛𝑔)

× 𝑛𝑜. 𝑜𝑓 𝑠𝑐𝑟𝑎𝑝𝑒𝑟𝑠 ×𝑣𝑜𝑙. 𝑝𝑒𝑟 𝑙𝑜𝑎𝑑 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑠𝑐𝑟𝑎𝑝𝑒𝑟, 𝑚𝑖𝑛 50 𝑚𝑖𝑛/ℎ𝑟

×5 ×19.82 𝑏𝑐𝑚 = 636.89 𝑏𝑐𝑚/ℎ𝑟

In this portion, the calculation of production efficiency is shown. Given that there are 5 scrapers, the formula used estimates the hourly production capacity in bank cubic meters (bcm). The formula considers the number of scrapers, the volume per load of each scraper (19.82 bcm), and the cycle time of the scrapers. The cycle time is given as 7.78 minutes, and the operational efficiency allows for 50 minutes of work in an hour. The calculations lead to a production output of approximately 636.89 bcm/hour.

Think of a factory assembly line where each worker (scraper) can assemble 10 toys (bcm) in a 20-minute time frame. If only 5 workers are available, you calculate how many toys can be produced in an hour. Similar to the scrapers, the total productivity depends on how efficient each worker is, how many workers are present, and how long each can work before needing a break.

Now let us compare unit production costs associated with both cases and then let us make the decision...Let us estimate the unit production cost...Cost per bank meter cube...

This section discusses estimating the unit production costs for both 5 and 6 scrapers. The formula shown accounts for the total costs of the pusher and scrapers, divided by the productivity rates obtained earlier. For 5 scrapers with a total hourly cost of rupees 16,300 and a productivity of 636.89 bcm/hour, the cost per bcm is calculated to be ₹44.12. Comparatively, if 6 scrapers are used, the cost per bcm is slightly higher at ₹45.07, emphasizing the importance of operational efficiency and cost management when determining the optimal number of scrapers.

Imagine you run a small bakery. If you have a small oven that bakes 20 loaves of bread per hour, and it costs you $40 per hour to operate it, then each loaf costs you about$2. Now, if you buy a bigger oven that can bake 50 loaves per hour but costs $70 per hour to run, the individual loaf cost decreases with higher output as long as you sell enough bread to cover the increased cost. Thus, you must analyze productive output against operational costs, just like with scrapers.

So, if you are more concerned about the productivity, if you have a very tight deadline...the combination of 5 scrapers and 1 pusher gives you the minimum unit production costs.

The discussion wraps up by emphasizing that when deciding between task urgency and cost, using 5 scrapers leads to minimal costs compared to using 6 scrapers, despite the latter providing greater productivity. It suggests that while productivity is crucial, minimizing production costs is often a priority for projects with tight budgets.

Consider a road construction project where you can either hire more workers for increased speed (higher productivity) but at a higher cost, or opt for fewer workers who can only finish the job more slowly, saving money. The decision depends on whether the immediate completion time outweighs the extra expenses, much like choosing between different numbers of scrapers.

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