OPS928 Logistics Systems Assignment Sample

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OPS928 Logistics Systems Assignment Sample

Exercise 1

Transporting Fruits at Future Logistics

Future Logistics (FL) ships avocados and mangos once a week from Queensland to Sydney. This morning they have 39 tons of avocados and 36 tons of mangos on hand. The fruits all go to the Fruit Market in Sydney and therefore can be mixed on the company’s three trucks. The capacities of the three trucks are 27, 31, and 28 tons, respectively.

To make it easy for transportation, fruits are packed in 20 pound cartons. Assume that there are 2000 pounds in a ton, so that 39 tons of avocado are packed into 3900 cartons, and 36 tons of mangos are packed into 3600 cartons.

The travelling costs of the trucks are negligible and independent of what fruits they ship; all three trucks will be used in this shipment.

Spoilage occurs during the transportation of fruit from Queensland to Sydney. Because of differences in their refrigeration systems, the fruit losses differ by truck as follows:

 

Table 1. Percentage Losses in Transit

For example, 5% of avocados in each carton placed in truck 1 and 11% of the mangoes placed in truck 3 will be spoiled upon arrival in Sydney.

FL sells the unspoiled avocadoes for $20 per carton and unspoiled mangoes for $32 per carton. Because of spoilage during transport to Sydney, however, FL must discount the amounts for which it sells cartons of fruit. For example, because 5% of the avocados shipped in truck 1 will be spoiled by the time they reach Sydney, FL will be able to sell cartons shipped on truck 1 for only $20*(1-0.05) = $19. Similarly, because 11% of the mangoes shipped on truck 3 will have spoiled, FL can sell cartons of mangoes shipped on truck 3 for only $32*(1-0.11) = $28.48. As such, the number of cartons of each fruit loaded on each truck will impact its revenue from selling fruits in Sydney.

Let A1, A2, and A3 be the number of cartons of avocado loaded on trucks 1, 2, and 3, respectively, and let M1, M2, and M3 be the numbers of cartons of mango loaded on trucks 1, 2, and 3, respectively.

Questions:

(a) Suppose that FL plans to put the same number of cartons for each fruit on each truck, in other words, suppose that FL sets A1 = A2 = A3 = 1300 and M1 = M2 = M3 = 1200. Is this a feasible plan?

(b) Irrespective of whether or not the plan in part (a) is feasible, what is the total revenue that FL would earn under this plan?

(c) Intuitively, do you think the plan in part (a) is a good plan? Why or why not?

(d) Suppose FL plans to fill up truck 1 with mangos because truck 1 has the lowest spoilage rate for mango, fill up truck 3 with avocados because truck 3 has the lowest spoilage rate for avocados, and then put all the remaining fruit to truck 2. What is the resulted plan? Is this plan feasible? What is the total revenue?

(e) How should FL load the avocado and mango to the three trucks, in order to maximize its total revenue? What is the maximized total revenue?

Use the Excel file “Exercise1_StartFile.xlsx” as a template to set up a spreadsheet containing FL’s data, and solve the above questions.

For questions (d) and (e), please include a screenshot of your Excel spreadsheet showing the results.

Solution

a)

Suppose that FL plans to put the same number of cartons for each fruit on each truck, in other words, suppose that FL sets A1 = A2 = A3 = 1300 and M1 = M2 = M3 = 1200.
The total weight of avocados and mangos loaded on each truck does not exceed the truck's capacity. Let's calculate the total weight of avocados and mangos for each truck.

For Avocados:

Total weight of avocados = (A1 + A2 + A3) * 20 pounds

Total weight of avocados = (1300 + 1300 + 1300) * 20 pounds

Total weight of avocados = 39,000 pounds

For Mangos:

Total weight of mangos = (M1 + M2 + M3) * 20 pounds

Total weight of mangos = (1200 + 1200 + 1200) * 20 pounds

Total weight of mangos = 36,000 pounds

Now, let's check if the total weight of avocados and mangos for each truck exceeds its capacity:

Truck 1 Capacity: 27 tons * 2000 pounds/ton = 54,000 pounds

Truck 2 Capacity: 31 tons * 2000 pounds/ton = 62,000 pounds

Truck 3 Capacity: 28 tons * 2000 pounds/ton = 56,000 pounds

For avocados:

Truck 1: 39,000 pounds (OK)

Truck 2: 39,000 pounds (OK)

Truck 3: 39,000 pounds (OK)

For mangos:

Truck 1: 36,000 pounds (OK)

Truck 2: 36,000 pounds (OK)

Truck 3: 36,000 pounds (OK)

It is clear that the total weight of the fruits loaded into each truck is less than the allotted weight for each vehicle, hence it is possible to load each truck with an equal number of avocados and mangoes for university assignment help.

b)

Under the plan where FL puts the same number of cartons for each fruit on each truck (as in part a), the number of cartons for each fruit on each truck is A1 = A2 = A3 = 1300 and M1 = M2 = M3 = 1200.

Revenue from avocados on each truck:

Truck 1: 1300 cartons * $20 * (1 - 0.05) = $25,350

Truck 2: 1300 cartons * $20 * (1 - 0.04) = $24,960

Truck 3: 1300 cartons * $20 * (1 - 0.03) = $24,740

Revenue from mangos on each truck:

Truck 1: 1200 cartons * $32 * (1 - 0.10) = $34,560

Truck 2: 1200 cartons * $32 * (1 - 0.12) = $33,792

Truck 3: 1200 cartons * $32 * (1 - 0.11) = $34,048

Total revenue under this plan:

Total revenue = (Revenue from avocados on Truck 1 + Revenue from mangos on Truck 1) + (Revenue from avocados on Truck 2 + Revenue from mangos on Truck 2) + (Revenue from avocados on Truck 3 + Revenue from mangos on Truck 3)

Total revenue = ($25,350 + $34,560) + ($24,960 + $33,792) + ($24,740 + $34,048) = $213,450
Hence, Total revenue that FL would earn under this plan = $213,450

c)

In light of the rate of transit losses, the plan is poor. Equal amounts of fruits per truck might not be a good idea because the percentages vary per vehicle. Because it presupposes an equal distribution of avocados and mangoes on each truck, regardless of their rates of deterioration, the proposal in part (a) does not seem to be a good one. The differing avocado and mango rotting rates in various vehicles are not taken into account in this design. Compared to a more optimised design that takes spoilage rates into account, it could lead to increased spoilage and lower income.

Taking advantage of the scenario with the lowest probability of loss might be a better strategy. For instance, it is preferable to convey greater quantities of the avocado by Truck 3. It has the lowest loss percentage, so there is less of a discount, which results in higher revenue. The same is true for the mangoes; it is preferable to have them delivered via Truck 1 with only a 10% loss.

d)

Under this plan:

Truck 1 is filled with mangos: M1 = 3600 cartons
Truck 3 is filled with avocados: A3 = 3900 cartons
Truck 2 is filled with the remaining fruit: A2 = 1300 cartons, M2 = 1200 cartons
Now, let's check if this plan is feasible:

For avocados:

Truck 1: 0 cartons (OK)
Truck 2: 1300 cartons (OK)
Truck 3: 3900 cartons (OK)

For mangos:

Truck 1: 3600 cartons (OK)
Truck 2: 1200 cartons (OK)
Truck 3: 0 cartons (OK)

Plan:

Put Truck 1 with 2 700 containers of mangoes.

Then load Truck 2 with the remaining 900 boxes of mangoes.

Truck 3 should include 2800 cartons of avocados.

Truck 2 should contain the remaining 1100 boxes of avocados.

Yes, this plan is feasible because the total weight of avocados and mangos loaded on each truck does not exceed its capacity.
Now, let's calculate the total revenue under this plan:

Revenue from avocados on each truck:

Truck 1: 0 cartons * $20 = $0

Truck 2: 1300 cartons * $20 * (1 - 0.04) = $24,960

Truck 3: 3900 cartons * $20 * (1 - 0.03) = $75,060

Revenue from mangos on each truck:

Truck 1: 3600 cartons * $32 * (1 - 0.10) = $103,680

Truck 2: 1200 cartons * $32 * (1 - 0.12) = $33,792

Truck 3: 0 cartons * $32 = $0

Total revenue under this plan:

Total revenue = ($0 + $103,680) + ($24,960 + $33,792) + ($75,060 + $0) = $237,492
Given that truck capacity was not exceeded, the approach is workable.
$237,492 is the total revenue for this plan.

e)

The steps of the solver are given as:

Step 1:



Step 2

 

Step 3

The best strategy is to:

Pack Truck 1 with 2700 boxes of mangos.

Put 3,100 avocado boxes in Truck 2.

Pack Truck 3 with 800 cartons of mangoes and 2000 cartons of avocados.

The entire revenue at its maximum will be $209,760

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