Sunocoil is a company that commercializes five different types of petroleum prod
ID: 366666 • Letter: S
Question
Sunocoil is a company that commercializes five different types of petroleum products: gasoline of grades 80, 90, and 93, diesel, and engine oil. The company receives the products from its suppliers and stores them in 9 tanks of different sizes. Sunocoil is expecting several orders from the suppliers to satisfy the demands of the following month and requires to identify the best possible way of storing the products into its tanks. Clearly, the products must be stored in the tanks without mixing them. In other words, only one type of product can be stored in each tank, but several tanks may contain the same product. Suppose that Suncoil is expecting 1,200 gallons, 700 gallons, and 1,000 gallons of gasoline of grades 80, 90, and 93, respectively; 450 gallons diesel; and 1,200 gallons engine lubricant. The sizes of the tanks are given in the following table. Some of the tanks are already partially filled with a product.
Tank
You must identify which is the best possible way of filling the tanks in such a way that the number of tanks used is minimized.
Propose a formulation for the above problems that includes decision variables, parameters, constraints, objective function.
Tank
1 2 3 4 5 6 7 8 9 Capacity 500 400 400 600 600 900 800 800 800 Current Product - 80-grade gasoline - - - - lubricant - - Quantity 0 100 0 0 0 0 300 0 0Explanation / Answer
Decision Variables are binary represented as Xij taking the value 1 if ith tank is selected to store jth product, otherwise it takes the value zero.
Therefore, Objective to use minimum number of tanks is to Minimize Sigma(i,j) Xij.
Problem is similiar to assignment problem subject to constraints of capacities of tanks matching with the quantities of the products to be stored. Parameters are capacities of tanks and quantities of products for storage as well as quantities already stored.
Given data is represented as follows:
Looking at the quantities to be stored and the capacity of the tanks, it is obvious that for diesel and GG90 minimum number of tanks is one whereas for other products minimum two tanks are required. In all minimum eight.
Tank2 is already having GG80, therefore it can be fully filled upto its capacity of 400 leaving 900 (1200-300) that may be stored in Tank6
Tank7 is already having 300 units of Engine luricant, therefore needs to be filled to its capacity of 800 leaving 700 (1200-500) that may be stored in either tank8 or tank9. Let us allocate Tank8 to store 700 units of lubricant.
Similarly allocations are made for other products keeping the number of tanks minimum as follows:
Tank5 remains empty.
Tanks Product 1 2 3 4 5 6 7 8 9 Required GG80 100 1200 GG90 700 GG93 1000 Diesel 450 Engine oil 300 1200 Total 4550 Capacity 500 400 400 600 600 900 800 800 800 5800Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.