Portfolio of Problems: GT4Downsizing ProblemPROBLEM DESCRIPTIONPROBLEM DATAAvalon Computer Depot Downsizing ProblemProduct CodeProduct TypeBrandCost to Liquidate (£ 1000s)Cost to...

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need help in designing a integer programming problem formulating various logical conditions through use of binary variables


Portfolio of Problems: GT4 Downsizing Problem PROBLEM DESCRIPTIONPROBLEM DATA Avalon Computer Depot Downsizing ProblemProduct CodeProduct TypeBrandCost to Liquidate (£ 1000s)Cost to Restock (£ 1000s)Space Required (m2) Avalon Computer Depot is currently in the process of downsizing. Among other things, it needs to change the current location of its storage to a new one, which does not have enough capacity to fit all the products currently in stock. The CEO of the company has entrusted you with the task to find the best plan to reduce the current stock. Essentially, you will need to determine which products should be eliminated and which products should be kept. The products to be eliminated will be sent to liquidation sale while the products to be kept will have to be restocked. You are given the estimates on both, liquidation cost and restocking cost, for each product currently carried by the company. These are given in the fourth and the fifth column in the Problem Data table. In the last column, you are also provided with the estimates on the required floor space for each product . This is important to know since the maximum capacity of the new storage location is only 150 square meters while the storage currently in use has a capacity of 400 square meters. The CEO wants you to find the solution that would minimise the loss incurred through liquidation while respecting all of the following limitations:203171TabletMicrosoft593.2 212811TabletHannspree4123.4 221352TabletSamsung4.583.4 223072TabletAsus1.5153.2 256917TabletDell5103.1 264960TabletFujitsu3153.6 273406TabletSamsung5.572.9 274498TabletAcer6.5123.5 281659TabletSony1.5143.1 282597TabletApple7.5132.9 289410TabletMicrosoft2.5113.3 296450TabletAsus6.5133.0 318044LaptopAsus6.5135.0 327894LaptopToshiba1.5115.7 351066LaptopLenovo4.586.1 356769LaptopAcer585.7 ¨At least 18 products will be eliminated.361711LaptopLenovo3.5105.0 375269LaptopHP8105.3 396633LaptopAsus585.3 ¨No more than £180,000 can be spent to restock all the products kept.413122DesktopHP6.5921.6 424242DesktopGigabyte2.5917.1 427777DesktopYoyotech5.51518.7 ¨The products kept should use no more than 150 square meters of space in total.440294DesktopAcer51221.9 450085DesktopZoostorm21419.2 451548DesktopApple7.51520.6 ¨If any Acer or any Asus computer is to be kept, then Lexmark printers will also be kept. ozren despic: Computer is a programmable electronic device designed to accept data, perform prescribed mathematical and logical operations at high speed, and display the results of these operations. Mainframes, desktop and laptop computers, tablets and smartphones are some of the different types of computers.469347DesktopViglen7920.9 492082DesktopIntel6.5916.5 507203MonitorAOC3.5810.4 ¨If one product of a certain brand is eliminated than all the products of that brand should be eliminated.557148MonitorBenq41311.8 559720MonitorLG4.5912.2 578406MonitorIiyama61310.1 ¨At least six different tablet models need to be kept.579193MonitorTyco2128.8 579333MonitorViewsonic5.51014.4 597995MonitorPhilips61414.5 ¨At least three different laptop models need to be kept.608733PrinterBrother2814.9 611489PrinterOKI4.5913.0 651631PrinterRicoh7812.3 ¨If any desktops are to be kept, then at least two different monitor models will also be kept.679473PrinterCannon6.51212.5 680966PrinterLexmark5.51013.5 698203PrinterEpson61312.7 &"+,Regular"Group Portfolio - Problem No. 3&"+,Regular"BN2290 ORT
downsizingproblem-gynoptge.xlsx
Answered Same DayMar 02, 2023

Answer To: Portfolio of Problems: GT4Downsizing ProblemPROBLEM DESCRIPTIONPROBLEM DATAAvalon...

Banasree answered on Mar 02 2023
45 Votes
At least 18 products will be eliminated.
Ans.
To formulate an integer programming problem that will eliminate at least 18 products, use binary variables to represent whether each product will be eliminated or not.
Let x_i be a binary variable that equals 1 if product i is eliminated, and 0 otherwise. Then use the following constraints to ensure that at least 18 products are eliminated:
1. Sum of all x_i is at least 18:
Σ x_i ≥ 18
2. If a tablet is eliminated, all other tablets from the same brand must also be eliminated:
x_i ≥ x_j for all i, j where Product Type = "Tablet" and Brand_i = Brand_j
3. If a laptop is eliminated, all other laptops from the same brand must also be eliminated:
    x_i ≥ x_j for all i, j where Product Type = "Laptop" and Brand_i = Brand_j
4. If a desktop is eliminated, all other desktops from the same brand must also be eliminated:
x_i ≥ x_j for all i, j where Product Type = "Desktop" and Brand_i = Brand_j
5. If a monitor is eliminated, all other monitors from the same brand must also be eliminated:
x_i ≥ x_j for all i, j where Product Type = "Monitor" and Brand_i = Brand_j
6. If a printer is eliminated, all other printers from the same brand must also be eliminated:
x_i ≥ x_j for all i, j where Product Type = "Printer" and Brand_i = Brand_j
7. On given data cannot eliminate more than 50% of the products from any type:
Σ x_i ≤ 0.5 * Σ (Product Type = type_i) for all types
8. Given data cannot eliminate products that are cheaper to liquidate than to restock:
x_i = 0 for all i where Cost to Liquidate_i < Cost to Restock_i
9. Given data cannot eliminate products that require more space than the available storage:
x_i = 0 for all i where Space Required_i > 40
The objective function can be to minimize the total cost of restocking the remaining products:
minimize Σ (1-x_i) * Cost to Restock_i
The storage capacity constraint (constraint 9) assumes that the available storage is 40 m2. This can be adjusted to the actual available storage capacity.
No more than £180,000 can be spent to restock all the products kept.
Ans.
$\sum_{i} cost_restock_i \leq 180,000$
where $cost_restock_i$ represents the cost to restock product $i$. This ensures that the total cost to restock all the products kept does not exceed £180,000.
The products kept should use no more than 150 square meters of space in total.
Ans.
To formulate this constraint, need to multiply the space required by each product by the corresponding decision variable (i.e., whether the product is kept or not), and then sum up these values for all products. Then set an upper bound of 150 on this sum.
Let x_i be a binary...
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