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Portfolio of Problems: GT4 Downsizing Problem PROBLEM DESCRIPTION PROBLEM DATA Avalon Computer Depot Downsizing Problem Product Code Product Type Brand Cost to Liquidate (£ 1000s) Cost to...

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Portfolio of Problems: GT4
Downsizing Problem
    PROBLEM DESCRIPTION            PROBLEM DATA
    Avalon Computer Depot Downsizing Problem            Product Code    Product Type    Brand    Cost to Liquidate (£ 1000s)    Cost to Restock (£ 1000s)    Space Required (m2)
    Avalon Computer Depot is cu
ently in the process of downsizing. Among other things, it needs to change the cu
ent location of its storage to a new one, which does not have enough capacity to fit all the products cu
ently in stock. The CEO of the company has entrusted you with the task to find the best plan to reduce the cu
ent 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 cu
ently ca
ied 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 cu
ently in use has a capacity of 400 square meters. The CEO wants you to find the solution that would minimise the loss incu
ed through liquidation while respecting all of the following limitations:            203171    Tablet    Microsoft    5    9    3.2
                212811    Tablet    Hannspree    4    12    3.4
                221352    Tablet    Samsung    4.5    8    3.4
                223072    Tablet    Asus    1.5    15    3.2
                256917    Tablet    Dell    5    10    3.1
                264960    Tablet    Fujitsu    3    15    3.6
                273406    Tablet    Samsung    5.5    7    2.9
                274498    Tablet    Acer    6.5    12    3.5
                281659    Tablet    Sony    1.5    14    3.1
                282597    Tablet    Apple    7.5    13    2.9
                289410    Tablet    Microsoft    2.5    11    3.3
                296450    Tablet    Asus    6.5    13    3.0
                318044    Laptop    Asus    6.5    13    5.0
                327894    Laptop    Toshiba    1.5    11    5.7
                351066    Laptop    Lenovo    4.5    8    6.1
                356769    Laptop    Acer    5    8    5.7
    ¨    At least 18 products will be eliminated.        361711    Laptop    Lenovo    3.5    10    5.0
                375269    Laptop    HP    8    10    5.3
                396633    Laptop    Asus    5    8    5.3
    ¨    No more than £180,000 can be spent to restock all the products kept.        413122    Desktop    HP    6.5    9    21.6
                424242    Desktop    Gigabyte    2.5    9    17.1
                427777    Desktop    Yoyotech    5.5    15    18.7
    ¨    The products kept should use no more than 150 square meters of space in total.        440294    Desktop    Acer    5    12    21.9
                450085    Desktop    Zoostorm    2    14    19.2
                451548    Desktop    Apple    7.5    15    20.6
    ¨    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.        469347    Desktop    Viglen    7    9    20.9
                492082    Desktop    Intel    6.5    9    16.5
                507203    Monitor    AOC    3.5    8    10.4
    ¨    If one product of a certain
and is eliminated than all the products of that
and should be eliminated.        557148    Monitor    Benq    4    13    11.8
                559720    Monitor    LG    4.5    9    12.2
                578406    Monitor    Iiyama    6    13    10.1
    ¨    At least six different tablet models need to be kept.        579193    Monitor    Tyco    2    12    8.8
                579333    Monitor    Viewsonic    5.5    10    14.4
                597995    Monitor    Philips    6    14    14.5
    ¨    At least three different laptop models need to be kept.        608733    Printer    Brother    2    8    14.9
                611489    Printer    OKI    4.5    9    13.0
                651631    Printer    Ricoh    7    8    12.3
    ¨    If any desktops are to be kept, then at least two different monitor models will also be kept.        679473    Printer    Cannon    6.5    12    12.5
                680966    Printer    Lexmark    5.5    10    13.5
                698203    Printer    Epson    6    13    12.7
&"+,Regular"Group Portfolio - Problem No. 3        &"+,Regular"BN2290 ORT
downsizingproblem-gynoptge.xlsx
Answered Same Day Mar 02, 2023

Solution

Banasree answered on Mar 02 2023
46 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
and 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
and 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
and 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
and 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
and 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 co
esponding 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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