Prelim BidWiser

8/11/2019 Prelim BidWiser

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BIDWISER Prelims

The SettingIts the Age of the Old Kingdoms, a long time back when food and survival used to be moreimportant than choosing between a Nexus 5 and a Samsung Galaxy S5 (or even S4 for that matter).It is no surprise then that the King had to make many an important strategic decision with the helpof his ministers. One such decision used to be regarding optimizing the food production system ofthe Kingdom amidst the race between different civilizations for the scarce resources.

You are the Chief Advisor the minister in charge ofone such well-developed Food ProductionSystem of your kingdom, and your team is your council. One fine day, worried about the decreasingtrade surplus due to the rising inefficiency in the procurement of inputs and production& export of

the food output, the King summons you to express his concerns. You realize the gravity of thesituation and decide to analyze the mechanisms in detail in order to come up with a moresystematic way of approaching the input procurement and food production planning.

Here is a stylized version of the problem in front of the Chief Advisor.

ProblemThe major inputs required for food production are land, labor and transportation.

Your aim is to maximize your Kingdoms profits from the export of the food produce. Since theresources are scarce, you are required to compete with the other Kingdoms and obtain themandatory inputs through a bidding system. The mandatory inputs are Land and Labour.

A few non-mandatory inputs are also available at fixed prices: Manure andLabor-training Sessions.These can be bought with the remaining capital in order to reduce the production cost. Also, theKingdom can also buy any number of carriages to transport their food produce to the market.Revenue is realized only if the produceis transported to the market. In case the Kingdom exhaustsits capital on mandatory and non-mandatory inputs, it can take debt from one of its allies at a fixedinterest rate of 20% per annum .

Event GuidelinesA final demand function will be given based on which the Price at which you can sell your exportswill be calculated. The judging criterion is the profit generated at the end of 1 st year.

Your task is divided into two stages as described from Page 3 onwards. A pictorial representation ofthe same is shown below.


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L1 L2 L3 L4

LB1 LB2 LB3 LB4

To the market

MANDATORYINPUTS

BID FORMANDATORY

INPUTS

ALLOTEDINPUTS

Manure+

Labour Training

Output(Farm Produce)

STAGE

1

STAGE

2


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Stage : Procurement of Mandatory Inputs: Land and Labour

An initial capital of 80,000,000 is provided to all teams. The council needs to bid for the mandatory factors of production Land and Labor. There are four types of land (L1, L2, L3 and L4) and four types of labor (LB1, LB2, LB3, LB4)

out of which every team participating will get one type of Land and one type of Labor. This would be a closed bidding process.Teams will be mentioning the bid amount of each

type of land and each type of labor and their preference order, for the land and the labor.The top 25% bidders for each land type and each labor type will get that land and labor at aprice of the lowest winning bid in that 25% bracket.

For Example :If 100 teams are participating, the top 25 bidders for a particular land type, say L1, will be allottedL1 at a price = minimum bid amount in this bracket of 25 teams. A similar procedure will befollowed for allocating labor type also.

Note: In the above example, if more than 1 person occupies the 25 th position, the ranking would begiven based on the time of bid placed, i.e. The teams that bid earlier would be given preference incase of equal value of bids.

Land is valued by its soil fertilityand Labor by its efficiency. Better land/labor is expected toreduce the average cost of production. Refer to the matrix in the data sheet for thenumbers which capture this information.

The results of the above closed bid process will be put up on the website and e-mails will besent to the teams by 22.08.2014

Note that your bids in Stage 1 are likely to be influenced by your strategic choices in Stage 2.

Base price for mandatory itemsL1 10,000,000L2 8,000,000L3 6,500,000L4 5,000,000

LB1 8,000,000

LB2 6,000,000LB3 4,000,000LB4 4,500,000


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Stage 2: Production Planning

The teams can now buy non-mandatory inputs such as carriages, manure upgrade, andlabor training sessions, to reduce their cost of production. The total maximum output ofyourLand per day, however, is constant.

With the remaining capital, the teams can produce an output of anywhere between 0 unitsand the Maximum Capacity of the Land.

Example: If a team gets L1, you can produce output q


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Case 2:If I produce 15,000 kg/day and have 3carriages, and I decide to send 1carriage on the first day and2carriage on the second day then,

Day 1:

Production = 15,000 kgTransported = 10,000 kgRemaining = 5,000 kgInventory holding cost = 5,000/-

Day 2:Production = 15,000 kgTransported = 20,000 kgRemaining = 0 kgInventory holding cost = 0/-

Hence for every 2 day cycle, 30,000 kgs will be transported and inventory holding cost of 5,000 ischarged. This is repeated for the entire year (182 cycles).

DATA SHEETBase price for mandatory itemsL1 10,000,000L2 8,000,000L3 6,500,000L4 5,000,000

LB1 8,000,000LB2 6,000,000LB3 4,000,000LB4 4,500,000

Maximum output of labor with no upgrades (in kgs per day)LB1 20,000LB2 18,000LB3 15,000LB4 12,000

*Note that theQuantity is stepped up only in multiples of 250

Fixed Costs of upgrades:Manure (U1) 1,500,000Labor Training (U2) 400,000Carriage (C) 1,000,000

*U1 is capped at 10 units, U2 at 8 units

Carriage carrying capacity : 10,000 kg Inventory holding cost : 1/- per kg/day Demand Function :Q(in thousands) = 24-P


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Average Operational Cost:

For different combinations of A and B, Land and Labour are given as follows:

L1 L2 L3 L4

LB1A 12 14 13 15

B 16 15 60 60

LB2A 14 16 14 12

B 15 60 2 15

LB3A 13 11 15 14

B 60 5 8 20

LB4A 12 15 16 13

B 25 30 30 30

Net profit can be calculated as follows:Net Profit = Total revenue (p*q) - Cost of mandatory inputs (Land + Labour) - cost of add-ons ifpurchased - cost of debt if taken inventory holding cost - operational cost

Please refer to a detailed example of the entire process given in the next page.


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Detailed Example:

Lets sayteam 1 bid for Land and Labour in the following preference order:

Land Type Preference Order Bid Amount

L3 3 21,000,000L1 1 25,000,000L2 2 17,000,000L4 4 8,000,000

Labour Type Preference Order Bid AmountLB1 1 12,500,000LB2 2 11,000,000LB3 3 9,000,000LB4 4 3,000,000

After biding, say Team 1 lies in top 25% bidders for Land L3, so they will be allotted L3. If theminimum bidding price for L3 in this bracket is 19,000,000, team 1 will get L3 for 19 million.However, team 1 did not lie in top 25% bracket of LB1 or LB2, its first two preferences, but lies intop 25% bracket for LB3, with minimum bid in that bracket as 9,000,000, so it will be allotted LB3for 9 million.

So after bidding, Team 1 is left with L3 and LB3 and cash of 52,000,000 (= 80 19 9). LB3 canproduce maximum 15,000 units per day.

Now Team1 has to decide what amount of U1 and U2 to buy, how many carriages to buy and thequantity of output to be produced.

Team 1 decides to buy 4 units of U1 and 4 units of U2 and 3carriages to transport its products tomarket. So basically team 1 is spending 10,600,000 more on these inputs and is finally left with41,400,000 (= 52 10.6).

The maximum possible production is 1500 0 units per day. Lets say Team 1 decides to produce12000 units per day. Then, operating cost of Team 1 as per the cost function above is 12. Also, usingthe inverse demand function we can see that the price of its product will be P = 24-12 = 12 per unit.

Therefore the daily cost of producing 12000 units is = 12000*12=144,000

On day 1, 12,000 units are produced, and 10,000 are transported out using one carriage. Theremaining 2,000 incur an inventory cost of 2000.One day 2, another 12,000 units are produced, and the total manufacture (=12,000 + 2,000) istransported out using two carriages, and no inventory cost is incurred.Therefore, the annual cost of production is the inventory cost for half the number of days in theyear + cost of manufacture = 2000*182 + (144,000)*365 = 364000 +52,560,000= 52,924,000

Since the amount left with Team 1 was41.4 million, it will have to take a debt of 11,524,000in orderto operate at this capacity.


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Hence the net profit for firm can be calculated as= Total Revenue - Operational cost - Cost of Upgrades - Cost of bid inputs - Interest on Debt= 12*12000*365 - 52,924,000- 10,600,000 - 28,000,000 - 0.2*(11,524,000)= -10,964,000 - 28,000,000 - 0.2*(11,524,000)= -41,268,800

So, with this production planning, Team 1 would end up with a loss of about 41.27 million after thefirst year.

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