Smart Procurement
Rakesh Kumar Tiwari Archana Singh
Smart Procurement is of multi unit nature.This is designed for multi-item procurement auctions in capacity-constrained environments.In our implementation we assumed that supplier will supply with full capacity.This assumption is not to make problem simple.
-There is no limit on number of goods traded.
-Buyers(can be any industry for whom materials are required etc.) can give there requirements,whenever a particular supplier comes a list of Buyers displayed to him by the SmartMarket and she can choose any one or any number of Buyers from their whom she can supply.
-Capacity of supplier is known by SmartMarket and during allocation it considers capacity constraint.
-Our SmartMarket assumes whatever amount of product or item supplier want to supply is her maximum capacity.
SmartMarket allows each supplier to place her BID on her turn in each rounds t {1,2,......,N}.Bids will only be modified when there is no optimal solution of winner determination problem.
It is LP problem .Solution of this LP gives the optimal solution.
Suppose there are j items={1,2,..........,m};
i suppliers={1,2............,n};
a[i][j] is the quantity of item j that ith agent(supplier) want to supply,jand c[i] is the quantity of all items that agent(supplier) i can supply q[j] is the quantity of item j that is required by Buyers.
x[i][j] is the allocation of agent(supplier) i for item j.
b[i][j](t) is the BID of agent(supplier) i on item j in round t and x[i][j] is the corresponding allocation.
We have to minimize the value of the sum of b[i][j]*x[i][j] for all i and j.
subject to-
a[i][j]*x[i][j]<= c[i] sum over all j.
x[i][j]= q[j] sum over all i.
and x[i][j]>=0 for all i and j.
Suppliers will update the Bids only if b[i][j]+e>=v[j], where e a fixed amount,and v[i][j] is the inventory of agent(supplier) i for item j.
1.Bids are sealed.
2.It is multiround and each agent(supplier) is allowed only one in each round to place her bids on item j{1,2,.......,m}.
3.Non-reneging rule, b[i][j](t)<=b[i][j](t'),if t'<=t(to increase the efficiency of auction).
4.Common multiple rule, b[i][j] belongs to eN,for some e>0.
1.There is device Myopic best response calculation device to help bidders.
2.After each round allocation of each Bidder will be known only by him,after knowing her allocation she can take the help of this device.
Calculation method of Myopic best response calculation device-
This device first calculate Payoff function of each Bidder i- II[b(T)]=(b[i][j](T)-v[i][j])*x[i][j](T),sum over all j.Where T is the terminal bidding round such that b(T)=b(T-1).II[b(T)] is the utility function of the agent(supplier) i(it shows what is the profit of agent(supplier) i for final allocation,(b[i][j]-v[i][j]) is the suppliers unit margin for final allocation).If this is positive supplier will place the bid otherwise it wouldn't(because she will in loss).
- b*(t+1)= sup{arg maxII(w,b[-i](t))},where w is varying for 0 to b[i](t) and w belongs to (eN)^m,II() is payoff function,b[-i] are all
competitors of agent(supplier).
-This function is maximizing the bid of agent(supplier) i whose payoff function remains positive after decreasing her bid by a minimum constant amount. This maximization increases the probability of winning of agent(supplier) i.
1.Buyers know all about suppliers except v[i][j].
2.Suppliers doesn’t know anything about their other competitors.
3. Suppliers know only about Buyers and their requirements.
The SmartMarket will terminate the bidding only if -
1. Optimal allocation is reached ,or
2. b(T)=b(T-1).