Safe Haskell	None
Language	Haskell2010

ProductMixAuction.LP.Core

Contents

Core auction representation
Results
Solving a single auction LP
Utilities
Lenses

Description

Describes the basic structure of auctions and implements the translation into a linear programme. This does not include features that require multiple LP runs, such as the TQSS.

Synopsis

Core auction representation

data Auction bid Source #

Represents an auction that can be translated directly into a single run of a linear program.

Constructors

Auction

Fields

_auction_supply :: Supply Units
Seller's supply curves for the goods available in the auction.
_auction_bids :: [Bid bid]
Bids from the bidders seeking goods from the auction.
_auction_scale :: ScaleFactor
Scale factor to control precision with which allocations are calculated.
_auction_preferences :: [Good]
Goods listed in decreasing order of preference for selling them (i.e. the first list item is the most preferred), used to resolve ambiguity in quantities by tweaking the prices appearing in the objective function. If a good is missing from the list, do not tweak its price at all.
_auction_constraints :: [AdditionalConstraint bid]
Additional linear constraints to impose on quantities allocated to bidders.
_auction_size_limit :: Maybe TotalSizeLimit
If specified, a limit on the total allocation to steps on base goods.
_auction_tweak_supply :: Bool
Whether the quantities in the supply curves should be tweaked to ensure unique prices.
_auction_verbosity :: Verbosity
Controls how much debug output is generated when solving the auction.

data TotalSizeLimit Source #

Limit on the total quantity allocated by an auction, for use implementing a TQSS.

Constructors

FixedLimit Units	Limit the total quantity allocated to a constant.
TQSSLimit [Step Units]	Limit the total quantity allocated by the given TQSS steps.

mkAuction :: Supply Units -> [Bid bid] -> Auction bid Source #

Smart constructor for auctions, given a description of the supply curves and a list of bids, using sensible defaults for the other fields.

defaultPreferences :: Supply Units -> [Good] Source #

By default, the preference permutation for the supply lists the goods in reverse order, so that the highest good is most preferred.

auctionBidLabels :: Auction bid -> [bid] Source #

List labels of bids in the auction.

auctionGoodLabels :: Auction bid -> [Good] Source #

List labels of goods in the auction, in no particular order.

lookupBid :: Eq bid => bid -> Auction bid -> Maybe (Bid bid) Source #

Look up a bid in the auction by its label.

showAuction :: Show bid => Auction bid -> String Source #

Render an auction in a vaugely human-readable format.

mapAuction :: Ord bid' => (bid -> bid') -> Auction bid -> Auction bid' Source #

Change the representation of bid labels in an auction. Requires the codomain to have an Ord instance, hence not a Functor.

Results

data AuctionResult bid Source #

Results from a single run of the LP, including a price for each good and a quantity value for each primal variable.

Constructors

AuctionResult
Fields _ar_prices :: Map Good Price Prices for the goods (values of the dual variables `z_j`) _ar_quantities :: Map (AVar bid) Units Quantities assigned to the primal variables (`x^i_j` and `y^q_j`) _ar_normalised_price :: Maybe Price Normalised price, if a normalised TQSS is in use

Instances

Show bid => Show (AuctionResult bid) Source #
Methods showsPrec :: Int -> AuctionResult bid -> ShowS # show :: AuctionResult bid -> String # showList :: [AuctionResult bid] -> ShowS #

data AVar bid Source #

Variables used in the linear program corresponding to an auction.

Constructors

AllocVar bid Good	`x^i_j`, the amount of good `j` allocated to bid `i`
ExtraAllocVar Good	`x^0_j`, the amount of good `j` allocated to the "extra" bid
StepVar Good Int	`y^q_j`, the amount of good `j` allocated using step `q` of the supply curve
TQSSStepVar Int	`t_l`, the total amount allocated using step `l` of the TQSS

Instances

Eq bid => Eq (AVar bid) Source #
Methods (==) :: AVar bid -> AVar bid -> Bool # (/=) :: AVar bid -> AVar bid -> Bool #
Ord bid => Ord (AVar bid) Source #
Methods compare :: AVar bid -> AVar bid -> Ordering # (<) :: AVar bid -> AVar bid -> Bool # (<=) :: AVar bid -> AVar bid -> Bool # (>) :: AVar bid -> AVar bid -> Bool # (>=) :: AVar bid -> AVar bid -> Bool # max :: AVar bid -> AVar bid -> AVar bid # min :: AVar bid -> AVar bid -> AVar bid #
Show bid => Show (AVar bid) Source #
Methods showsPrec :: Int -> AVar bid -> ShowS # show :: AVar bid -> String # showList :: [AVar bid] -> ShowS #

Solving a single auction LP

runAuctionCore :: Goodly bid => String -> Auction bid -> IO (AuctionResult bid) Source #

Convert the auction description to a linear program, solve it using GLPK and return the results.

Utilities

type Goodly x = (Ord x, Show x, Read x) Source #

Constraints that must be satisfied by the bid label types.

data AuctionException Source #

Errors that can be thrown when solving an auction

Constructors

GLPKFailed ReturnCode	LP solver failed to produce a result, with the given return code
SupplyCurveDecreasing Good	Good with the given label has a decreasing supply curve
TQSSDecreasing	TQSS step function is decreasing
TQSSEmpty	TQSS has no steps
TQSSMinAboveMax Units Units	Lower bound of TQSS search exceeds upper bound
TQSSGoodMissing Good	Single-good TQSS refers to a good not in the auction
TQSSBadLambda	Non-vertical auction with a non-zero supply scale lambda
TQSSFirstStepNonZero	First TQSS step has a non-zero price
TQSSFirstStepTooSmall Units Units	First TQSS step smaller than initial auction size
TQSSNormalisedNotHorizontal	Normalised prices used with a non-horizontal TQSS
MaxProfitComplexBid	Maximising profitability used with a generalised or asymmetric bid
MaxProfitNotHorizontal	Maximising profitability used with a non-horizontal TQSS
MaxProfitTQSS	Maximising profitability used with a TQSS
MaxProfitNoSolution	No solution when maximising profitability

Instances

Show AuctionException Source #
Methods showsPrec :: Int -> AuctionException -> ShowS # show :: AuctionException -> String # showList :: [AuctionException] -> ShowS #
Exception AuctionException Source #
Methods toException :: AuctionException -> SomeException # fromException :: SomeException -> Maybe AuctionException # displayException :: AuctionException -> String #
ToJSON AuctionException Source #
Methods toJSON :: AuctionException -> Value toEncoding :: AuctionException -> Encoding toJSONList :: [AuctionException] -> Value toEncodingList :: [AuctionException] -> Encoding

Lenses

auction_supply :: forall bid. Lens' (Auction bid) (Supply Units) Source #

auction_bids :: forall bid. Lens' (Auction bid) [Bid bid] Source #

auction_scale :: forall bid. Lens' (Auction bid) ScaleFactor Source #

auction_preferences :: forall bid. Lens' (Auction bid) [Good] Source #

auction_constraints :: forall bid. Lens' (Auction bid) [AdditionalConstraint bid] Source #

auction_size_limit :: forall bid. Lens' (Auction bid) (Maybe TotalSizeLimit) Source #

auction_tweak_supply :: forall bid. Lens' (Auction bid) Bool Source #

auction_verbosity :: forall bid. Lens' (Auction bid) Verbosity Source #

ar_prices :: forall bid. Lens' (AuctionResult bid) (Map Good Price) Source #

ar_quantities :: forall bid bid. Lens (AuctionResult bid) (AuctionResult bid) (Map (AVar bid) Units) (Map (AVar bid) Units) Source #

ar_normalised_price :: forall bid. Lens' (AuctionResult bid) (Maybe Price) Source #