Safe Haskell	None
Language	Haskell2010

ProductMixAuction.LP.TQSS

Contents

TQSS representation
Search strategies
Solving the TQSS
Utilities
Lenses

Description

Search for a solution to a TQSS by running the LP multiple times for different sizes of auction, and comparing the resulting demand prices to the TQSS function.

Synopsis

TQSS representation

data TQSS fun Source #

A Total Quantity Supply Schedule (TQSS) is a function from prices to the total number of units that should be made available at those prices. It must be weakly increasing (i.e. increasing any price must not decrease the TQSS).

This type represents a TQSS along with options to control how the search for the solution should take place.

The first parameter determines how the function on the price measure is represented; it will typically be TQSSFun or TQSSTable.

Constructors

TQSS
Fields _tqss_fun :: fun Function giving total quantity to be supplied at given prices _tqss_type :: TQSSType

Instances

Eq fun => Eq (TQSS fun) Source #
Methods (==) :: TQSS fun -> TQSS fun -> Bool # (/=) :: TQSS fun -> TQSS fun -> Bool #
Show fun => Show (TQSS fun) Source #
Methods showsPrec :: Int -> TQSS fun -> ShowS # show :: TQSS fun -> String # showList :: [TQSS fun] -> ShowS #
Generic (TQSS fun) Source #
Associated Types type Rep (TQSS fun) :: * -> * # Methods from :: TQSS fun -> Rep (TQSS fun) x # to :: Rep (TQSS fun) x -> TQSS fun #
ToJSON tqss => ToJSON (TQSS tqss) Source #
Methods toJSON :: TQSS tqss -> Value toEncoding :: TQSS tqss -> Encoding toJSONList :: [TQSS tqss] -> Value toEncodingList :: [TQSS tqss] -> Encoding
FromJSON tqss => FromJSON (TQSS tqss) Source #
Methods parseJSON :: Value -> Parser (TQSS tqss) parseJSONList :: Value -> Parser [TQSS tqss]
Default tqss => Default (TQSS tqss) Source #
Methods def :: TQSS tqss
type Rep (TQSS fun) Source #
type Rep (TQSS fun) = D1 (MetaData "TQSS" "ProductMixAuction.LP.TQSS" "product-mix-auction-0.1.0.0-inplace" False) (C1 (MetaCons "TQSS" PrefixI True) ((:*:) (S1 (MetaSel (Just Symbol "_tqss_fun") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 fun)) (S1 (MetaSel (Just Symbol "_tqss_type") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 TQSSType))))

data TQSSType Source #

Constructors

TQSSAbsolute AbsoluteTQSS
TQSSNormalised

Instances

Eq TQSSType Source #
Methods (==) :: TQSSType -> TQSSType -> Bool # (/=) :: TQSSType -> TQSSType -> Bool #
Show TQSSType Source #
Methods showsPrec :: Int -> TQSSType -> ShowS # show :: TQSSType -> String # showList :: [TQSSType] -> ShowS #
Generic TQSSType Source #
Associated Types type Rep TQSSType :: * -> * # Methods from :: TQSSType -> Rep TQSSType x # to :: Rep TQSSType x -> TQSSType #
ToJSON TQSSType Source #
Methods toJSON :: TQSSType -> Value toEncoding :: TQSSType -> Encoding toJSONList :: [TQSSType] -> Value toEncodingList :: [TQSSType] -> Encoding
FromJSON TQSSType Source #
Methods parseJSON :: Value -> Parser TQSSType parseJSONList :: Value -> Parser [TQSSType]
Default TQSSType Source #
Methods def :: TQSSType
type Rep TQSSType Source #
type Rep TQSSType = D1 (MetaData "TQSSType" "ProductMixAuction.LP.TQSS" "product-mix-auction-0.1.0.0-inplace" False) ((:+:) (C1 (MetaCons "TQSSAbsolute" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 AbsoluteTQSS))) (C1 (MetaCons "TQSSNormalised" PrefixI False) U1))

data AbsoluteTQSS Source #

Constructors

AbsoluteTQSS

Fields

_atqss_price_measure :: TQSSPriceMeasure
Measure on prices using which TQSS is defined
_atqss_search :: TQSSSearchMode
Search algorithm for finding the intersection
_atqss_scale :: TQSSScale
How to rescale the supply as the total quantity changes
_atqss_min_bound :: Maybe Units
Minimum bound for the search.
_atqss_max_bound :: Maybe Units
Maximum bound for the search.
_atqss_step_size :: Maybe Units
The step size for search modes other than BinarySearch.

Instances

Eq AbsoluteTQSS Source #
Methods (==) :: AbsoluteTQSS -> AbsoluteTQSS -> Bool # (/=) :: AbsoluteTQSS -> AbsoluteTQSS -> Bool #
Show AbsoluteTQSS Source #
Methods showsPrec :: Int -> AbsoluteTQSS -> ShowS # show :: AbsoluteTQSS -> String # showList :: [AbsoluteTQSS] -> ShowS #
Generic AbsoluteTQSS Source #
Associated Types type Rep AbsoluteTQSS :: * -> * # Methods from :: AbsoluteTQSS -> Rep AbsoluteTQSS x # to :: Rep AbsoluteTQSS x -> AbsoluteTQSS #
ToJSON AbsoluteTQSS Source #
Methods toJSON :: AbsoluteTQSS -> Value toEncoding :: AbsoluteTQSS -> Encoding toJSONList :: [AbsoluteTQSS] -> Value toEncodingList :: [AbsoluteTQSS] -> Encoding
FromJSON AbsoluteTQSS Source #
Methods parseJSON :: Value -> Parser AbsoluteTQSS parseJSONList :: Value -> Parser [AbsoluteTQSS]
type Rep AbsoluteTQSS Source #
type Rep AbsoluteTQSS = D1 (MetaData "AbsoluteTQSS" "ProductMixAuction.LP.TQSS" "product-mix-auction-0.1.0.0-inplace" False) (C1 (MetaCons "AbsoluteTQSS" PrefixI True) ((::) ((::) (S1 (MetaSel (Just Symbol "_atqss_price_measure") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 TQSSPriceMeasure)) ((::) (S1 (MetaSel (Just Symbol "_atqss_search") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 TQSSSearchMode)) (S1 (MetaSel (Just Symbol "_atqss_scale") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 TQSSScale)))) ((::) (S1 (MetaSel (Just Symbol "_atqss_min_bound") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe Units))) ((:*:) (S1 (MetaSel (Just Symbol "_atqss_max_bound") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe Units))) (S1 (MetaSel (Just Symbol "_atqss_step_size") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Maybe Units)))))))

data TQSSPriceMeasure Source #

Choice of measure used to convert the vector of prices (one for each good) into a single price on which the TQSS is defined.

Constructors

SingleGoodPrice Good	Define the TQSS on the price of a single good.
MeanPrice	Define the TQSS on the mean price of all the goods.

Instances

Eq TQSSPriceMeasure Source #
Methods (==) :: TQSSPriceMeasure -> TQSSPriceMeasure -> Bool # (/=) :: TQSSPriceMeasure -> TQSSPriceMeasure -> Bool #
Show TQSSPriceMeasure Source #
Methods showsPrec :: Int -> TQSSPriceMeasure -> ShowS # show :: TQSSPriceMeasure -> String # showList :: [TQSSPriceMeasure] -> ShowS #
Generic TQSSPriceMeasure Source #
Associated Types type Rep TQSSPriceMeasure :: * -> * # Methods from :: TQSSPriceMeasure -> Rep TQSSPriceMeasure x # to :: Rep TQSSPriceMeasure x -> TQSSPriceMeasure #
ToJSON TQSSPriceMeasure Source #
Methods toJSON :: TQSSPriceMeasure -> Value toEncoding :: TQSSPriceMeasure -> Encoding toJSONList :: [TQSSPriceMeasure] -> Value toEncodingList :: [TQSSPriceMeasure] -> Encoding
FromJSON TQSSPriceMeasure Source #
Methods parseJSON :: Value -> Parser TQSSPriceMeasure parseJSONList :: Value -> Parser [TQSSPriceMeasure]
Default TQSSPriceMeasure Source #
Methods def :: TQSSPriceMeasure
type Rep TQSSPriceMeasure Source #
type Rep TQSSPriceMeasure = D1 (MetaData "TQSSPriceMeasure" "ProductMixAuction.LP.TQSS" "product-mix-auction-0.1.0.0-inplace" False) ((:+:) (C1 (MetaCons "SingleGoodPrice" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Good))) (C1 (MetaCons "MeanPrice" PrefixI False) U1))

data TQSSScale Source #

How to change the total quantity available in the auction when solving a TQSS.

Constructors

ScaleSupply SupplyScaleLambda	Scale the supply curves using the given parameter `lambda`.
AddConstraint	Do not change the supply curves, but add a constraint to the LP bounding the total quantity supplied.

Instances

Eq TQSSScale Source #
Methods (==) :: TQSSScale -> TQSSScale -> Bool # (/=) :: TQSSScale -> TQSSScale -> Bool #
Show TQSSScale Source #
Methods showsPrec :: Int -> TQSSScale -> ShowS # show :: TQSSScale -> String # showList :: [TQSSScale] -> ShowS #
Generic TQSSScale Source #
Associated Types type Rep TQSSScale :: * -> * # Methods from :: TQSSScale -> Rep TQSSScale x # to :: Rep TQSSScale x -> TQSSScale #
ToJSON TQSSScale Source #
Methods toJSON :: TQSSScale -> Value toEncoding :: TQSSScale -> Encoding toJSONList :: [TQSSScale] -> Value toEncodingList :: [TQSSScale] -> Encoding
FromJSON TQSSScale Source #
Methods parseJSON :: Value -> Parser TQSSScale parseJSONList :: Value -> Parser [TQSSScale]
Default TQSSScale Source #
Methods def :: TQSSScale
type Rep TQSSScale Source #
type Rep TQSSScale = D1 (MetaData "TQSSScale" "ProductMixAuction.LP.TQSS" "product-mix-auction-0.1.0.0-inplace" False) ((:+:) (C1 (MetaCons "ScaleSupply" PrefixI False) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 SupplyScaleLambda))) (C1 (MetaCons "AddConstraint" PrefixI False) U1))

type TQSSFun = Double -> Units Source #

Representation of a TQSS function as a Haskell function from the price measure to the number of units.

type TQSSTable = [TQSSStep] Source #

Representation of a TQSS function as a list of steps.

type TQSSStep = Step Units Source #

Single step in a TQSS step function.

Search strategies

data TQSSSearchMode Source #

Choice of strategy used to search for the intersection between the TQSS and the demand curve.

Constructors

BinarySearch	Find a solution to the TQSS by binary search on the interval. This minimises the number of LP iterations, but does not guarantee which solution will be returned if multiple solutions exist.
LinearSearchAll	Evaluate the TQSS at all points in the interval (separated by the step size) and choose the point at which supply and demand are closest.
LinearSearchBelow	Find a solution to the TQSS by linear search on the interval, moving in increments of the step size from the lower bound, and stopping if the upper bound is reached before the demand curve meets the TQSS.
CombinedSearch	Like `LinearSearchAll`, but additionally uses binary search to deliver a more precise result.

Instances

Eq TQSSSearchMode Source #
Methods (==) :: TQSSSearchMode -> TQSSSearchMode -> Bool # (/=) :: TQSSSearchMode -> TQSSSearchMode -> Bool #
Show TQSSSearchMode Source #
Methods showsPrec :: Int -> TQSSSearchMode -> ShowS # show :: TQSSSearchMode -> String # showList :: [TQSSSearchMode] -> ShowS #
Generic TQSSSearchMode Source #
Associated Types type Rep TQSSSearchMode :: * -> * # Methods from :: TQSSSearchMode -> Rep TQSSSearchMode x # to :: Rep TQSSSearchMode x -> TQSSSearchMode #
ToJSON TQSSSearchMode Source #
Methods toJSON :: TQSSSearchMode -> Value toEncoding :: TQSSSearchMode -> Encoding toJSONList :: [TQSSSearchMode] -> Value toEncodingList :: [TQSSSearchMode] -> Encoding
FromJSON TQSSSearchMode Source #
Methods parseJSON :: Value -> Parser TQSSSearchMode parseJSONList :: Value -> Parser [TQSSSearchMode]
Default TQSSSearchMode Source #
Methods def :: TQSSSearchMode
type Rep TQSSSearchMode Source #
type Rep TQSSSearchMode = D1 (MetaData "TQSSSearchMode" "ProductMixAuction.LP.TQSS" "product-mix-auction-0.1.0.0-inplace" False) ((:+:) ((:+:) (C1 (MetaCons "BinarySearch" PrefixI False) U1) (C1 (MetaCons "LinearSearchAll" PrefixI False) U1)) ((:+:) (C1 (MetaCons "LinearSearchBelow" PrefixI False) U1) (C1 (MetaCons "CombinedSearch" PrefixI False) U1)))

type TQSSSearchStrategy = forall bid. Goodly bid => TQSSFun -> AbsoluteTQSS -> Maybe [Step Units] -> Auction bid -> IO [TQSSPoint] Source #

A TQSS search strategy is given the lower and upper bounds for the total size, a description of the TQSS and a scaled auction. It returns a list of points at which the TQSS was evaluated; the solution is the point at which demand is closest to supply.

Solving the TQSS

data TQSSPoint Source #

A point at which the TQSS has been evaluated.

Constructors

TQSSPoint

Fields

_tqp_demand_target :: Units
The total size of the auction that was selected.
_tqp_demand :: Units
The total size of the auction (i.e. the "demand") that was evaluated (this may differ from _tqp_demand_target because when rescaling the supply curves we may change the total).
_tqp_price :: Double
The price measure resulting from solving the auction at the demand size.
_tqp_supply :: Units
The desired supply given by evaluating the TQSS function at the price measure.

Instances

Eq TQSSPoint Source #
Methods (==) :: TQSSPoint -> TQSSPoint -> Bool # (/=) :: TQSSPoint -> TQSSPoint -> Bool #
Show TQSSPoint Source #
Methods showsPrec :: Int -> TQSSPoint -> ShowS # show :: TQSSPoint -> String # showList :: [TQSSPoint] -> ShowS #
Generic TQSSPoint Source #
Associated Types type Rep TQSSPoint :: * -> * # Methods from :: TQSSPoint -> Rep TQSSPoint x # to :: Rep TQSSPoint x -> TQSSPoint #
ToJSON TQSSPoint Source #
Methods toJSON :: TQSSPoint -> Value toEncoding :: TQSSPoint -> Encoding toJSONList :: [TQSSPoint] -> Value toEncodingList :: [TQSSPoint] -> Encoding
FromJSON TQSSPoint Source #
Methods parseJSON :: Value -> Parser TQSSPoint parseJSONList :: Value -> Parser [TQSSPoint]
Default TQSSPoint Source #
Methods def :: TQSSPoint
Arbitrary TQSSPoint Source #
Methods arbitrary :: Gen TQSSPoint shrink :: TQSSPoint -> [TQSSPoint]
type Rep TQSSPoint Source #
type Rep TQSSPoint = D1 (MetaData "TQSSPoint" "ProductMixAuction.LP.TQSS" "product-mix-auction-0.1.0.0-inplace" False) (C1 (MetaCons "TQSSPoint" PrefixI True) ((::) ((::) (S1 (MetaSel (Just Symbol "_tqp_demand_target") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Units)) (S1 (MetaSel (Just Symbol "_tqp_demand") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Units))) ((:*:) (S1 (MetaSel (Just Symbol "_tqp_price") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Double)) (S1 (MetaSel (Just Symbol "_tqp_supply") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 Units)))))

runTQSS :: Goodly bid => Auction bid -> TQSS TQSSTable -> IO (Auction bid, AuctionResult bid, Units, Maybe [TQSSPoint]) Source #

Check the validity of the TQSS and solve it using either runNormalisedTQSS or runAbsoluteTQSS as appropriate.

runNormalisedTQSS :: Goodly bid => Auction bid -> TQSSTable -> IO (Auction bid, AuctionResult bid, Units, Maybe a) Source #

Solve an auction with a normalised TQSS using a single LP solver run and including the TQSS in the structure of the LP.

The resulting auction will have auction_size_limit set.

runAbsoluteTQSS :: Goodly bid => Auction bid -> Maybe [TQSSStep] -> TQSSFun -> AbsoluteTQSS -> IO (Auction bid, AuctionResult bid, Units, Maybe [TQSSPoint]) Source #

Iteratively solve an auction with a TQSS, by re-running the LP with variable total quantities and using the search strategy to find the smallest quantity for which demand is no less than the TQSS. Returns the auction scaled to the final size, the prices/allocations at that size, the total size itself and the points of the TQSS graph evaluated to determine it.

Note that if an additional constraint is being used to fix the auction size, the resulting auction will have auction_size_limit set.

Utilities

interpolateTQSS :: TQSS TQSSTable -> TQSS TQSSFun Source #

Convert a TQSS function represented as a list of steps into a proper Haskell function. If a maximum bound for the TQSS search is not set, use the upper limit of the domain of the step function.

isNondecreasingTQSSTable :: TQSSTable -> Bool Source #

Test that the TQSS function is non-decreasing.

isConstrainedTQSS :: TQSS fun -> Bool Source #

Does this TQSS work by constraining the total quantity supplied?

tqssTypeLabel :: TQSSType -> Text Source #

Text label for the prices used by this TQSS type.