Find the LP model for the following problem and then find the solution by using Excel, TORA, GAMS and Express (Use all of them, not only one).


In today's global economy, a multinational company must deal with currencies of the countries in which it operates. Currency arbitrage, or simultaneous purchase and sale of currencies in different markets, offers opportunities for advantageous movement of money from one currency to another. For example, converting £1000 to U.S. dollars in 2001 with an exchange rate of $1.60 to £1 will yield $1600. Another way of making the conversion is to first change the British pound to Japanese yen and then convert the yen to U.S. dollars using the 2001 exchange rates of £1 = ¥175 and $1=¥105. The resulting dollar amount is

10000 £ x 175 ¥ / 105 ¥ = 1.6667 $

This example demonstrates the advantage of converting the British money first to Japanese yen and then to dollars.
This section shows how the arbitrage problem involving many currencies can be formulated and solved as a linear program.
Suppose that a company has a total of 5 million dollars that can be exchanged for euros (€), British pounds (£), yen (¥), and Kuwaiti dinars (KD). Currency dealers set the following limits on the amount of any single transaction: 5 million dollars, 3 million euros, 3.5 million pounds, 100 million yen, and 2.8 million KDs.The table below provides typical spot exchange rates. The bottom diagonal rates are the reciprocal of the top diagonal rates. For example, rate(€->$) =l/rate( $ -> €) = 1/.769 = 1.30.

1$ = 0,769 €
1$ = 0,625 £
1$ = 105 ¥
1$ = 0.342 KD

1€ = 0,813 £
1€ = 137 ¥
1€ = 0,445 KD

1£ = 169¥
1£ = 0,543 KD

1 = 0,0032 KD

Is it possible to increase the dollar holdings (above the initial $5 million) by circulating currencies through the currency market?


I need these to be coded in excell and express for my linear modeling homework. Any help will be much appreciated.

This post was edited by CanisLupus on Jul 18 2013 04:20pm

ohhhh these problems

ok, so first thing lets first the decision variables.

let Xij be the amount of money we convert from currency i to currency j

let the constant Aij of the forward conversion rate

then the total number of a currency Yi in the end would be sum over j of AjiXji for each currency i

let Bi be the reciprocal conversion rates

now our objective function becomes

max sum over i of BiYi

now we need to make sure what we are doing is physically possible

first, the constraints described above can be seen as:

sum over j for j!=i Xij < Ci for currency i. where Ci is the transaction limits in the currency we are interested in. This means the total outflow of that currency is less than the limit.

secondly, we need to make sure the there is balance, ie we can never have "negative money" in any currency (ie, suppose we convert into 200 EUR, we cant then convert away more than 200EUR)

therefore, sum over j for of XjiAji (the total inflows)= sum over j, i!=j of Xij (the total outflows), except for USD, where we can account for the infusion by

inflows into USD+5000000=outflows from USD

lastly, we need to make sure that

Xij >=0

realistically though you will have a transaction cost, ie the inflows would be (1-r)inflow

i dont have solver or excell on my tablet so cant really do this for you

shouldnt take too long though