Reference no: EM133076693

Business - Decision Modeling

In this assignment, you are required to solve optimization models using only LINGO or the Excel Solver. Most students find that LINGO is easier forthree reasons:

(a) The LINGO model resembles the algebraic model.

(b) Because only variables with non-zero variables are included in LINGO, but ev- ery variable requires a column in Excel, LINGO models are more compact. The advantage of this increases as the models become larger.

(c) Once the model has been setup, all that is needed in LINGO is to use the Solve command, but the Excel Solver requires that the Solver be setup as well.

(iii) If you solve the models in Excel Solver, you will have to write them in standard form,
i.e. all variables on the left-hand side, and a number of the right-hand side.If you use LINGO, you are not bound by this restriction. For each question, do the following:

(a) Formulate an algebraic model for the problem. If written by hand, scan it and imbed the image into the Word or pdf submission document.

(b) Use LINGO or the Excel Solver to solve this model, with your name and student number included in a comment line. Copy-and-paste the model and solution LINGO files (or two tabs for the model and the Answer Report from the Excel file) into the Word or pdf submission document.

(c) State the solution in words in the Word or pdf submission document.
When you attempt to solve these models, you might receive a message about the solution being infeasible. While this is a theoretical possibility, it won't happen for any of these questions. It means that a mistake has been made in formulating the model.

Question 1: A company blends two gasolines from Avalon Energy and Bonavista Petroleum (in- puts) into two commercial products, Premium and Regular gasoline (outputs). Forthe inputs, the octane ratings, the vapour pressures in kilopascals, and the amounts available in cubic metres (m3) and their prices are known. These are:

For the Premium and Regular gasolines the requirements are:

We define the variables as follows: A and B are respectively the amount of gasolinein m3 purchased from Avalon Energy/Bonavista Petroleum. P and R are respec- tively the amount of Premium/Regular gasoline in m3 blended and sold. AP, AR, BP, and BR are respectively the amounts in m3 of Avalon/Bonavista gasoline usedto make Premium/Regular gasoline.

Question 2. Drivers in the London (England) Underground railway system work two four-hour shifts per day. In some cases, the two shifts are consecutive (effectively one eight- hour shift), but usually they are not. All Underground drivers earn a base rate of £21 per hour (i.e. £168 per day). Because of the inconvenience of breaking up the day, those who work non-consecutive shifts are paid a £15 per day bonus. The London Underground has the following daily requirements for drivers:

No-one will be asked to work on both shifts 1 and 5. Subject to meeting all its requirements for drivers, the London Underground wishes to minimize its daily labour cost (regular and bonus). Formulate the model so that the £21 (or £168) and the £15 are entered only once.

Question 3. A company makes robots, mostly for industrial use, but as a novelty item they also make robotic pets. These robotic cats and dogs are not aimed at children, but due to their high cost of production the target market is seniors, who are now in a retirement home and cannot have a living pet. One of their products is a calico cat,which in addition to purring and meowing, can twist her head, lick her paw, and roll over onto her side. They have received orders for units of this cat six months inadvance of the desired delivery. Hence the company knows that the demand over the next six months will be:

It is now December 1. Based on what has already been planned for this month,the inventory of this robotic cat as of December 31 will be 800 units. Up to 5000 units can be manufactured each month based on each employee working on regulartime. Each cat costs $120 if manufactured on regular time. It is also possible to manufacture up to 1200 robotic calico cats per month on overtime. Each cat so produced would cost $170.

Robotic pets can be kept in inventory at a cost of $5 per robot per month. This charge represents the cost of tied-up capital, warehouse, and insurance expenses. As a buffer against potentially high demand at the end of the planning horizon, the ending inventory should be at least 500 units.

Back-ordered units are permitted (except at the end of month 6), but at a penalty cost of $40 per robotic pet per month.
We wish to formulate a model which seeks to minimize the sum of production costs, inventory holding costs, and shortage penalty costs.

Question 4. A lumber store stocks dowels in one standard length of 200 cm. Each dowel costs
$26.50. A customer wants the store to cut her thirty dowels of length 95 cm, four- teen dowels of length 63 cm, thirty-five dowels of length 37 cm, and fifty dowels of length 20 cm. She will receive a recycling credit of 5 cents per cm for any wood declared to be "waste". The objective is to minimize the net cost (the cost of the dowels minus the credit for the recycled wood).

You might wish to use Excel to help create the list of patterns needed in part (a).

Question 5. A machine shop makes pipes for the oil and gas industry in lengths of 250 cm and 400 cm. The shorter pipes give a profit of $140 each, while each long pipe gives a profit of $270. They can sell at most 900 of the 250 cm pipes and at most 300 of the longer ones. Each pipe spends time on three machines as follows:

In addition to the minutes available given in the above table, they can purchase up to 500 minutes (all, none, or any fraction of this amount) of additional polishing timeat a cost of $2 per minute, and can purchase an unlimited amount of extra grindingtime at a cost of $3 per minute.

For every long pipe made, there must be at least two short pipes made. For every pair of long pipes made, there can be at most seven short pipes made.

Attachment:- Business Decision Modeling.rar