New road out of Auckland choked with traffic Sun, 25 Jan 2009 News: National Otago Daily TimesNews: National The toll road to ease congestion north of Auckland was clogged by curious motorists when it opened today, and is likely to be busy tomorrow when people return from a long weekend. The Northern Gateway Toll Road near Orewa, north of Auckland, to Puhoi is free until Tuesday, when it will cost $2 for cars or $4 for heavy vehicles over 3.5 tonnes. Motorists keen to travel the $400 million road for the first time, and people heading out of Auckland for the anniversary weekend, contributed to major traffic jams today. The NZ Transport Agency recommended State Highway 16 as an alternative for motorists heading south from Wellsford to Auckland this weekend. "We're expecting traffic to be heavy particularly tomorrow afternoon when motorists return home after the holiday weekend," said NZTA traffic management unit manager Mark Walker said. New Zealand's first fully electronic toll road, it was built to take the pressure off the main access road from Auckland to Northland through Orewa. The road north of Orewa is winding and narrow and not designed for the traffic volumes it has to cope with, becoming choked for kilometres at peak traffic times.

What are the costs and benefits of this new road?

Before the government chose to develop this new toll road they would have done COST-BENEFIT analysis. When private individuals and businesses make decisions they look at private costs and private benefits. If the benefits outweigh the costs, which for businesses usually means they will make more profit, they will take that choice. e.g. Coca-Cola used to mass produce in glass bottles, no cans nor plastic bottles. It cost less to produce in plastic and tin so they changed their containers.

They did not take into consideration the external cost – all costs not paid for by the consumer or producers in an economic activity. They ignored the cost passed onto other people and society. The cost of clearing up and disposing of plastic is not paid for by the coca-cola its paid for by society

COST-BENEFIT ANALYSIS CBA is a process that takes all costs and benefits of and economic activity into account. It is used to evaluate the social costs and benefits. Social cost = private cost + external cost Social benefit = private benefit + external benefit Can you think of businesses which might use CBA and what the real purpose might be behind their decisions.

Operational Research The OR approach to decision making uses models of real-world situations to investigate solutions to business problems. The aim of OR is to construct a model of this real- world situation and manipulate this model to attempt to find the best possible solution. The two OR decision models we look at are decision trees and linear programming.

Decision tree Definition: A diagram showing the options that are available when taking a decision and the possible outcome of those options.

Linear programming - blending Linear programming techniques lay out business problems as a series of linear or mathematical equations. Blending technique is one example of linear programming model. Blending is a model that is used to assist firms in deciding the best possible use of limited resources. Each resource constraint is represented by a mathematical formula or equation, when plotted on a graph creates a straight line.

To explain linear programming we will use a basic example: Scenario:  Ken’s bakery produces both cakes and biscuits.  Some of the machinery and staff are needed for both products. So, when machinery and staff are being used for cakes, the fewer there will be for biscuits.  Ken’s aim is to maximise profits, but in order to achieve this, which would be the best combination of cake and biscuit production?

Stage 1 Identify the resources which are needed for producing each product – these are called constraints as the quantity of them will determine the volumes of goods to be produced. Example resource; mixing machines, baking ovens, packaging staff

Stage 2 Identify the total resource available in each department: Example: 3 mixing machines for each 10 hour day 2 ovens available for each 10 hour day 2 packaging staff for each 10 hour day

Stage 3 Calculate the amount of resources needed to produce a certain quantity of each product; Example: A batch of cakes take 2.5hrs to mix; a batch of biscuits takes 2.5hrs to mix A batch of cakes takes 2hrs to bake; a batch of biscuits takes 1 hr to bake A batch of cakes takes one hour to pack; a batch of biscuits takes two hours to pack

Stage 4 Establish each constraint as an equation. Mixing: There are 30 mixing hours available. Both cakes (C) and biscuits (B) take 2.5hrs of mixing per batch. 2.5C + 2.5B must be less than or equal to 30hrs 2.5C + 2.5B < 30

Baking: There are 20 hrs of baking time available. Cakes take 2hrs and biscuits take 1hr per batch. 2C + 1B must be less than or equal to 20 hours. 2C + 1B <20

Packaging: There are 20 packaging hours available. Cakes take 1hr and biscuits take 2hrs to pack per batch 1C + 2B must be less than or equal to 20hrs 1C + 2B < 20

Stage 5 Plot these constraint equations on to a graph. This is done by calculating the maximum number of batches of both goods that can be made with each constraint, assuming that the other is not produced at all.

Mixing: 2.5C < 30 = 12 batches of cakes 2.5B < 30 = 12 batches of biscuits Baking: 2C < 20 = 10 batches of cakes baked 1B < 20 = 20 batches of biscuits baked Packaging 1C < 20 = 20 batches of cakes can be packed 2B < 20 = 10 batches of biscuits can be packed

The area outside of the constraints is shaded. It is not possible for the firm to produce in this area because of the constraints. This is called the “non-feasible” area.

Stage 6 Identify the profits made from each product. Construct a profit equation and plot on the graph. Example: Each batch of cakes makes a profit of $30 Each batch of biscuits makes a profit of $20 Total profit will therefore be $30C + $20B

Assume that the firm aims to make a profit of $300. To make this it will have to make and sell either 10 batches of cakes or 15 batches of biscuits. This line is then drawn on the graph as a profit line.

Stage 7 Optimise the model The business will want to make as much profit as possible. This is done by moving the profit line out to the furthest point in the feasible area – keeping it parallel to its original slope. This gives the combination that will maximise profit. (8x30) + (4x20) = $320

Advantages and Disadvantages Advantages Useful when deciding on best use of available resources Managers can use to allocate resources between different products so costs are minimised and profits are maximised Computer models can speed the process up Disadvantages  This simple version only allows for 2 products to be considered  It ignores the market demand for the product – the assumption being that the optimum output levels can all be sold profitably  It assumes that resources can be switched between the 2 products at a constant rate of productivity.