Question

To complete this project you have to make a presentation of 10 slides and a written report on the following:

1. Transportation models and its usage.
2. Analyze the following facility location case and solve it as a linear program formulation.
3. Which of the new locations will yield the lowest cost for the firm in combination with the existing plants and warehouses?

The Hardgrave Machine Company produces computer components at its plants in Cincinnati, Salt Lake City, and Pittsburgh. These plants have not been able to keep up with demand for orders at Hardgrave’s four warehouses in Detroit, Dallas, New York, and Los Angeles. As a result, the firm has decided to build a new plant to expand its productive capacity. The two sites being considered are Seattle and Birmingham; both cities are attractive in terms of labour supply, municipal services, and ease of factory financing. The tables below present the production costs and output requirements for each of the three existing plants, demand at each of the four warehouses, and estimated production costs of the new proposed plants. In addition, transportation costs from each plant to each warehouse are given.

WAREHOUSE	MONTHLY DEMAND	PRODUCTION PLANT	MONTHLY SUPPLY	COST TO PRODUCE ONE UNIT ($)
Detroit	10 000	Cincinnati	15 000	48
Dallas	12 000	Salt Lake City	6 000	50
New York	15 000	Pittsburg	14 000	52
Los Angeles	9 000
Total	46 000		35 000

Supply needed from new plant 46,000 - 35,000   = 11,000 units per month

ESTIMATED PRODUCTION COST PER UNIT AT PROPOSED PLANTS

Seattle	$53
Birmingham	$49

	Detroit	Detroit	Detroit	Detroit
Cincinnati	$25	55	40	60
Salt Lake City	35	30	50	40
Pittsburg	36	45	26	66
Seattle	60	38	65	27
Birmingham	35	30	41	50

Answer 1

a) The transportation model addresses the concept of moving a thing from one place to another without change. It assumes that any damage en route has negative consequences, and so it's used to analyze transportation systems and find the most efficient route for resource allocation.

A Transport Model is the tool providing a quantitative and qualitative output of the likely impacts of alternative solutions (hypotheses) formulated at planning level (“What if ?”). This then provides the analytical input to the planning and decision making process. The model can be used in many different ways to inform this process, including:  Understanding the function of existing infrastructure in terms of passenger groups, freight types, trip types and origins and destinations;  Identifying bottlenecks in the network and understanding the need for additional capacity;  Providing demand data for appropriate options analysis, design and dimensioning of new infrastructure and operational service (e.g. public transport timetables) responding to real forecast traffic and functional requirements;  Understanding the impact of a new transport scheme on transport flows through the modelled network (multi-modal if necessary), showing how demand responds to the new infrastructure and the resulting conditions that will exist;  Understanding how transport conditions will change in the future in response to changes in population, employment, economic activity, car ownership and development patterns;  Understanding the passenger and revenue impacts of changes in routing, frequency, speed or accessibility of public transport services; and  Understanding the relationship between changes in land use and the resulting transport demand. Ultimately, the outputs from the transport model provide quantitative information that informs scheme design, Cost Benefit Analysis, Financial Analysis, and Environmental Assessment. Modelling teams should be aware that those end-users of transport modelling outputs rely on robust transport forecasts. Weaknesses in a transport model can therefore reduce the ability to support those other specialists. As such, a good quality model, based on an appropriate dataset will generate a good quality set of concept and design inputs and assessment outputs. This will in turn allow a more informed design and appraisal.

b)

1. Quantity allocation if Seattle Plant is used for production

	Detroit		Dallas		New York		Los Angeles		Monthly Supply
											Cincinnati		$73*		$103.00		$   88.00		$108.00	15000
10000		$4,000		1000
Salt Lake City		$   85.00		$   80.00		$100.00		$   90.00	6000
			6000
Pittsburg		$   88.00		$   97.00		$   78.00		$118.00	14000
					14000
Seattle		$113.00		$   91.00		$118.00		$   80.00	11000
			2000				9000
Monthly Demand	10000		12000		15000		9000		46000

2. Quantity allocation if Brimingham Plant is used for production

	Detroit		Dallas		New York		Los Angeles		Monthly Supply
											Cincinnati		$   73.00*		$103.00		$88		$108	15000
10000				1000		4000
Salt Lake City		$   85.00		$   80.00		$100.00		$   90.00	6000
			1000				5000
Pittsburg		$   88.00		$   97.00		$   78.00		$118.00	14000
					14000
Birmingham		$   84.00		$   79.00		$   90.00		$   99.00	11000
			11000
Monthly Demand	10000		12000		15000		9000		46000

* Amount in $ represents the total Cost (Unit Cost+Transportation)

Quantity is allocated using Total cost as ranking .i.e, Max possible quantity is assigned to the lowest total cost transportation option.

c) Total Cost if Seattle Plant is used for production = Quantity Allocated at answer (b) above* total cost = $3,824,080.00

Total Cost Brimingham Plant is used for production = Quantity Allocated at answer (b) above* total cost = $3,761,080.00

Hence, Brimingham shall be choosen as new location for plant that will yield the lowest cost for the firm .