# Essays on North-West Corner Method versus Stepping-Stone Method Coursework

The paper "North-West Corner Method versus Stepping-Stone Method" is a perfect example of management coursework.   The methods that we are going to analyze are the Steppingstone model, the Modified distribution model (MODI), North-West corner method, Vogel’ s Approximation method and the assignment model. They are also referred to as special-purpose algorithms for solving linear programming problems. They are simple and easy to understand. They are a branch of management science called cost management. The methods apply statistical and mathematical knowledge to optimize costs. These models are used to solve linear programming problems. Suppose a firm has several production plants in different locations and several warehouses in different locations.

Transporting goods from each production plant to the warehouse will be faced with several obstacles like plant production capacity, warehouse capacity/demand, and transport costs. Given these constraints, managers are faced with the difficult task of scheduling transport routes, journeys and quantities to achieve minimum costs. In this study, we are going to adopt several methods to understand the techniques involved and the results achieved. We shall study the variations of the methods plus their results.

The models assume that transportation costs are constant, monthly demand and factory average production are fixed (Havlisek, January 2007). Let us consider a digital firm that has several production units and different warehouses where distribution activities are carried out i. e. unit1, unit2, unit3 and warehouse A, warehouse B & warehouse C. The number of paths is 9 i. e. 3*3 =9. Each path has its own cost as illustrated below: TRANSPORTATION COSTS FOR DIGITAL FIRM 3 WAREHOUSES-3 PRODUCTION PLANTS   WAREHOUSE     1 2 3 PLANT A 4 5 6   B 9 6 8   C 5 5 3 Table 1 The quantity of goods (for this case) is equal for both supply (production capacity) and demand (warehouse capacity).

It is represented in the following example: AMOUNT OF GOODS TO BE TRANSPORTED         Warehouse     plant capacity     1 2 3   Plant A 600 500 800 1900   B 500 900 400 1800   C 900 700 500 2100 warehouse capacity   2000 2100 1700 5800 Table 2 The paths to be taken for the transportation of the goods from the production plants to the destined warehouses are as follows: plant A plant B   Warehouse 1 Warehouse 2 plant C   Warehouse 3 Table 3 The diagram above shows all the possible routes that can be used to transport goods from the three production plants to the warehouses. Each route has its own specific cost per unit of goods transported. Various combinations of these routes to supply goods to the warehouses have different total costs.

The objective of these models is thus to minimize such costs using the optimum combination of routes. Using the above assumptions, we are going to analyze how we can achieve optimum costs using the following methods: METHOD 1: North-West Corner Method versus Stepping-Stone Method Both of these methods are used together to achieve a common purpose. The objective function of the problems is usually to minimize transport costs. It is a step-by-step analysis that sets up a viable solution and then works on improving the results to an optimum level.

It might be complex when done manually but very simple when the algorithm is computerized. The method is good since you can use any number of variables i. e. n production plants and n warehouses (where n is an integer from 1 to 100+). The steps involved are as follows: Step 1: form a matrix with rows representing the production plants available and columns representing the warehouses, add a row and a column each end to represent the totals i. e. production capacity of each plant and demand capacity of each warehouse. Step 2: for the first plant and the first warehouse, allocate the total production until the warehouse capacity is depleted or the plant capacity is depleted whichever comes first.

If there is a remainder of goods, move to the second warehouse and allocate the goods until the warehouse is depleted and so on. Step3: Repeat step two for all the plants until all the warehouses are allocated the maximum available goods. Step 4: multiply each amount in each tablet with its transport cost and sum to get the initial feasible solution. This solution could be the optimal solution or not.

The second method is applied to improve this result until an optimum solution is achieved i. e. stepping-stone method.

References

Bassin, W., M., (1981). Quantitative business Analysis: linear programming: transportation and assignment models.

Budnick, F., S., (25 May 2011). Finite Mathematics with Applications, digital edition pp. 243: Extensions of linear programming.

Charnes, A., & Cooper, W., W., (October, 1954). The stepping stone method of explaining linear programming calculations in transport problems: management science: Carnegie Institute of technology.

Dantzig, G., B., (1998). Linear Programming and extensions, eleventh edition: A transportation problem.

Havlisek, J., (1 January 2007). Linear programming: transport and assignment models: transportation problem. Accessed on 9 December 2011 at http://orms.pef.czu.cz/text/transProblem.html

Martin, R., K., (2000). Quantitative methods for businesss, eleventh edition: linear programming