Transportation and assignment models are special purpose algorithms of the linear programming. The simplex method of Linear Programming Problems(LPP) proves to be inefficient is certain situations like determining optimum assignment of jobs to persons, supply of materials from several supply points to several destinations and the like. More effective solution models have been evolved and these are called assignment and transportation models.
The transportation model is concerned with selecting the routes between supply and demand points in order to minimize costs of transportation subject to constraints of supply at any supply point and demand at any demand point. Assume a company has 4 manufacturing plants with different capacity levels, and 5 regional distribution centres. 4 x 5 = 20 routes are possible. Given the transportation costs per load of each of 20 routes between the manufacturing (supply) plants and the regional distribution (demand) centres, and supply and demand constraints, how many loads can be transported through different routes so as to minimize transportation costs? The answer to this question is obtained easily through the transportation algorithm.…
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Mathematical model is an idealized representation expressed in mathematical symbols and expressions. A mathematical model of a business problem might be in the form of a set of equations and related mathematical expressions that describe the essence of the problem. An economic order quantity model is given by: EOQ = √2AO/C where A – annual requirement, O – ordering cost and C – carrying cost. A linear programming model is given by objective function: Say Maximize Z = 10a + 12b, subject to 2a + b < = 60, 3a + 4b < = 120, a, b > = 0, where a and are units of products A and B, respectively to be produced to maximize total contribution given individual contribution of Rs.10 per unit of A and Rs.12 per unit of B, the resource constraints being that resource 1 and 2 are available respectively to the extent of 60 and 120 units only. An internal rate (IRR) model is given by: -I + Cft/(1 + k)t = 0, where ‘k’ is the IRR to be found, while ‘I’ is the initial investment, CFt refers to periodic cash flows. To construct a mathematical model objective of the firm, variables, constants and constraints must be known, besides the relationship amongst the variables. The relationship may be linear or non-linear. The EOQ and linear programming models given above are linear relationship based, while the IRR model is non-linear based as its exponential form.…
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A decision model is an idealized representation of the problem. Decision model refers to structured presentation of the problem, solution there to and stimulation of working of the solution. The mode’s purpose is to enable the decision analyst to forecast the effect of factors crucial to the solution of the problem.
Types of Models
There are different types of models. Ionic and Symbolic models are the prime two types. Ionic Models are concretized. It is a physical representation of any real life object on a different scale. Think of a prototype of a plane/car/machine/globe/idol and so on. Symbolic models re abstract models. A cost curve, a supply curve, marginal revenue curve, a production possibility curve, etc., is a symbolic model. A forecast profit and lost account is also a symbolic model. The statement symbolizes summary of financial effects of commercial activities planned over the next period. An equation is a symbolic model of variables, their relationship and effect of independent variables on the dependent variable.…
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Quantitative analysis is a scientific approach to decision making. As a first step to decision making, decision model has to be evolved. The decision model depends on two factors, namely the problem and the problem environment.
Defining the Problem
The first step in decisions making is defining the problem. The problem (i.e. the threat, opportunity, etc.) must be fully understood as to its nature, dimensions, intensity and so on. Take a labour absenteeism. It becomes a problem when it is rampant affecting work schedules. (one or two absentees, here and there is no problem). What is its nature? Deliberate absenteeism, absenteeism due to unavoidable causes, absenteeism as a mark of protest to certain managements attitudes/actions, absenteeism due to healthy/family/social reasons, etc. are indicative of the nature of the problem of absenteeism. Specific nature must be understood, since each type of absenteeism needs a different approach to solving the same. Dimensions of absenteeism comes next. How does it affect production? How does it affect inter-departmental relations, work flow, co-ordination, morale, etc? What is its impact on turnover and customer satisfaction? What is the scale of idle capacity resulting from labour absenteeism? Will motivational/coercive courses work containing absenteeism? There are but a few dimensions of the problem. How much grave the problem is? Should it be solved immediately? These indicate the intensity of the problem. The wholesome knowledge of the problems is very essential so that we can solve the problem. Not all problems can be known fully. Some keep change from time to time. So, to the extent possible the decision maker must grasp the problem. This step/function is also called as the ‘intelligence’ function of decision making. All this help to recognize the problem. Problem definition goes a little for.…
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Critical Path Analysis:
Critical path analysis, an important aid to planning, scheduling and coordinating the activities if large scale projects. Is a synthesis of two independent techniques: Programme Evaluation and Review Technique (PERT) and Critical Path Method (CPM).
Though the two techniques were developed independently, they are only superficially different. The two methods have many features in common and are now combined into a technique called Critical Path Analysis (CPA) or Network Analysis.
There are three basic different between a PERT network and CPM network:
- PERT is event oriented while CPM is activity oriented (i.e. PERT prepares network from events while CPM builds if from activities)
- PERT provides for an allowance for uncertainty while CPM does not (i.e. PERT makes three time estimates for each activity while CPM makes one time estimate)
- Activity time in CPM technique are related to costs while it is not so in PERT since it is event oriented
Significance of critical path:
Critical path analysis offers several advantages.…
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Initial basic feasible solution of a transportation problem can be obtained by any of the following methods:
1. North–west corner rule
The major advantage of the north–west corner rule method is that it is very simple and easy to apply. Its major disadvantage, however, is that it is not sensitive to costs and consequently yields poor initial solutions. The steps involved in determining an initial solution using north–west corner rule are as follows:
Step1. Write the given transportation problem in tabular form (if not given).
Step2. Go over to the north-west corner of the table. Suppose it is the (i, j)th cell.
Step3. Allocate min (ai, bj) to this cell. If the min (ai , bj) = ai, then the availability of the ith origin is exhausted and demand at the jth destination remains as bj-ai and the ith row is deleted from the table.…
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