Q. 1 Suppose that the R & D Beverage Company has a soft drink product that shows a constant annual demand rate of 3600 cases. A case of soft drink costs R & B $3. Ordering costs are $20 per order and holding costs are 25% of the value of inventory. R & B has 250 working days per year, and the lead time is 5 days. Identify the following aspects of the inventory policy.

Ans.

(i) Economic Order Quantity

Q = √ ((2DCo)/Ch

where D = Annual Demand Rate

Co = Order Costing

Ch = Cost of Holding

2 * 3600 * 20/25% of $3

Square base of 108000

=439 units

(ii) Reorder Point

Reorder point = Aggregate demand/ No. of working days * lead time

=3500/250

= 72 days

(iii) Cycle Time

Number of orders = 3600/439 = 8.20

=Number of days organization stays operational/number of orders

=250/8.00

= 31 days

(iv) Total Yearly Cost

Total Annual Cost = ½ QCh + (D/Q)Co

½ * 439 * 0.75 + 3600/439 * 20

164.625 +164.01

328.635$

Q. 2 ‘Model building is central to the operational research (OR) methodology. The models used in OR are usually of mathematical form, although examples of iconic and even analogue models do occur. With relatively simple or standardized models, analytic “solutions” are sometimes possible, often based on appropriate algorithm or heuristics. In many situations, however, such solutions are either impossible or inappropriate and, as a consequence, a simulation approach would invariably be used. This type of model often tends to be of a descriptive rather than normative (or prescriptive) nature.'

(i) Describe mathematical, iconic, and analogue models, giving an example of each type.

Ans.

Mathematical models: It is a system for model building which incorporates changing over or imparting bona fide circumstances or conditions into numerical scientific articulations, tree plot, scatter layouts, etc. to find a solution to the problem. For example - As a consumer to maximise the utility amongst the given options within a given budget.

Iconic models: It is a process for model building which incorporates making a impersonation of a present component on a smaller, identical or greater scale. The model can be any dimensional. For example – Small chocolate replicas of cartoon characters, Small replicas of famous monuments such as Red Fort, Qutub Minar etc.

Analogue model: It is a strategy for model building which incorporates the representation of segments in a structure by similar segments in a basic model. It can either be a two dimensional depiction, for instance, graphs, diagrams, and so on or a three dimensional outline such as demo cell phones etc.

ii) Explain how the use of a mathematical model to simulate a particular

situation differs from an analytic approach problem to problem solving.

Use as a foundation for your answer the basic net-present value model of

capital investment.

Ans.

An informative model uses distinctive steps and takes after an intelligible framework to go to a cautious result, which can be affirmed. On the off chance that there ought to be an event of the net present worth model, by separating given conditions and choosing expected future cash streams, a particular markdown rate can be gotten a positive net present regard. On the other hand, a numerical model presents an unpleasant result. They use counts to keep running over the answer. In the NPV case, the numerical model would not have the ability to give exact future cash inflows

(iii) Explain the meaning of the terms, ‘algorithm' and ‘heuristic' in the

context of problem solving

Ans.

Algorithm is a methodology or set of rules to be followed in figuring's or other basic deduction operations.

Heuristic means counting or serving as a manual for learning, disclosure, or basic intuition by trial and hit experimentation methods.

(iv) Using relevant examples, explain the distinction between a ‘descriptive'

and a ‘normative' model.

Ans.

DESCRIPTIVE - It is the model which depicts what exactly exists and is based on evident information. It takes after the "What is" methodology. These don't take into thought singular feelings, feelings, or judgment. It is exploratory, predictable additionally, clear in nature. For example – Extraction of diesel from crude oil.

NORMATIVE – It is a model which depicts what should exist. It is based upon feelings and individual conclusions i.e the model is subjective from individual to person. For example - Movie review, Feedback of different people regarding a hotel.

Q. 3 ‘Accurately forecasting the consumer demand is considered to be one of

toughest tasks of a marketing manager.' In light of the above sentence,

explain following forecasting techniques:

(i) Moving Average Method

(ii) Exponential Smoothing Method

(iii) Least Square Method

(iv) Delphi Method

How do managers find the accuracy of a particular technique? Give one

example to substantiate your argument.

Ans:

(i) Moving Average Method - Moving typical methodology is a guaging technique which enables the data customer to shape an example from a given course of action generally certain data. The entire data set is disengaged into subsets of moving time periods. Each past discernment are given identical weightage. For example -

(ii) Exponential Smoothing Method is a deciding system like the moving ordinary procedure which apportions more unmistakable weightage to the latest observations.

(iii) Least Square Method – It is a suspecting technique that incorporates consigning the 'best fit line'- y=ax+b, to a given plan of data.

(iv) Delphi System is a strategy for figuring out which incorporates searching for the opinion of a leading group of experts through a movement of studies expected to accomplish meeting of a common conclusion/conviction. The reactions to these surveys are strange and are at risk to change as coming about overviews are given on nearby the prevailing part sentiment the past overviews.

Q. 4 A company sells two different products A and B, making a profit of Rs. 40 and Rs. 30 per unit on them respectively. They are produced in a common production process has a total capacity of 30,000 man-hours. It takes three hours to produce a unit of A and one hour to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 8000 units and that of B is 12000 units. Products can be sold in any combination when subjected to these constraints.

i) Formulate this problem as a linear programming model

ii) Find the solution using the graphical method. Explain the answer.

Ans. (i)

Let x' = number units of product A

Let y' = number units of product B

MAX Z = 40x' + 30y'

Subject to constraints ;

3x' + 1y' <= 30000 production hours

x' <= 8000 demand

y' <= 1200 demand

x', y' >= 0

Find using graphical method

Constraint 1

Let x' = 0

3x' + y' = 30000

y' = 30,000

Let y' = 0

3x' = 30,000

x' = 10,000

From the graph we found

P = (8000, 0)

Q = (8000, 5000)

R = (6000, 12000)

S = (0, 12000)

Optimization function

Max Z = 40x' + 30y'

Point P

40*8000+30*0

480,000

Point Q

40*8000 +30*5000

470,000

Point R

40*6000 +30*12000

600,000

Point S

40*0 +30*12000

360,000

Hence, as per the calculations, the company would be most profitable by producing combination R of 6000 units of product A and 12000 units of product B.

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