Chapter 1- Introduction to Management Science. The Management Science Approach to Problem Solving Model Construction: Production Management Science Modeling Techniques Breakeven Analysis and Excel Model Example Indifference Point Analysis.
Is it worth doing?(Break-even analysis, Forecasting)
What seating capacity should we build? (Decision analysis)
How much food material to prepare?
4. How to schedule the staff to ensure a certain customer service level?
(Linear programming, Waiting line management)
The Management Science Process
Information and Data:
- A bakery makes and sells birthday cakes (Cake A and Cake B)
- Cake A costs $100 to produce, Cake B costs $120
- Cake A sells for $200 while Cake B sells for $250
- Cakes A and B require 0.5 and 0.8 pounds of double cream to make, respectively
- The bakery has 20 pounds of double cream for each day
Business problem: Assuming all cakes produced can be sold out, determine the numbers of different cakes to produce to make the most profit given the limited amount of double cream available.
Decision Variable: x = number of Cake A to produce
y = number of Cake B to produce
Z = total profit
Model: Z = $200x +$250y- $100x - $120y (objective function)
0.5x +0.8y <= 20 lb of double cream (resource constraint)
Parameters: $200, $100, 0.5 lb, 20 lbs (known values)
Formal specification of model:
maximize Z = $200x + $250y - $100x - $120y
subject to 0.5x +0.8y <= 20
x >= 0, y>= 0
Total Revenue = Fixed Costs + Total Variable Costs
Total cost (TC) - fixed cost plus total variable cost
cf + Qcv
Fixed cost (cf) - cost that remains constant regardless of number of units produced. For example, rent and salaries are fixed costs; a company will pay rent and salaries even if the company does not produce any product.
Unit Variable cost (cv) - unit cost of product. For example, material cost, shipment cost and sales commission.
Total variable cost (Qcv) - Cost that changes based on activity. Increase or decrease when the company produces more or less products. It is a function of production volume (Q) and unit variable cost.
Total revenue (TR) - selling price per unit x sales volume
pQ where p is the selling price per unit
Profit(Z) - difference between total revenue Qp (p=price) and total cost:
Z = pQ – (cf+ Qcv)
Computing the Break-Even Point
The break-even point is the volume at which total revenue equals total cost and profit is zero:
Qb/e = cf/(p-cv)
The Special Products Company produces expensive and unusual gifts to be sold in stores that cater to affluent customers who already have everything. The latest new-product proposal to management from the company’s research department is a limited edition grandfather clock. Management needs to decide whether to introduce this new product and, if so, how many of these grandfather clocks to produce. Before making this decision, a sales forecast will be obtained to estimate how many clocks can be sold. Management wishes to make the decision that will maximize the company’s profit. If the company goes ahead with this product, a fixed cost of $50,000 would be incurred for setting up the production facilities to produce this product. (Note that this cost would not be incurred if management decided not to introduce the product since the setup then would not be done.) In addition to this fixed cost, there is a production cost that varies with the number of clocks produced. The unit variable (marginal) cost is $400 per clock produced. Each clock sold would generate a revenue of $900 for the company.
Q = Number of grandfather clocks to produce (Decision Variable)
cf = $50000 if Q > 0 (cf = 0 if Q = 0)
cv = $400 per unit
p = $900 per unit
Total variable cost = $400Q
Total cost = $50000 + $400Q
Total revenue = $900Q
Profit = Total revenue – Total cost
= $900Q – ($50000 + $400Q)
Qb/e = 100 units, break-even point
To cover fixed and variable costs and break even the company will need to sell 100 clocks.
Sell more clocks and as long as the fixed cost doesn't increase, each additional sale will generate an incremental gross profit of $500.
On the other hand if the company sells less than 100 clocks the company will not cover its fixed cost and will operate at a loss.
A management science study usually devotes considerable time to investigating what happens to the recommendations of the model if any of the estimates turn out to considerably miss their targets.
Building an Excel Model
to Find a Break-even Point
Mailing, buying names = $0.15
To create this model, proceed through the following steps.
VcostEnvelopes) in the Cost cells (E10, E11, E12).
The indifference point analysis determines the point at which there is no difference in profit (cost) between two alternative methods. That is, at a particular point, the decision maker has no preference for one option over another, they are equally preferred.
Example: Site Selection
A firm will set-up a production line of a new product in Hong Kong or in Shenzhen.
If the production line is set up in Hong Kong, the annual fixed cost and unit variable cost would be $10,000,000 and $300 respectively.
If the production line is set up in Shenzhen, the annual fixed cost and unit variable cost would be $8,000,000 and $400 respectively.
Determine the indifference annual demand volume (Q) of the product for which both alternatives are equally good.
TC(HK) = $10,000,000 + $300 *Q
TC(SZ) = $8,000,000 + $400 * Q
At the indifference annual demand quantity,
TC(HK) = TC(SZ)
$10,000,000 + $300 *Q = $8,000,000 + $400 * Q
Solving the equation,
Q = 20,000
At this point, both options will give a total cost of $16,000,000