# SBA Module 5 ```Dalubhasaan ng Lungsod ng Lucena
S.Y. 2020-2021
MODULE 5: QUANTITATIVE MANAGEMENT AND TECHNIQUES
Learning Objectives:
a. Understand the nature and concepts of quantitative management and techniques.
b. Apply quantitative techniques in solving business problems
Metalanguage
Quantitative techniques – refer to the application of mathematics in actual business operations.
It is also known as quantitative methods.
Operations research - refers to the discipline of applying quantitative methods in organizational
planning and control.
Introduction
Managerial activities have become complex and it is necessary to make right decisions to avoid
heavy losses. Whether it is a manufacturing unit, or a service organization, the resources have to
be utilized to its maximum in an efficient manner. The future is clouded with uncertainty and fast
changing, and decision-making – a crucial activity – cannot be made on a trial-and-error basis or
by using a thumb rule approach. In such situations, there is a greater need for applying scientific
methods to decision-making to increase the probability of coming up with good decisions.
Quantitative Technique is a scientific approach to managerial decision-making. The successful
use of Quantitative Technique for management would help the organization in solving complex
problems on time, with greater accuracy and in the most economical way. Today, several
scientific management techniques are available to solve managerial problems and use of these
information to select an optimal decision.
The Quantitative Analysis Approach
The methodology adopted in solving problems is as follows:
Network Models
Network models involve project scheduling techniques that are designed to aid the planning and
control of large-scale projects having many interrelated activities. These models aid management
in predicting and controlling costs that pertain to certain projects or business activities.
Common project scheduling techniques (Network Models)
1.
2.
3.
4.
5.
6.
7.
Gantt or bar chart
Program Evaluation and Review Technique (PERT)
Critical Path Method (CPM)
Probability Analysis
Learning Curves
Inventory Models
Linear Programming
1. GANTT OR BAR CHARTS
The project is divided into different sub-projects called activities or tasks. The starting and
completion time of activity is estimated and a bar chart is prepared showing each activity as a
horizontal bar along a time scale.
2&amp;3. PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) – CRITICAL PATH METHOD
(CPM)
PERT is developed to aid managers in controlling large-scale, complex problems.

PERT diagram is a probabilistic diagram of the interrelationship of a complex series of
activities; it is a free-form network showing each activity as line between events.
 EVENTS – discrete moment in time representing the start or finish of an activity; they
consume no resources.
 ACTIVITES – tasks to be accomplished; they consume resources (including time)
The following are the common type of activities:
o Series – an activity cannot be performed unless another activity is undertaken
o Parallel – can be performed simultaneously
CPM, like PERT, is a network technique, but unlike PERT, it uses deterministic time and cost
estimates; its advantages include cost estimates plus the concept of crash efforts and costs.


CRITICAL PATH – is longest path through the PERT network.
EXPECTED TIME – is the average time an activity would require if it were repeated
several times.
te = (to + 4 tm + tp) / 6
Where to –optimistic time; tm – most likely time; tp – pessimistic


SLACK TIME – the amount of time that can be added to an activity without increasing
the total time required on the critical path; the length of time an activity can be
delayed without forcing a delay for the entire project.
CRASH TIME – the amount of time to complete an activity assuming that, under rush
or urgent condition, all available resources were devoted to the task (e.g., overtime,
extra labor, etc.); any crash time spent in an activity normally would incur crash cost.
PERT VS. CPM Key Differences
PERT
CPM
4. PROBABILITY ANALYSIS
Probability Analysis is important to decision-making because of the unpredictability of future events.
Decision-making involves:


RISK – this occurs when the probability distribution of the possible future state of nature is
known.
UNCERTAINTY – this occurs when the probability distribution of possible future state of
nature is not known and must be subjectively determined.

The probability of an event varies from 0 to 1 (0% to 100%). 100% or probability of 1.0 means that
event is certain to occur while zero probability means the event cannot occur under any circumstances.
THE CONCEPT OF EXPECTED VALUE
The expected value of an action is found by multiplying the probability of each outcome by its payoff and summing up the products. A decision tree diagram is normally devised to show the several decisions
or acts and the possible consequences (outcome or events) of each act.






Objective probabilities – calculated from either logic or actual experience.
Subjective probabilities – estimates, based on judgment, of the likelihood of future events.
Two events are said to be mutually exclusive if they cannot occur simultaneously.
Two events are said to be independent if occurrence of one has no effect on probability of another.
The joint probability of two events is the probability that both will occur.
The conditional probability of two events is the probability that one will occur given that the other
5. LEARNING CURVES
Learning curves describes the efficiencies arising from experience, because with experience
comes increased productivity. This productivity increases with production size, but at decreasing
rate as diagrammed below:
The time required to perform a given task becomes progressively shorter, but this is applicable
only to the early stages of production or any new stages
The curve is expressed as a percentage of reduced time (usually between 60% and 80%) to
complete a task of each doubling of cumulative production. Hence, the time required is reduced
by 20% to 40% each time cumulative production is doubled.


The cumulative average time per unit is reduced by a certain percentage each time
production doubles
Incremental unit time (time to produced the last unit) is reduced when production
6. INVENTORY MODELS
Inventory models are usually devised to minimize the cost associated with inventory while
maintaining certain level of inventories needed to sustain smooth operations.
The total inventory costs are comprised of:

CARRYING COSTS: This cost increases with order size or quantity of inventory on hand
Example: Storage cost, insurance on inventory, normal spoilage, record keeping cost, etc.

ORDERING COSTS: This cost decreases with order size or quantity of inventory on hand
THE CONCEPT OF ECONOMIC ORDER QUANTITY (EOQ)
EOQ is the quantity to be ordered that minimizes the sum of ordering cost and carrying cost. EOQ
tries to answer the question “How many units should be ordered (and when to order) to minimize
inventory costs?”
Where: o = Cost of placing one order (ordering cost)
D = Annual demand in units
K = Annual cost of carrying one unit for one year
EOQ =
2 Do
k
At EOQ, a firm incurs the minimum total inventory costs computed as follows:
TC 
EOQ
D
(k ) 
(o)
2
EOQ
Average inventory is computed as follows:



No safety stock: EOQ/2
With safety stock: EOQ/2 + safety stock
If EOQ is not available: (beginning inventory + Ending Inventory)/2
Assumptions of EOQ models:



Annul determinable demand for inventory is spread evenly throughout the year.
Lead time does not vary and each order is delivered in a single delivery.
The unit costs of the time ordered are constant; thus, there can be no quantity discounts.
When applied to production operations, the EOQ formula is used to compute the Economic Lot
Size (ELS)
ELS =
2 Do
k
Where: o = Set-up cost
D = Annual production requirement
K = Annual cost of carrying one unit for one year
EOQ-RELATED TERMINOLOGIES
 Lead time is period between the time the order is placed and received
 Normal time usage is derived by multiplying normal lead time with average usage
 Safety stock = (maximum lead time – normal lead time) x average usage or demand
 Order (Reorder) point is the inventory level that automatically calls for a new order
When to order is a stock-out problem; the objective is to order at a point in time so as not to run
out of stock before receiving the inventory ordered but not so early that an unnecessary quantity
of safety stock is maintained. When order point is computed, there may be stock-out situation if:
 Demand is greater than expected during the lead time, or
 The order time exceeds the lead time


Re-order point (without safety stock)
Re-order point (with safety stock)
= Normal lead time usage + safety stock
= Maximum lead time x average usage
7. LINEAR PROGRAMMING
Linear programming is a mathematical technique that helps managers to determine the volume
of various products to produce when resources are limited or scarce in order to maximize net
income. It is a technique used to optimize an objective function (maximize revenue of profit
function, or minimize a cost of function), subject to constraints (such as scarce resources,
minimum/maximum levels of production, performance, etc.)
Maximize revenue
OBJECTIVE
Maximize net profit
Minimize costs and expenses
Limited resources must be allocated to the company’s most profitable products so that net
income is maximized. Linear programming models are extremely helpful in the analysis and
solution of resource allocation problems.
Simplex method is a more complex linear programming technique especially useful if there are
more than two variables in a linear programming problem.
Exercises
Problem 1 Network Analysis
Palafox Construciton Firm, Inc. will soon begin to work on a building for US Tea that was initially
started by another firm that has gone out of business. The construction firm’s schedule of
activities and related expected completions times for US Tea project are presented in the
following time table:
Activity Code
Activity Description
Estimated Time (in
weeks)
A-B
Obtain on-site work permits
1
B-E
Repair damages done by vandals
6
B-C
Inspect construction materials left on
1
site
C-E
Order
and
2
construction materials
C-D
Apply for waiver to add new materials
2
D-E
Obtain waiver to add new materials
2
E-F
Perform electric work
12
F-G
Complete interior partitions
4
Required:
a. Prepare the PERT network.
b. Identify critical path and determine the path’s expected time in weeks for the project.
c. Which path requires the shortest time to complete? What is the path’s slack time?
Problem 2. Probability Analysis
Tamansky Sports Club sells cold sodas at Far East College’s home basketball games. In the year
2021, the frequency of distribution of the demand for cups of sodas per day is presented below:
Sales Volume in Cups
Frequency
2,000
48 days
5,000
80 days
6,000
144 days
8,000
32 days
10,000
16 days
Required: Determine next years’ estimated daily demand for cups of sodas at Far East College’s
home games using:
a. Deterministic approach (based on most likely event)
b. Expected value approach
Problem 3. Learning Curves
A particular manufacturing job is subject to an estimated 80% learning curve. The first unit
required 20 direct labor hours to complete.
Required:
a. What is the cumulative average time per unit after four units are completed?
b. What is the total time required to produce 2 units?
c. How many hours are required to produce the second unit
Problem 4. Inventory Models
Shirley Company requires 40,000 shells for its P500-signature product, “pearly Shirl”. The shells,
which are purchased from outside suppliers, will be used evenly throughout the year. The cost
to place one order is P20, while the cost to carry the shells in inventory for one year is P0.40
Required:
a. The optimal order (economic order quantity)
b. The number of times the company should place orders within a year.
c. The average inventory.
Problem 5. Economic Order Quantity
Based on EOQ analysis, the optimal order quantity is 3,000 units. Annual inventory carrying cost
equal 30% of the average inventory level. The company pays P 5 per unit to buy the product,
selling for P 12. The company pays P112.50 to place an order. The monthly demand for the
product is 5,000 units.
Required:
a. Annual inventory carrying cost
b. Annual inventory ordering cost
c. Total inventory costs
Problem 6. Linear Programming
Following are the data about Maximin Company’s two products that it produces through its
production facilities:
Product A
Product B
Contribution Margin Per Unit
P3
P4
Materials Used:
Material X
2 units
5 units
Material Y
4 meters
2 meters
Available Quantity of Materials:
Material X
120 pieces
Material Y
80 meters
Required:
a. Objective function – involving maximization of the company’s contribution margin.
b. Constraint function for Material X
c. Constraint function for Material Y
d. The optimal mix of products that must be produces by Maximin Company.
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