Quantitative Methods in Business: Inventory Control, Transportation, Distribution and Network Model

Assignment 3: Quantitative Methods in
Business

Table of Contents
Question 1: Inventory Control...................................................................................................3
Question 2: Transportation.........................................................................................................5
Solution by applying Northwest Corner Rule........................................................................7
Solution by applying stepping stone method.........................................................................7
Question 3: Distribution and network model...........................................................................10
References................................................................................................................................12

QUESTION 1: INVENTORY CONTROL
Inventory control can be broadly defined as procedure relating to assessment and evaluation
of the inventory of company. The main objective of the inventory control is to maximize the
profit by maintaining the minimum inventory (Larsen, and Thorstenson, 2014). Inventory
control also known as stock control which involves the procedure of coordination and the
supervision of the supply, distribution, storage , and recording of the raw material to maintain
stock sufficient in accordance with requirement of business (Garrido-Jurado& et.al 2016).
Thus, inventory control assists the company to avoid excessive stock of its products so that
cost of maintaining the stock can be minimized. There are several methods of inventory
control which assists in determining the optimum level of inventory. Linear Programming
method is one of the best techniques which is applied for ascertaining the optimum level of
inventory (Gleixner, Steffy, and Wolter, 2016).
Linear programming method presents the comprehensive connections through the linear
functions and then assesses the optimum points. There are some common terms, which are
used in this method and same have been discussed defined below –
Decision Variable
The result of discussed issue is determined through application of the decision variable. They
reflect the ultimate outcome. In order to address any problem, it is necessary to ascertain the
decision variable on mandatory basis (Dokeroglu, 2015).
Objective function
It can be referred as goal of making decision. In the given problem, the company wants to
maximize its profit. It is denoted by Z. thus, the objective function of the current problem is
maximization of profit (Ma, and Saunders, 2015).
Constraints
The decision variable of the problem is limited or restricted by the constraints. Generally,
they restrict (limit) the value of the decision variable. In the given problem, advertising
budget, square footage and rental limits are constraints.
Non-Negativity limitation

In Linear Programming Method, the non-negativity limitation must be satisfied. In other
words, it can be said that values of the decision variable must be 0 or more than 0.
In order to solve Linear Programming problem, simplex method is one of the most
appropriate method. For solving the problem through the simplex method, objective function
is required. The objective may be maximization of the profit or the minimization of the cost
which depends on the nature of problem (METLO, SOLANGI, and MEMON, 2016). Present
discussed problem is related with the maximization of the profit. There are one or more
constraints in the problem, which represents the real value number. It is required to put the
problem in the standard manner. The inequalities in the constraints should be modified
through inserting slack or the surplus variable in the equation (Bisht, and Srivastava, 2017).
The new variables present about the unutilized capacity of the company. After this, the
problem should be arranged in the matrix form and objective function is required to added at
the bottom of the matrix. The first step of this method is to find out the initial basic feasible
solution by allocating zero values to the decision variable. It is also known as initial simplex
table. Thus, optimum solution is attained after accomplishment of test of optimality and test
of feasibility (Reyes, Solano-Charris, and Montoya-Torres, 2019).
In the given problem, Ghourfa warehousing Ltd. wants to determine the number of storage
room of each size.
X1 X2
Maximize Monthly earnings 60 0 Z
C 50 20 3000
Constraints Total b
Advertising Budget Available 2 4 120 <= 400