or percentage of average inventory value (say 20% per year to hold inventory) or
as cost per unit per time period (say Rs. 2.50 per unit per month to hold
inventory).
It can be observed, that for increasing quantities of items, the ordering costs
decrease, while the carrying costs increase with the quantity.
Economic Order Quantity (EOQ) is then calculated by balancing the two costs.
When to order, requires fixing the re-order level. This is the stock level at which
the order replenishment is sent. This stock level is equal to the lead time multiplied
by the demand during the lead time, where lead time is the time period (in days,
weeks, etc.) between the order placement and the receipt of the goods. The re-order
level is calculated by balancing the two costs – the inventory carrying costs and the
cost of disservice to the customers in case of stockout (shortages) when the orders are
not met in time. Besides EOQ equations, linear, dynamic and quadratic programming are used to solve inventory models.
13.3.4 Allocation Models
Allocation models are applicable to problems where:
(a) a number of tasks need to be performed, with alternative ways of carrying
them out
(b) scarce resources or facilities are available.
In such situations, the goal is to assign the resources to the tasks such that the
overall effectiveness is optimised. (e.g. the total profit may be maximised or the total
cost is minimised). This is known as mathematical programming.
If the constraints can be stated as linear equalities/inequalities, this is known as
linear programming. When any of the constraints are non-linear, the outcome is
non-linear programming. In addition to linear and non-linear programming, there
are other types of programming such as integer programming where the variables
are constrained to have only integer values, parametric programming which is some
sort of sensitivity analysis, on the linear programming optimal solution, which
investigates the effect of predetermined continuous changes in the parameters of
the problem on it (optimal solution), geometric programming wherein the variables
are multiplicative unlike linear programming in which they are additive.
The simplest type of allocation model requires associating a number of tasks or
jobs to the same number of resources (men). This is called the assignment model. If
some of the tasks need more than one resource or if the resource can be used for more
than one task, the assignment problem starts developing some complexity. Such a
problem is called a transportation problem.
13.3 Types of Mathematical Models
361
as cost per unit per time period (say Rs. 2.50 per unit per month to hold
inventory).
It can be observed, that for increasing quantities of items, the ordering costs
decrease, while the carrying costs increase with the quantity.
Economic Order Quantity (EOQ) is then calculated by balancing the two costs.
When to order, requires fixing the re-order level. This is the stock level at which
the order replenishment is sent. This stock level is equal to the lead time multiplied
by the demand during the lead time, where lead time is the time period (in days,
weeks, etc.) between the order placement and the receipt of the goods. The re-order
level is calculated by balancing the two costs – the inventory carrying costs and the
cost of disservice to the customers in case of stockout (shortages) when the orders are
not met in time. Besides EOQ equations, linear, dynamic and quadratic programming are used to solve inventory models.
13.3.4 Allocation Models
Allocation models are applicable to problems where:
(a) a number of tasks need to be performed, with alternative ways of carrying
them out
(b) scarce resources or facilities are available.
In such situations, the goal is to assign the resources to the tasks such that the
overall effectiveness is optimised. (e.g. the total profit may be maximised or the total
cost is minimised). This is known as mathematical programming.
If the constraints can be stated as linear equalities/inequalities, this is known as
linear programming. When any of the constraints are non-linear, the outcome is
non-linear programming. In addition to linear and non-linear programming, there
are other types of programming such as integer programming where the variables
are constrained to have only integer values, parametric programming which is some
sort of sensitivity analysis, on the linear programming optimal solution, which
investigates the effect of predetermined continuous changes in the parameters of
the problem on it (optimal solution), geometric programming wherein the variables
are multiplicative unlike linear programming in which they are additive.
The simplest type of allocation model requires associating a number of tasks or
jobs to the same number of resources (men). This is called the assignment model. If
some of the tasks need more than one resource or if the resource can be used for more
than one task, the assignment problem starts developing some complexity. Such a
problem is called a transportation problem.
13.3 Types of Mathematical Models
361