13.3.7 Competitive Models
These models are used when two individuals (or organizations) or more having
conflicting goals attempt to make decisions. In such circumstances, one decisionmaker’s choice affects the decision taken by another or more of the outstanding
decision-makers.
Competitive models can be applied to a wide range of cases such as two players
trying to win a chess game, candidates standing for an election, two enemies
preparing war tactics, firms planning to preserve their market shares, collective
bargaining situations, etc. The contending individuals or organisations may not
always be at cross purposes. For example, a car dealer and a customer may be at
cross purposes with respect to the car’s price, but wish to reach a bargain for their
mutual benefit. Similarly, during a collective bargaining process, the trade union and
management endeavour to strike a mutually advantageous agreement and maintain
the ongoing company operations.
13.3.8 Queuing Models
Queuing models deal with the arrival of units to be served at one or more service
channels.
These units (or customers) may be trucks arriving at a loading station, customers
entering a departmental store, patients coming to a doctor’s clinic, ships reaching a
port, letters landing on a typist’s desk, etc. The arriving units may form one line and
get serviced, as at a cash counter in a small shop. This will occur when the system
has a single service channel (queue). It is also possible for the system to present a
number of service channels, installed in parallel or in series or a composite combination of both. In the case of parallel channels, several customers may be served
concurrently, as in a departmental store. For series channels, service is deemed to be
completed only after the customer has successively gone through all the channels. e.g., the typical administrative red tape, or a product being produced by different
processes through different equipment.
In queuing systems there is either too much or too little demand on the facilities so
that either the units or the facilities have to wait. Both types of waiting times have
associated costs. In either case, the solution lies between either scheduling arrivals or
providing extra facilities or both in order to achieve an optimum balance between
waiting time costs and idle time costs.
13.3.9 Dynamic Programming Models
Dynamic programming models are applicable when a series of inter-related decisions are required for multi-stage problems extending over several time periods
13.3 Types of Mathematical Models
363
These models are used when two individuals (or organizations) or more having
conflicting goals attempt to make decisions. In such circumstances, one decisionmaker’s choice affects the decision taken by another or more of the outstanding
decision-makers.
Competitive models can be applied to a wide range of cases such as two players
trying to win a chess game, candidates standing for an election, two enemies
preparing war tactics, firms planning to preserve their market shares, collective
bargaining situations, etc. The contending individuals or organisations may not
always be at cross purposes. For example, a car dealer and a customer may be at
cross purposes with respect to the car’s price, but wish to reach a bargain for their
mutual benefit. Similarly, during a collective bargaining process, the trade union and
management endeavour to strike a mutually advantageous agreement and maintain
the ongoing company operations.
13.3.8 Queuing Models
Queuing models deal with the arrival of units to be served at one or more service
channels.
These units (or customers) may be trucks arriving at a loading station, customers
entering a departmental store, patients coming to a doctor’s clinic, ships reaching a
port, letters landing on a typist’s desk, etc. The arriving units may form one line and
get serviced, as at a cash counter in a small shop. This will occur when the system
has a single service channel (queue). It is also possible for the system to present a
number of service channels, installed in parallel or in series or a composite combination of both. In the case of parallel channels, several customers may be served
concurrently, as in a departmental store. For series channels, service is deemed to be
completed only after the customer has successively gone through all the channels. e.g., the typical administrative red tape, or a product being produced by different
processes through different equipment.
In queuing systems there is either too much or too little demand on the facilities so
that either the units or the facilities have to wait. Both types of waiting times have
associated costs. In either case, the solution lies between either scheduling arrivals or
providing extra facilities or both in order to achieve an optimum balance between
waiting time costs and idle time costs.
13.3.9 Dynamic Programming Models
Dynamic programming models are applicable when a series of inter-related decisions are required for multi-stage problems extending over several time periods
13.3 Types of Mathematical Models
363