4 research outputs found
A first course on operations research and information theory
The text, self-contained in every possible way, attempts to furnish both theoretical and computational aspects of the subject as well as a number of practical applications. Suitable numerical examples and graphical illustrations are also provided to help the readers understand the concepts and methods discussed. Each chapter contains many exercise many exercise, which include: 1. Simple numerical problems to reinforce the materials discussed in the text. 2. Problems introducing new materials related to those developed in the text and some exercise for advanced students
The constrained gravity model with power function as a cost function
A gravity model for trip distribution describes the number of
trips between two zones, as a product of three factors, one of the
factors is separation or deterrence factor. The deterrence factor
is usually a decreasing function of the generalized cost of
traveling between the zones, where generalized cost is usually
some combination of the travel, the distance traveled, and the
actual monetary costs. If the deterrence factor is of the power
form and if the total number of origins and destination in each
zone is known, then the resulting trip matrix depends solely on
parameter, which is generally estimated from data. In this paper,
it is shown that as parameter tends to infinity, the trip matrix
tends to a limit in which the total cost of trips is the least
possible allowed by the given origin and destination totals. If
the transportation problem has many cost-minimizing solutions,
then it is shown that the limit is one particular solution in
which each nonzero flow from an origin to a destination is a
product of two strictly positive factors, one associated with the
origin and other with the destination. A numerical example is
given to illustrate the problem
Development of a Fuzzy Economic Order Quantity Model of Deteriorating Items with Promotional Effort and Learning in Fuzziness with a Finite Time Horizon
This study investigates an economic order quantity model of deteriorating items, where demand is fuzzy in nature and depends on promotional effort with full backorder for a given time horizon. The learning effect in the fuzzy environment is added in this model. A constant deterioration rate is assumed. Under these circumstances, a mathematical model is developed to curtail the total cost over a finite time horizon by determining the replenishment order quantity, number of replenishments, and the fraction of the replenishment cycle when inventory is positive. A solution algorithm is developed to find the optimal solutions. The applicability of the proposed model is illustrated through numerical examples. To get further insights, sensitivity analysis is carried out for the main parameters in crisp, fuzzy, and fuzzy-learning environments