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Inventory model for deteriorating items with negative exponential demand, probabilistic deterioration and fuzzy lead time under partial back logging

100%
SEN N., SAHA S.
Operations Research and Decisions
|
2020
|
vol. 30
|
issue 3
97-112
EN
The effect of lead time plays an important role in inventory management. It is also important to study the optimal strategies when the lead time is not precisely known to the decision-makers. This paper aimed to examine the inventory model for deteriorating items with fuzzy lead time, negative exponential demand, and partially backlogged shortages. This model is unique in its nature due to prob-abilistic deterioration along with fuzzy lead time. The fuzzy lead time was assumed to be triangular, parabolic, trapezoidal numbers. The graded mean integration representation method was used for the defuzzification purpose. Three different types of probability distributions, namely uniform, triangular and beta were used for rate of deterioration to find optimal time and associated total inventory cost. The developed model was validated numerically, and values of optimal time and total inventory cost are given in a tabular form, corresponding to different probability distributions and fuzzy lead-time. The sensitivity analysis was performed on the variation of key parameters to observe its effect on the devel-oped model.
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An inventory model to study the effect of the probabilistic rate of carbon emission on the profit earned by a supplier

100%
BHATTACHARJEE N., SEN N.
Operations Research and Decisions
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2021
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vol. 31
|
issue 4
5-33
XX
The inventory of suppliers providing raw materials to industries producing green products faces two challenging problems. The first one is that raw materials are usually deteriorating items and the second one is that they emit carbon-based gases durin g deterioration. Moreover, each item has its unique carbon emission rate and composition, called the pattern of carbon emission, which is a function of the rate of carbon emission. In this present research, we attempt to develop a stochastic inventory model with price, stock, and pattern of carbon emission-dependent demand to maximise the profit of a supplier selling a single product. The rate of deterioration is a function of the rate of carbon emission and effective investment in preservation. The cost of carbon emission is a function of green investment and the pattern of carbon emission. Holding costs and purchase costs are constant. We consider three patterns of carbon emission, and each pattern is defined by a negative exponential function. The rate of carbon emission is assumed to be probabilistic and follows one of the three probabilistic distributions: uniform, triangular, and beta. Numerical validation is provided together with sensitivity analysis of the parameters for managerial insights. Analysis of the effect of carbon emission on the profit earned is made and results are interpreted. Particle swarm optimisation (PSO) and genetic algorithm (GA) are applied to solve the model, while statistical analysis and sensitivity analysis of the parameters of the algorithm are provided along with the graphical representation of convergence.
3
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An inventory model for deteriorating items with imperfect quality under advance payment policy

100%
NATH B. K., SEN N.
Operations Research and Decisions
|
2021
|
vol. 31
|
issue 3
109-135
EN
In the business world, it is generally observed that the supplier gives a cash discount due to advance payment. The buyer may either pay off the total purchase cost or a fraction of the total purchase cost before receiving the products. If the buyer makes full payment then he receives a cash discount instantly. If the buyer pays a fraction of the total pur chase cost, then he receives the cash discount while paying the remaining amount at the time of receiving the lot. Moreover, in most of the inventory models, it is generally assumed that the delivered lot contains only perfect items. But in reality, the presence of imperfect items in the received lot cannot be overlooked as it will affect the total profit of the system. Thus, the study of inventory models considering the presence of imperfect items in the lot makes the model more realistic and it has received much attention from inventory managers. This paper develops a model that jointly considers imperfect quality items and the concept of an advance payment scheme (full and partial). The objective is to determine optimal ordering quantity to maximise the total profit of the system. The necessary theoretical results showing the existence of global maximum is derived. The model is illustrated with the help ofnumerical examples, and sensitivity analysis is carried out on some important system parameters to see the effects on the total profit of the system. The study shows that a full advance payment scheme is beneficial for the buyer.
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