Jayanta Kumar Dey

Two storage inventory problem with dynamic demand and interval valued lead-time over finite time horizon under inflation and time-value of money

A finite time horizon inventory problem for a deteriorating item having two separate warehouses, one is a own warehouse (OW) of finite dimension and other a rented warehouse (RW), is developed with interval-valued lead-time under inflation and time value of money. Due to different preserving facilities and storage environment, inventory holding cost is considered to be different in different warehouses. The demand rate of item is increasing with time at a decreasing rate. Shortages are allowed in each cycle and backlogged them partially. Shortages may or may not be allowed in the last cycle and under this circumstance, there may be three different types of model. Here it is assumed that the replenishment cycle lengths are of equal length and the stocks of RW are transported to OW in continuous release pattern. For each model, different scenarios are depicted depending upon the re-order point for the next lot. Representing the lead-time by an interval number and using the interval arithmetic, the single objective function for profit is changed to corresponding multi-objective functions. These functions are maximized and solved by Fast and Elitist Multi-objective Genetic Algorithm (FEMGA). The models are illustrated numerically and the results are presented in tabular form.

An interactive method for inventory control with fuzzy lead-time and dynamic demand

Abstract Normally, the real-world inventory control problems are imprecisely defined and human interventions are often required to solve these decision-making problems. In this paper, a realistic inventory model with imprecise demand, lead-time and inventory costs have been formulated and an inventory policy is proposed to minimize the cost using man–machine interaction. Here, demand increases with time at a decreasing rate. The imprecise parameters of lead-time, inventory costs and demand are expressed through linear/non-linear membership functions. These are represented by different types of membership functions, linear or quadratic, depending upon the prevailing supply condition and marketing environment. The imprecise parameters are first transformed into corresponding interval numbers and then following the interval mathematics, the objective function for average cost is changed into respective multi-objective functions. These functions are minimized and solved for a Pareto-optimum solution by interactive fuzzy decision-making procedure. This process leads to man–machine interaction for optimum and appropriate decision acceptable to the decision maker’s firm. The model is illustrated numerically and the results are presented in tabular forms.

Imperfect production inventory model with production rate dependent defective rate and advertisement dependent demand

Defective rate of items is production rate dependent in an imperfect production model.Production rate and screening rate are different.Demand of perfect items is advertisement dependent.Advertisement rate is increasing with time at a decreasing rate.Some demand of perfect items is lost due to depreciation and long run of the business. In this article, an economic production quantity (EPQ) model with imperfect production system and advertisement dependent demand has been presented. The advertisement rate has been assumed to be a function of time which has been increased with respect to time at a decreasing rate i.e., it has grown exponentially with respect to time but rate of growth gradually has decreased. Here, the rate of producing defective units has been followed to be a function of production rate. Also, the produced units have been inspected in order to screen the defective units but the screening rate is less than or equal to the production rate and greater than the demand rate. For the developed EPQ model, the total profit has been maximized to obtain the optimum production rate and production run time in the system. Here, algorithms have been developed for finding the optimal profit of the imperfect production inventory model. Finally, different numerical examples have been considered to illustrate the feasibility of the model taking different special cases in the system and then some sensitivity analyses have been carried out to get the impact of some parameters on the objective function of the model.

An EPQ model with promotional demand in random planning horizon: population varying genetic algorithm approach

One of the economic production quantity problems that have been of interest to researchers is the production with reworking of the imperfect items including waste most disposal form and vending the units. The available models in the literature assumed that the decay rate of the items is satisfied from three different points of view: (i) minimum demands of the customer’s requirement, (ii) demands to be enhanced for lower selling price and (iii) demands of the customers who are motivated by the advertisement. The model is developed over a finite random planning horizon, which is assumed to follow the exponential distribution with known parameters. The model has been illustrated with a numerical example, whose parametric inputs are estimated from market survey. Here the model is optimized by using a population varying genetic algorithm.

Multi-item EPQ model with learning effect on imperfect production over fuzzy-random planning horizon

Uncertainty is certain in the world of uncertainty. This study revisits an economic production quantity (EPQ) model with shortages for stock-dependent demand of the items with reworking and disposing of the imperfect ones over a random planning horizon under the joint effect of inflation and time value of money, where the expected time length is imprecise in nature. Transmission of learning effect has been incorporated to reduce the defective production. The total expected profit over the random planning horizon is maximized subject to the imprecise space constraint. The possibility, necessity and credibility measures have been introduced to defuzzify the model. The simulation-based genetic algorithm is used to make decision for the above EPQ model in different measures of uncertainty. The model is illustrated through an example. Sensitivity analysis shows the impacts of different parameters on the objective function in the model.

An inventory model under development cost-dependent imperfect production and reliability-dependent demand

This paper considers a model that deals with an imperfect production process where both perfect and imperfect quality items are produced. Here, demand depends on selling price and reliability of the product. Each manufacturing company expects to produce perfect quality items. But due to the long-run process, several kinds of problem such as labor, machinery, and technology arise. As a result, the manufacturing system becomes out-of-control state and consequently produces both perfect and imperfect quality items. Perfect items are ready to sell but imperfect items are reworked at a cost to become perfect. Reworking cost, reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the development cost and also by improving the quality of the raw material of the production system. Under such circumstances, a profit function has been developed to find the optimum values of reliability parameter of the manufacturing system, reliability of the product and dura...

Advertisement policy and reliability dependent imperfect production inventory control problem in bi–fuzzy environment

In this study, a problem for advertising policy and an imperfect production for single item are formulated with reliability parameter over a finite time horizon. The advertisement and production rates are function of time which are taken as control variables. In a competitive market on long run business, the demand face the depreciation of sale which is at a constant rate and decrease the demand rate but the advertisement policy has the positive effect to the demand rate. The reliability of the production process is an important factor to improve the quality of product and decrease the defective rate. So the quality of the product and advertisement policy play an important role to capture the customers in a competitive market. The selling price, holding cost and advertisement cost are bi-fuzzy in nature and using bi-fuzzy technique, the problem is converted into equivalent crisp problem and solved using Pontryaginns maximum principle and generalised reduced gradient (GRG) method. Finally, numerical experiment and graphical representation are provided to illustrate the model.

Optimal dynamic production and price for reliability-dependent imperfect production with inventory-level-dependent demand in uncertain environment

An inventory system for reliability-dependent imperfect production is introduced in uncertain environment. The demand rate depends on the stock quantity displayed in the store as well as the sales price. With the goal to realize profit maximization, an optimization problem is addressed to seek for the optimal joint dynamic pricing and production policy which are obtained by solving the optimization problem by Euler-Lagrange equation of optimal control theory. Here, initial selling price, holding cost, and raw material cost are taken as uncertain variables, and using uncertain expectation mathematics, the uncertain variables are converted into crisp value. The numerical results demonstrate the advantages of the joint dynamic one and further show the effects of different system parameters on the optimal dynamic policy and the maximal total profit.

Two layers supply chain in an imperfect production inventory model with two storage facilities under reliability consideration

Abstract This article focuses on an imperfect production inventory model with production system reliability under two layer supply chain management. Here, we consider the production system may be shift from in-control state to an out-of-control after a time which is a random variable. A development cost is incurred to improve the reliability of the production system where the reliability parameter depends on the production rate. The rate of defectiveness of the imperfect quality items is also assumed as random and depends upon the production rate and time length of the out-of-control state. A disposal cost per unit of disposed items is incurred to minimize the environmental pollution. Finally, average profit of the integrated model has been maximized by optimizing the production rate as well as defective rate of the production system and some numerical examples have been given to illustrate the feasibility of the model.

An Interactive Method for Two-plants Production Inventory Control with Two-warehouse Facility under Imprecise Environment

This paper develops an integrated production inventory model with an aim to minimize the cost of production per unit of the product and maximization of profit without compromising the quality of the product. In this model we consider two plants, two secondary warehouses (SWs) and two showrooms (SRs) those are adjacent to the respective plants. For the purpose, we assume to be erected by a firm two plants: Plant-I and Plant-II. Plant-I is situated in an urban area with a lower production capacity in comparison to its product demand where the demand meets through SR-I. On the other hand, Plant-II is situated in a rural area with higher production capacity in comparison to its product demand where the demand meets through SR-II. The excess production in Plant-II meets the current market demand in the area of Plant-I. Here, demand is assumed to be stock dependent in both the showrooms (SR-I and SR-II). Average profit in the integrated model is calculated and global optimum is obtained through a descriptive-cum-analytical review. The inventory parameters are taken as fuzzy numbers. The fuzzy numbers are first transformed into corresponding interval numbers and then follow the interval mathematics, the objective function for average profit is converted into respective multi-objective functions. Furthermore, the objective functions are being maximized and solved for a Pareto-optimum solution by interactive fuzzy decision-making procedure. The model also illustrates graphically and numerically.