Showing papers by "S.R. Singh published in 2012"

An Optimal Returned Policy for a Reverse Logistics Inventory Model with Backorders

Abstract: Environmental responsibility plays a significant role in the firm’s agendas nowadays. In this paper, we address the environmental operations of reverse logistics. Here we developed an integrated supply chain model with coordinated production and remanufacturing due to time-dependent rates. To study the problem we consider the demand to be satisfied with newly manufactured (produced) and the remanufactured products, so there is no difference between manufactured and remanufactured items. The shortages are allowed and excess demand is backlogged as well. The returned items are collected from the end user to be remanufactured. Optimal expression is obtained for the acceptable returned quantity, maximum inventory level, production and remanufacturing scheduling period, and the total average cost. Illustrative examples, which explain the application of the theoretical results as well as their numerical verifications, are given. The sensitivity of these solutions to change in underling parameter values is also discussed.

Inventory model of deteriorating items with two-warehouse and stock dependent demand using genetic algorithm in fuzzy environment

Abstract: Multi-item inventory model for deteriorating items with stock dependent demand under two-warehouse system is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise ) under inflation and time value of money. For display and storage, the retailers hire one warehouse of finite capacity at market place, treated as their own warehouse (OW), and another warehouse of imprecise capacity which may be required at some place distant from the market, treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) functions as well as some constraints are imprecise in nature, too. The model is formulated so to optimize the possibility/necessity measure of the fuzzy goal of the objective functions, and the constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve the model, which is illustrated on a numerical example. Keywords: Possibility/Necessity Measures, Inflation, Time Value of Money, Deterioration, Genetic Algorithm.

An economic production lot-size (EPLS) model with rework and flexibility under allowable shortages

Abstract: This paper develops a model to determine the optimal reliability and production rate that achieves the biggest total integrated profit for an imperfect production process under allowable shortage. This paper extends the paper of Sana (2010). Here, we consider two type of production process in a cycle time. One is 'in-control' state at the starting of the production which provides conforming quality items and second one is 'out-control' state after certain time due to higher production rate and production run time. In this study, we also consider that selling price of the units depends upon the unit production cost and screening cost of the items. The total cost function is illustrated by numerical examples and also its sensitivity analysis is carried out.

Three echelon supply chain inventory model for deteriorating items with limited storage facility and lead-time under inflation

Abstract: In this study, we have explored a three echelon supply chain inventory model with limited storage facility under inflation. The supplier experiences the problem of lead-time at his end. So even though the retailer has placed the order, he has to wait for the supplier to deliver. The lead-time of the supplier is a probability density function of his managing cost. The more the supplier is ready to spend as managing expenses, smaller will be the lead time and vice versa. However, there is a constraint upon the amount the supplier can afford to spend; hence there involved capital constraint also. For the retailer, we have considered the two situations according to rented and own warehouse used. Due to the life time in RW, the product has no deterioration but in OW, the product has deterioration. The setup has been explored numerically and the sensitivity has also been analysed.

An Inventory Model with Time-Dependent Demand and Limited Storage Facility under Inflation

Abstract: The main objective of this paper is to develop a two-warehouse inventory model with partial backordering and Weibull distribution deterioration. We consider inflation and apply the discounted cash flow in problem analysis. The discounted cash flow (DCF) and optimization framework are presented to derive the optimal replenishment policy that minimizes the total present value cost per unit time. When only rented or own warehouse model is considered, the present value of the total relevant cost is higher than the case when two-warehouse is considered. The results have been validated with the help of a numerical example. Sensitivity analysis with respect to various parameters is also performed. From the sensitivity analysis, we show that the total cost of the system is influenced by the deterioration rate, the inflation rate, and the backordering ratio.

A Warehouse Imperfect Fuzzified Production Model with Shortages under Inflationary Conditions

Abstract: We develop a two-warehouse production model with imperfect items. Production rate is taken as the linear combination of on-hand inventory and demand, while demand rate is taken as function of time. Most of the researchers consider that the production rate is independent from the demand rate. In this paper we assume production rate as being dependent on the demand rate, and this assumption is more realistic. Shortages are allowed and partially backlogged with time-dependent backlogging rate. Due to different preservation facilities we consider that the deterioration rate is time dependent in own warehouse (OW) and Weibull distribution deterioration in rented warehouse (RW). Holding cost in RW is greater than in OW. We developed a fuzzy model with fuzzifying all the costs of the model as triangular fuzzy numbers. The present model is developed in both crisp and fuzzy senses. Finally, numerical example is shown, and sensitivity is also illustrated.

Effect of demand boosting policy on optimal inventory policy with backorder in fuzzy environment under the effect of learning

Abstract: Most of inventory control policies are very sensitive to different marketing strategy (especially in chemical, food and automotive industries) under the learning effect. Realising the importance that there is a functional relationship between demand rate and advertisement frequency of such inventory, a marketing model is developed for determining the economic order quantity and backorder level. This model also incorporates the effect of learning in holding cost, ordering cost and on the number of defective items present in each lot. Profit expression is fuzzy due to impreciseness in demand. In order to determine the optimal values, we obtained equivalent crisp expression by applying signed distance method. In place of complex and tedious method of calculus a closed form solution is obtained by using algebraic method. A numerical example is presented to study the feasibility and applicability of the proposed model.

Production Scheduling for Damageable Items with Demand and Cost Flexibility Using Genetic Algorithm

Abstract: In this paper, a production inventory model is designed with the assumption made about the cost function that will influence the empirical results obtained regarding measurement of volume flexibility. We consider a particular kind of products which are usually stored in stacks and damaged during the storage due to accumulated stress of heaped stock. These are known as damageable items. Here the model is developed for such items with stock-time-price sensitive demand and shortages. The unit production cost is taken to be a convex function of the production rate. The mathematical expression for the total relevant cost is derived and it is minimized subject to different constraints of the system. Because of the nonlinearity and complexity of the problem, the model is solved numerically and the final evaluations are made using genetic algorithm (GA). A numerical example is given and sensitivity analyses are performed to analyze the influence of various parameters on the overall cost. The results can help those manufacturing firms which deal in damageable products.

Application of minimax distribution free procedure and Chebyshev inequality for backorder discount inventory model with effective investment to reduce lead-time and defuzzification by signed distance method

Abstract: This paper considers the mixture inventory model involving variable lead-time with discounted backorder model. We first fuzzify the demand rate, based on triangular fuzzy number and obtain the total cost in the fuzzy sense. Defuzzification of expected annual cost is performed by signed distance. We provide a solution procedure to find the optimal values of lead-time, order quantity and backorder price discount by using minimax distribution free approach and Chebyshev inequality. We also prove the concavity and convexity of the estimate of total variable cost per unit time in fuzzy sense. Through numerical example, it is shown that there is a significant saving in cost due to crashing cost to reduce the lead-time.

Integrated management of collar rot of lentil caused by Sclerotium rolfsii.

Abstract: Several diseases are known to infect lentil (Lens culinaris Medik) during its growth stages. Among them, collar rot caused by Sclerotium rolfsii Sacc., is very common in all the major lentil growing areas (Butler and Bisby, 1931). The disease causes appreciable loss in yield due to which, area under this crop is consistently decreasing. For restoring the area production and productivity of lentil, it is necessary to reduce the loss caused by this disease. Therefore, some new seed dressing fungicides along with existing ones were tested in the present study to the manage the above disease in-vitro and results are reported in this investigation. MATERIALS AND METHODS