Production Lot Size Inventory Model Research Articles

A partial backlogging production-inventory lot-size model for deteriorating items with time-varying production and demand rate over a finite time horizon

In this article, I extend Balkhi ((2001), ‘On a Finite Horizon Production Lot Size Inventory Model for Deteriorating Items: An Optimal Solution’, European Journal of Operational Research, 132, 210–223), by considering a generalised mathematical production-inventory model for deteriorating items with partial backlogging. The demand, production and backlogging rates are assumed to be continuous and varying with time. The objective is to find the optimal production restarting and stopping time to keep the total relevant cost as low as possible. To ascertain the optimal solution exists, the conditions for the total relevant cost in the system which attains its global minimum are provided. In addition, based on the minimum total relevant cost, an alternative among the proposed four cases is also suggested. Finally, a numerical example and sensitivity analysis is illustrated and some management insights are presented.

A production lot-size model with Fuzzy-Ramp type demand and fuzzy deterioration rate under permissible delay in payments

A production lot-size inventory model is developed with finite production rate, fuzzy deterioration and demand rate under permissible delay in payments. Here it is assumed that the initial demand rate of ramp-type demand and the deterioration rate are uncertain in fuzzy sense i.e., imprecise in nature. The initial demand rate and deterioration rate are taken as triangular fuzzy number. Using α -cut for defuzzification, the total variable cost per unit time is derived. The multi-objective model is solved using Global Criteria Method and is illustrated with a numerical example. Sensitivity analysis has been made for different values of α .

Improving production policy for a deteriorating item under permissible delay in payments with stock-dependent demand rate

This paper presents a production lot size inventory model in which the production rate constitutes of productions during both regular time and overtime. The demand rate is assumed as stock-dependent and the stock itself is depleted due to demand and deterioration. Supplier’s incentives include price discounts and granting of credit periods for account settlement within time M 1 , or the supplier allows interest-free credit upto an extended period M 2 . This formulation leads to a single objective optimization problem for maximum average profit evaluation through a real-coded genetic algorithm (GA) with rank-based selection and arithmetic crossover. The model is illustrated through a numerical example, and sensitivity analyses have been done with the variation of demand and deterioration parameters on optimal profit.

An optimal solution of a general lot size inventory model with deteriorated and imperfect products, taking into account inflation and time value of money

This paper considers a general production lot size inventory model with deteriorated and imperfect products taking into account inflation and time value of money. The production, demand, and deterioration rates are known, continuous, and differentiable functions of time. Shortages are allowed, but only a fraction of the stock out is backordered, and the rest is lost. Under these general assumptions, the inventory model is formulated, and a closed form of the total relevant costs of the underlying inventory system is obtained. Sufficient conditions which lead to a minimal solution of the considered problem are derived. Then, a rigorous mathematical analysis is used to prove that such a minimal solution is unique and global-optimal. A numerical verification of the proposed model is also given.

On a finite horizon production lot size inventory model for deteriorating items: An optimal solution

A generalized production lot size inventory model for deteriorating items over a finite planning horizon is considered. The demand, production, and deteriorating rates are assumed to be known and continuous functions of time. Shortages are allowed and completely backlogged. The conditions under which the system total cost attains its (unique) global minimum are derived. An example which illustrate the applicability of theoretical results is also introduced.

A production lot size inventory model for deteriorating items with time-varying demand

A production lot size inventory model for deteriorating items with time-varying demand

A production lot size inventory model for deteriorating items with time-varying demand

This paper presents a production lot size model for deteriorating items with time-varying demand. The replenishment cycle and deterioration rates are allowed to vary over a finite planning horizon. A solution procedure for this model is developed to provide the optimal replenishment cycle number. Also three numerical examples are solved for different deterioration rates. Finally, a sensitivity analysis is conducted to study the effect of changes in the related parameters on the objective function.

A production lot size model for deteriorating items with inventory level dependent production and demand rate

In this paper, a production lot size inventory model for deteriorating items with inventory-level dependent production and demand rate is developed. The production rate and demand both are dependent on the instantaneously level, and an alternative optimization technique is presented to derive an optimal production policy. The method is illustrated by a numerical example and a sensitivity analysis of the optimal solution with respect to parameters of the system is also carried out.

Multi-item production lot-size inventory model with varying order cost under a restriction: A geometric programming approach

In this paper we present a geometric programming approach for determining the inventory policy for multiple items having varying order cost, which is a continuous function of the order quantity, and a limit on the total average inventory of all items. Our model is a generalization of that of Gupta and Gupta for unrestricted single-item order quantity model with varying order cost and assumes the same order cost function. This cost function relates well to real-life situations since it increases as the order quantity increases and, at the same time, it is easy to handle when deducing previous work as special cases of our model since it is easily reducible to a constant. An example is solved to illustrate the method.

A production lot size inventory model for deteriorating items and arbitrary production and demand rates

In this paper, we present a method for finding the optimal replenishment schedule for the production lot size model with deteriorating items, where demand and production are allowed to vary with time in an arbitrary way and in which shortages are allowed. The method is illustrated by a numerical example.

An advertising-inclusive production lot size model under continuous discount pricing

This article deals with the interaction of a deterministic production lot size inventory model with uniform replenishment rate and differential pricing conditions. We present a method for arriving at a production lot size formula, which takes into account the effect of varying marketing conditions on demand and the possibility of defective items in the production process. Additionally, based upon the previous studies, different model formulations are introduced to deal with the issue of defective items. The profile maximization problem for this model is derived for two quantity discount cases: hyperbolic-decreasing and linear-decreasing. A numerical example along with sensitivity analysis is provided to illustrate the results derived. Furthermore, an easy-to-use computer algorithm is developed to determine the optimal values of production lot-size and profit.

A production lot size inventory model for deteriorating items

In this paper, an attempt has been made to develop a production lot size model which incorporates an unfilled-order backlog for an inventory system with exponential decaying items. Approximate expressions are obtained for the optimum production lot size, the production cycle time and the total cycle time. The theory is illustrated by considering a numerical example of this class. Also it is shown that earlier models developed by Ghare and Schrader [3] and Misra [5] can be obtained as particular cases by choosing appropriate values for the various parameters of the model.