An EOQ model for time-dependent deteriorating items with alternating demand rates allowing shortages by considering time value of money

The present paper deals with an economic order quantity (EOQ) model of an inventory problem with alternating demand rate: (i) For a certain period, the demand rate is a non linear function of the instantaneous inventory level. (ii) For the rest of the cycle, the demand rate is time dependent. The time at which demand rate changes, may be deterministic or uncertain. The deterioration rate of the item is time dependent. The holding cost and shortage cost are taken as a linear function of time. The total cost function per unit time is obtained. Finally, the model is solved using a gradient based non-linear optimization technique (LINGO) and is illustrated by a numerical example

An Inventory Model for Deteriorating Commodity under Stock Dependent Selling Rate

Economic order quantity (EOQ) is one of the most important inventory policy that have to be decided in managing an inventory system. The problem addressed in this paper concerns with the decision of the optimal replenishment time for ordering an EOQ to a supplier. This Model is captured the affect of stock dependent selling rate and varying price. We developed an inventory model under varying of demand-deterioration-price of commodity when the relationship of supplier-grocery-consumer at stochastic environment. The replenishment assumed instantaneous with zero lead time. The commodity will decay of quality according to the original condition with randomize characteristics. First, the model is addressed to solve a problem phenomenon how long is the optimum length of cycle time. Then, an EOQ of commodity to be ordered by will be determined by model. To solve this problem, the first step is developed a mathematical model based on reference’s model, and then solve the model analytically. Finally, an inventory model for deteriorating commodity under stock dependent selling rate and considering selling price was derived by this research. Keywords: deterioration commodity, expected profit, optimal replenishment time stock dependent selling rate

Optimal Ordering and Trade Credit Policy for EOQ Model

Trade credit is the most prevailing economic phenomena used by the suppliers for encouraging the retailers to increase their ordering quantity. In this article, an attempt is made to derive a mathematical model to find optimal credit policy and hence ordering quantity to minimize the cost. Even though, credit period is offered by the supplier, both parties (supplier and retailer) sit together to agree upon the permissible credit for settlement of the accounts by the retailer. A numerical example is given to support the analytical arguments.Trade Credit, Optimal ordering quantity, Lot-size

Optimal order quantities with volume discounts before and after price increase

An inventory problem in which annual demand is normally distributed with known means and standard deviations is considered. A purchase price increase is imminent before the next order is placed. Volume discounts are also given in accordance to the size of the order. A model to compute an optimal order quantity and an optimal delivery point is presented. This model can also account for any price change that may occur from time to time

Simple heuristics for push and pull remanufacturing policies

Inventory policies for joint remanufacturing and manufacturing have recently received much attention. Most efforts, though, were related to (optimal) policy structures and numerical optimization, rather than closed form expressions for calculating near optimal policy parameters. The focus of this paper is on the latter. We analyze an inventory system with unit product returns and demands where remanufacturing is the cheaper alternative for manufacturing. Manufacturing is also needed, however, since there are less returns than demands. The cost structure consists of setup costs, holding costs, and backorder costs. Manufacturing and remanufacturing orders have non-zero lead times. To control the system we use certain extensions of the familiar (s,Q) policy, called push and pull remanufacturing policies. For all policies we present simple, closed form formulae for approximating the optimal policy parameters under a cost minimization objective. In an extensive numerical study we show that the proposed formulae lead to near-optimal policy parameters.inventory control;remanufacturing;heuristics

Optimizing price, order quantity, and backordering level using a nonlinear holding cost and a power demand pattern

Producción CientíficaIt is well-known that the demand rate for some products depends on several factors, such as price, time, and stock, among others. Moreover, the holding cost can vary over time. More specifically, it increases with time since a long period of storage requires more expensive warehouse facilities. This research introduces an inventory model with shortages for a single product where the demand rate depends simultaneously on both the selling price and time according to a power pattern. Shortages are completely backordered. Demand for the product jointly combines the impact of the selling price and a time power function, which is performed as an addition. Furthermore, the holding cost is a power of the time that the product is held in storage. The main objective is to derive the optimal inventory policy such that the total profit per unit of time is maximized. For optimizing the inventory problem, some theoretical results are derived first to prove that the total profit function is strictly pseudo concave with respect to the decision variables. Next, an efficient algorithm that obtains the optimal solution is provided. The proposed inventory model is a general model because it contains several published inventory models as special cases. Some numerical examples are presented and solved to illustrate and validate the proposed inventory model. Also, a sensitivity analysis is conducted in order to highlight and generate significant insights

A two-storage model for deteriorating items with holding cost under inflation and Genetic Algorithms

A deterministic inventory model has been developed for deteriorating items and Genetic Algorithms (GA) having a ramp type demands with the effects of inflation with two-storage facilities. The owned warehouse (OW) has a fixed capacity of W units; the rented warehouse (RW) has unlimited capacity. Here, we assumed that the inventory holding cost in RW is higher than those in OW. Shortages in inventory are allowed and partially backlogged and Genetic Algorithms (GA) it is assumed that the inventory deteriorates over time at a variable deterioration rate. The effect of inflation has also been considered for various costs associated with the inventory system and Genetic Algorithms (GA). Numerical example is also used to study the behaviour of the model. Cost minimization technique is used to get the expressions for total cost and other parameters