Production lot size models for perishable seasonal products

Seasonal items like fruits, fish, winter cosmetics, fashion apparel, etc. generally exhibits different demand patterns at various times during the season. Production and inventory planning must reflect this property for cost effectiveness and optimization of resources. This paper presents two production-inventory models for perishable seasonal products that minimize total inventory costs. The models obtains optimal production run time and optimal production quantity for cases when the production rate is constant and when it is allowed to vary with demand. The products are assumed to deteriorate at an exponential rate and demand for them follows a three-phase ramp type pattern during the season. Numerical examples and sensitivity analysis are carried out. Production run time and production quantity obtained by the model were found to be independent of cost parameters. The variable production rate strategy was also found to give lower inventory costs and production quantity than the constant production rate strategy

Inventory Model with Ramp-type Demand and Price Discount on Back Order for Deteriorating Items under Partial Backlogging

Modeling of inventory problems provides a good insight to retailers and distributors to maintain stock of different items such as seasonal products, perishable goods and daily useable goods etc. The deterioration of all these items exists to a certain extent due to several reasons like mishandling, evaporation, decay, environmental conditions, transportation etc. It is found from the literature that previously many of the researchers have developed inventory model ignoring deterioration and drawn conclusion. In the absence of deterioration parameter, an inventory model cannot be completely realistic. In this paper, we have made an attempt to extend an inventory model with ramp-type demand and price discount on back order where deterioration was not taken into account. In our study, deterioration and constant holding cost are taken into consideration keeping all other parameters same. As a result, the inventory cost function is newly constructed in the presence of deterioration. The objective of this investigation is to obtain optimal cycle length, time of occurrence of shortages and corresponding inventory cost. This extended model is solved for minimum value of average inventory cost analytically. A theorem is framed to characterize the optimal solution. To validate the proposed model, a numerical example is taken and convexity of the cost function is verified. In order to study the effect of changes of different parameters of the inventory system on optimal cycle length, time of occurrence of shortages and average inventory cost, sensitivity analyses have been performed. Also, the numerical result and sensitivity analyses are graphically presented in the respective section of this paper to demonstrate the model. This study reveals that a better solution can be obtained in the presence of our newly introduced assumptions in the existing model

An optimal EOQ model for perishable products with varying demand pattern

The demand pattern for most perishable products varies during their life cycle in the market. These variations must be properly reflected in inventory management in order to prevent unnecessary stock-out or excess inventory with associated increase in cost. In this paper, a multi-period economic order quantity (EOQ) model for managing the inventory of perishable items having varying demand pattern is presented. The model was formulated using a general ramp-type demand function that allows three-phase variation in demand pattern. These phases represent the growth, the steady and the decline phases commonly experienced by the demand for most products during their life cycle in the market. The model generates replenishment policies that guarantees optimal inventory cost for all the phases. Numerical experiments and sensitivity analysis were carried out to demonstrate the suitability of the model for a wide range of seasonal products. Result of the experiments revealed that the points at which demand pattern changes are critical points in managing inventory of products with ramp type demand

Analysis of an Inventory Model with Time-dependent Deterioration and Ramp-type Demand Rate: Complete and Partial Backlogging

The proposed model based on the global market strategies as for how the demand vary of the new seasonal products when they entered in the markets. The model has developed for the seasonal products or new consumer goods. The demand rate has considered Ramp-type based on the seasonal products having a time-dependent deterioration rate. The mathematical formulation of the proposed model is given. The present article consists two inventory model differ to each other as (a) in the first model stock-out situation is considered as completely backlogged; (b) in the second model partial backlogged stock-out situation is inserted. To obtain the optimal solution solved the proposed model analytically and shown the convexity of the proposed models graphically by using Mathematica 9.0. Numerical examples are given to test and verify the theoretical results. Ultimately, the sensitivity of the optimal solution with respect to major parameters with concluding remarks are discussed

Optimal Pricing Policies For Deteriorating items With Preservation Technology And Price Sensitive Demand

This paper considers the problem of determining the price, cycle time and preservation technology cost strategies for deteriorating items. It is assumed that preservation technology investment and demand rate do follow the function of selling price. The objective is to maximize the total profit per unit time with determining the optimal selling price, length of replenishment cycle and preservation technology investment. We will be proving that the optimal cycle length and selling price are unique with respect to given preservation cost. Also, total profit per unit time will be a concave function as it will reach its optimum value for optimum value of selling price, cycle length and preservation technology cost. Numerical examples are also presented to demonstrate the solution process

ONE-TIME ORDER INVENTORY MODEL FOR DETERIORATING AND SHORT MARKET LIFE ITEMS WITH TRAPEZOIDAL TYPE DEMAND RATE

Determining the end of the sales period for a one-time order inventory policy for technology products that see rapid innovation and improvement, such as smartphones, is a vital decision. While the market life cycle is short, with long lead times and expensive deliveries. Such situations can force the number of orders to be few or even only once. Products with the latest technology consist of many components that allow for deterioration from the start. This study discusses the effect of the market life cycle, as indicated by the trapezoidal demand rate, on deteriorating item inventory policies. This study will provide new insights into inventory policy. Mathematical models with a non-linear generalized reduced gradient approach can find the optimal end of the selling period and the order size to achieve maximum profit. A sensitivity analysis showed several findings that provide insight for management

The Optimal Replenishment Policy under Trade Credit Financing with Ramp Type Demand and Demand Dependent Production Rate

This paper investigates the optimal replenishment policy for the retailer with the ramp type demand and demand dependent production rate involving the trade credit financing, which is not reported in the literatures. First, the two inventory models are developed under the above situation. Second, the algorithms are given to optimize the replenishment cycle time and the order quantity for the retailer. Finally, the numerical examples are carried out to illustrate the optimal solutions and the sensitivity analysis is performed. The results show that if the value of production rate is small, the retailer will lower the frequency of putting the orders to cut down the order cost; if the production rate is high, the demand dependent production rate has no effect on the optimal decisions. When the trade credit is less than the growth stage time, the retailer will shorten the replenishment cycle; when it is larger than the breakpoint of the demand, within the maturity stage of the products, the trade credit has no effect on the optimal order cycle and the optimal order quantity

An EPQ model with trapezoidal demand under volume flexibility

In this paper, we explored an economic production quantity model (EPQ) model for finite production rate and deteriorating items with time-dependent trapezoidal demand. The objective of the model under study is to determine the optimal production run-time as well as the number of production cycle in order to maximize the profit. Numerical example is also given to illustrate the model and sensitivity analyses regarding various parameters are performed to study their effects on the optimal policy

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