FUZZY INVENTORY MODEL FOR ITEMS WITH WEIBULL DISTRIBUTION DETERIORATION, POWER DEMAND, LINEAR HOLDING COST, SALVAGE COST AND PARTIAL BACKLOGGING

The objective of this research article is to develop an inventory model which incorporates power pattern demand, Weibull distribution deterioration, shortages and partial backlogging of orders. Holding cost is taken as time dependent and deteriorated items are assumed to have a salvage value. The cost parameters are fuzzified and the total cost is defuzzified using Graded mean representation, signed distance and centroid methods. The values obtained by these methods are compared with the help of numerical examples. The convexity of the cost function is depicted graphically. Sensitivity analysis is performed to study the effect of change in some parameters. Keywords: Inventory, Power demand, Partial backlogging, Deterioration, Triangular Fuzzy Number, Defuzzification, Graded mean represented method, Signed Distance Method, centroid method

A study of inflation effects on an EOQ model for Weibull deteriorating/ameliorating items with ramp type of demand and shortages

This paper deals with the effects of inflation and time discounting on an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand. The model is studied under the replenishment policy, starting with shortages under two different types of backlogging rates, and their comparative study is also provided. We then use the computer software, MATLto find the optimal replenishment policies. Duration of positive inventory level is taken as the decision variable to minimize the total cost of the proposed system. Numerical examples are then taken to illustrate the solution procedure. Finally, sensitivity of the optimal solution to changes of the values of different system parameters is also studied

Supply chain finance for ameliorating and deteriorating products: a systematic literature review

Ameliorating and deteriorating products, or, more generally, items that change value over time, present a high sensitiveness to the surrounding environment (e.g., temperature, humidity, and light intensity). For this reason, they should be properly stored along the supply chain to guarantee the desired quality to the consumers. Specifically, ameliorating items face an increase in value if there are stored for longer periods, which can lead to higher selling price. At the same time, the costumers’ demand is sensitive to the price (i.e., the higher the selling price the lower the final demand), sensitiveness that is related to the quality of the products (i.e., lower sensitiveness for high-quality products). On the contrary, deteriorating items lose quality and value over time which result in revenue losses due to lost sales or reduced selling price. Since these products need to be properly stored (i.e., usually in temperature- and humidity-controlled warehouses) the holding costs, which comprise also the energy costs, may be particularly relevant impacting on the economic, environmental, and social sustainability of the supply chain. Furthermore, due to the recent economic crisis, companies (especially, small and medium enterprises) face payment difficulties of customers and high volatility of resources prices. This increases the risk of insolvency and on the other hand the financing needs. In this context, supply chain finance emerged as a mean for efficiency by coordinating the financial flow and providing a set of financial schemes aiming at optimizing accounts payable and receivable along the supply chain. The aim of the present study is thus to investigate through a systematic literature review the two main themes presented (i.e., inventory management models for products that change value over time, and financial techniques and strategies to support companies in inventory management) to understand if any financial technique has been studied for supporting the management of this class of products and to verify the existing literature gap

Replenishment Policy for Pareto Type Deteriorating Items With Quadratic Demand under Partial Backlogging And Delay in Payments

The present model develops a replenishment policy in which the demand rate is quadratic polynomial-time function. Deterioration rate is a Pareto type function. Shortages are partial backlogging and delay in payments are allowed. Holding cost is a linear function of time. The backlogging rate varies with the waiting duration for the next replenishment. The present paper determines the optimal policy for the individual by minimizing the total cost. The optimization procedure has been explained by a numerical example and a detailed sensitivity analysis of the optimal solution has been carried out to display the effect of various parameters

An Optimum Inventory Policy for Exponentially Deteriorating Items, Considering Multi Variate Consumption Rate with Partial Backlogging

Customer purchasing deeds may be affected by factors such as selling price and inventory level instead of demand which is considered either constant or function of a single variable which is not feasible. Consequently, in the present study, we have considered the demand rate as a function of stock-level and selling price both. In the present study, in order to develop this model, it has been assumed that items are exponentially decaying and shortages are partially backlogged and the most realistic backlogging rate is considered. In this research, we proposed a partial backlogging inventory model for exponentially decaying items considering stock and selling price dependent demand rate in fuzzy environment. In developing the model demand rate, ordering cost, purchasing cost, holding cost, back ordering cost and opportunity cost are considered as triangular fuzzy numbers. Graded mean integration representation method is used for defuzzification. A numerical example is provided to illustrate the problem. Sensitivity analysis of the optimal solution with respect to the changes in the value of system parameters is also discussed

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

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

Modelos de Inventarios con Productos Perecederos: Revisión de la Literatura

This paper presents a review of the main characteristics of the mathematical modelsdeveloped by the scientific community in order to determine an optimal inventory policyfor deteriorating items. Thus, a classified bibliography of 390 articles published from2001 to 2014 in high-impact journals is submitted while considering the type of demandand deterioration, the integration of inventory and pricing decisions, the inclusionof shortage and/or the time value of money, the consideration of multiple items and/ormulti-echelon systems, and the incorporation of uncertain parameters other than demand.Finally, research questions not yet addressed by the research community in the field ofinventory control for deteriorating items are pointed out.En el presente artículo se lleva a cabo una revisión de las principales características estudiadas por la comunidad científica en el desarrollo de modelos matemáticos que buscan definir una política de inventario óptima para productos que se deterioran. De este modo, se referencian 390 artículos publicados a partir del año 2001 en revistas de gran impacto, teniendo en cuenta: el tipo de demanda y deterioro representado en los modelos matemáticos, el estudio de una política de precio óptima, la inclusión de faltantes y/o valor del dinero en el tiempo, el estudio de múltiples productos y/o dos o más eslabones de la cadena de suministro, y la utilización de parámetros o variables difusas. Finalmente, se identifican oportunidades de investigación que a la fecha no han sido abordadas por la comunidad científica en este campo del conocimiento

A Two-Warehouse Model for Deteriorating Items with Holding Cost under Particle Swarm Optimization

A deterministic inventory model has been developed for deteriorating items and Particle Swarm Optimization (PSO) having a ramp type demands with the effects of inflation with two-warehouse 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 Particle Swarm Optimization (PSO) 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 Particle Swarm Optimization (PSO). 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