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

Optimal dynamic pricing and replenishment policies for deteriorating items

Marketing strategies and proper inventory replenishment policies are often incorporated by enterprises to stimulate demand and maximize profit. The aim of this paper is to represent an integrated model for dynamic pricing and inventory control of deteriorating items. To reflect the dynamic characteristic of the problem, the selling price is defined as a time-dependent function of the initial selling price and the discount rate. In this regard, the price is exponentially discounted to compensate negative impact of the deterioration. The planning horizon is assumed to be infinite and the deterioration rate is time-dependent. In addition to price, the demand rate is dependent on advertisement as a powerful marketing tool. Several theoretical results and an iterative solution algorithm are developed to provide the optimal solution. Finally, to show validity of the model and illustrate the solution procedure, numerical results are presented

A Two Warehouse Inventory Model with Stock-Dependent Demand and variable deterioration rate

In this paper we discuss a two warehouses inventory model for non-instantaneous deteriorating items. Throughout last so many years, mostly researchers have consideration to the situation where the demand rate is dependent on the level of the on-hand inventory. For inventory systems, such as fashionable commodities, the length of the waiting time for the next replenishment would determine whether the backlogging will be accepted or not. In real life situation, enterprises usually buy more goods than can be stored in their own warehouses (OW) for future production or sales. The surplus quantities are frequently stored in an extra storage space, represented by rented warehouses (RW).The rented warehouse is considered to charge high unit holding cost than the own warehouse. The necessary and sufficient conditions of the existence and uniqueness of the optimal solution are shown. We determine the optimal replenishment policy for non-instantaneous deteriorating items with partial backlogging and stock-dependent demand

Joint Pricing and Inventory Control for Non-instantaneous Deteriorating Items with Stochastic Demand

In recent years inventory and pricing of deteriorating items has gained an enormous attention by many researchers. In this study, an inventory system for non-instantaneous deteriorating items with stochastic demand is modeled. This model has the assumptions that shortages are allowed and backlogging rate is variable where the last one is defined as a function of waiting time for the next replenishment. The objective is to maximize the total profit per unit time by finding the optimal selling price and replenishment schedule simultaneously. The concavity of the function is proved with a unique optimal solution. Thereby we provide an algorithm for finding the optimal solution. Finally, the authors present a numerical example to illustrate the theoretical results. A sensitivity analysis for the optimal solution with respect to major parameters is also carried out

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

An inventory planning problem for time-varying linear demand and parabolic holding cost with salvage value

In this manuscript, a model is proposed for the inventory planning problem with items which deteriorate linearly with respect to time. The concept of salvage value for deteriorated items is considered and incorporated in this model. The solution procedure of proposed optimization model is illustrated by a couple of numerical examples. A convexity check of the average total cost function is performed by plotting a two dimensional graph. The sensitivity test of the proposed model is performed to study the effect of changing the least as well as the most sensitive parameters in the proposed optimization model. Some graphical representations are constructed to discuss the outcomes and results so obtained for a choice of various parameters</p

Deteriorating inventory model with quadratically time varying demand and partial backlogging

[EN] In this paper, a deterministic inventory model is developed for instantaneous deteriorating items in which shortages are allowed and partially backlogged. Deterioration rate is constant, demand rate is quadratic function of time and holding cost is linear function of time, backlogging rate is variable and depends on the length of the next replenishment. The model is solved analytically by minimizing the total inventory cost. This inventory model can also use as an inventory model for linear as well as constant demand rate by very small change in the incremental factor of the quadratic function. Numerical examples are provided to illustrate the solution and application of the model.Mishra, VK. (2013). Deteriorating inventory model with quadratically time varying demand and partial backlogging. Working Papers on Operations Management. 4(2):16-28. doi:10.4995/wpom.v4i2.1170SWORD16284

A partial backlogging inventory model for deteriorating items with time-varying demand and holding cost: An interval number approach

This paper proposes a differential equation inventory model that incorporates partial backlogging and deterioration. Holding cost and demand rate are time dependent. Shortages are allowed and assumed to be partially backlogged. Two versions are presented, the first one with deterministic values of the parameters and the second one taking into the account the interval uncertainty of the parameters. In the crisp case, Taylor’s series expansion is used, and graphically shown that the cost function is convex. While, in the case of intervals, the interval arithmetic is used and then the problem is transformed into a multi-objective non-linear optimization problem and an interval objective function. To solve this problem, the weighted-sum method is used. The proposed procedure is validated with the help of a numerical example. Sensitivity analysis on various parameters has also been carried out