Considering a Deteriorating EOQ Model Under Stochastic Demand and Shortage Allowed

A shortfall modelling-based solution approach for stochastic cyclic inventory routing

(ProQuest: ... denotes formulae omitted.)1. IntroductionMonk (1987) defined inventory as idle resources that possess economic value. In a broad sense, everyone keeps inventory such as food, clothes, domestic items, paper, pens and many other goods. Inventory applies to all types of work systems. Some types of inventory are raw materials inventory, in-process inventory, finished goods inventory, spare parts inventory, and so on.There are three basic reasons for keeping an inventory:a. Time - The time lags present in the supply chain, from supplier to user at every stage, requires that you maintain certain amounts of inventory to use during the lead time.b. Uncertainty - Inventories are maintained as buffers to address the problems of uncertainties in demand, supply and movements of goods.c. Economies of scale - Ideal condition of one unit at a time at a place where a user needs it, when he needs principle tends to incur lots of costs in terms of logistics. So bulk buying, movement and storing brings in economies of scale, thus inventory (Wikipedia, 2010).The total cost of inventory is calculated as the sum of the purchasing cost, setup cost, holding cost, and shortage cost (Taha, 2007).Economic order quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs.Several models exist depending on the assumptions taken in efforts to describe real life situations. Some considerations used are:a. Demand: the classical inventory model assumed demand to be known with certainty (deterministic). Chaudhuri (2003) considered a scenario where the demand varies with time, while Teng et. al. (2005) considered demand as deterministic but as an exponential function. Kar et. al. (2001) also considered demand as stochastic and price-dependent.b. Shortages: The classical model assumes that shortages are not allowed. Many works have been carried out under this assumption in times past and even recent times (e.g. Covert & Phillip (1973), Teng. et. al. (2005)). However, some works have also been done in which shortage-costs component is added to the inventory model (e.g. Kar et. Al,.2001; Mirzazadeh, 2010).c. Ordering pattern: Sharma (1987) identified five ordering policies namely:i. (s ,Q) policy: Place order for a fixed quantity, Q whenever the inventory position drops to a given level s or below.ii. (s ,S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S whenever the inventory position drops to a given level s or below.iii. (T, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length.iv. (T, s, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length if the inventory level is at level s or below.v. (T, Q) Policy: Place order for quantity Q at every ordering interval, T.Researchers (Sivakumar, 2009; Kalpakam & Sapna, 1995; Kalpakam & Sapna, 1994) have considered ordering policy in their studies.d. Inflation: Inflation can simply be defined as an increase in the supply of currency or credit relative to the availability of goods and services, resulting in higher prices and a decrease in the purchasing power of money. Buzacott (1975) stated that while classical EOQ formula assumes all costs are constant, it would be unreasonable to use the EOQ formula without investigating how it is modified when inflation causes cost to increase with time. The Buzacott model (1975) led to the consideration of inflation as an important factor in the determination of economic order quantity by many researchers and thus led to the development of many other models with inflation considerations (Mirzazadeh, 2010; Mirzazadeh et al. …

Inventory issues are often a major concern as they significantly impact operating costs. Lot sizing is one of the key decisions in managing inventory. However, in a real context, the demand for each item is often uncertain. It is supplied from the same supplier, requiring product orders to be placed in the same period. In addition, limited vehicle capacity and transportation costs are important factors to consider in making multi-item lot sizing decisions. The purpose of this study is to propose a new inventory model multi-item lot sizing model involving transportation cost and capacity constraints under stochastic demand. The decision variables involved in the model are each item's ordering cycle and safety factor with the objective function of minimizing the total inventory cost. To optimize the inventory model, this study also offers the advanced procedure of the Aquila Algorithm. This study also presents sensitivity analysis to the appropriate policy for optimizing the multi-item lot-sizing inventory problem involving transportation cost and capacity constraint under stochastic demand.

The replenishment policy of agri-products with stochastic demand in integrated agricultural supply chains

In this article, we integrate a non-linear holding cost with a stock-dependent demand rate in a maximising profit per unit time model, extending several inventory models studied by other authors. After giving the mathematical formulation of the inventory system, we prove the existence and uniqueness of the optimal policy. Relying on this result, we can obtain the optimal solution using different numerical algorithms. Moreover, we provide a necessary and sufficient condition to determine whether a system is profitable, and we establish a rule to check when a given order quantity is the optimal lot size of the inventory model. The results are illustrated through numerical examples and the sensitivity of the optimal solution with respect to changes in some values of the parameters is assessed.

This paper studies multiproduct inventory models with stochastic demands and a warehousing constraint. Finite horizon as well as stationary and nonstationary discounted-cost infinite-horizon problems are addressed. Existence of optimal feedback policies is established under fairly general assumptions. Furthermore, the structure of the optimal policies is analyzed when the ordering cost is linear and the inventory/backlog cost is convex. The optimal policies generalize the base-stock policies in the single-product case. Finally, in the stationary infinite-horizon case, a myopic policy is proved to be optimal if the product demands are independent and the cost functions are separable.

Standardized cargo network revenue management with dual channels under stochastic and time-dependent demand

An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit

In this paper, an inventory policy for the production units is presented with stochastic inflation, variable demand rate, deteriorating and ameliorating items in warehouse and permissible delay in payment. Shortages, backlogging and lost sale, are allowable. Also, inflation is constantly changing due to economic, political, social and cultural issues in the real world and we assume it uniform distribution. The demand rate is depended on selling price and permissible delay in payment and increases as delay in payment increases, however, decreases as selling price increases. The objective function considers optimal pricing policy, the number of production cycles and time fraction without shortage. So, the purpose is to derive the optimal replenishment policy that minimises the net present value of total cost per unit time. The study shows that the optimal solution not only exists but also is unique. Finally, some numerical examples and sensitivity analysis on parameters are made to validate the results of the proposed inventory system.

Contributors

Research on inventory models has been conducted intensively, including the model for stochastic demand. However, inventory models for stochastic demand are not easy to solve using an exact algorithm. In this paper, we develop a Monte Carlo simulation method to solve inventory problems with stochastic and intermittent demand. Simulation is conducted to evaluate continuous and periodic review policies. The simulation models are optimized using the evolutionary algorithm. The models are applied to data from one bicycle shop in Indonesia for five different items. The result shows that the economic order quantity ( R,Q ) policy is better than the ( s,S ) policy for two items and it is better than the ( S,T ) policy for three items.

The inventory routing problem (IRP) combines inventory management and delivery route‐planning decisions. This work presents a simheuristic approach that integrates Monte Carlo simulation within a variable neighborhood search (VNS) framework to solve the multiperiod IRP with stochastic customer demands. In this realistic variant of the problem, our goal is to establish the optimal refill policies for each customer–period combination, that is, those individual refill policies that minimize the total expected cost over the periods. This cost is the aggregation of both expected inventory and routing costs. Our simheuristic algorithm allows to consider the inventory changes between periods generated by the realization of the random demands in each period, which have an impact on the quantities to be delivered in the next period and, therefore, on the associated routing plans. A range of computational experiments are carried out in order to illustrate the potential of our simulation–optimization approach.

We consider a set of cybercafes faced with an optimal choice of bandwidth for internet service under stochastic stationary demand. The choice is made over uniformly time horizons with a goal of optimizing costs. Considering customer demand and operating costs of internet service at cybercafes, we formulate a finite state markov decision process model where states of a markov chain represent possible states of demand for internet service. An operational cost matrix is generated; representing the long run measure of performance for the markov decision process problem. The problem is to determine an optimal bandwidth adjustment policy at cybercafes so that the long run operational costs are minimized for the given state of demand. Using dynamic programming, the optimal bandwidth adjustment policies are determined at least cost over a finite period planning horizon. Results from the case study demonstrate the existence of an optimal state-dependent option for bandwidth adjustment policy and costs of internet service at cybercafes.

This research work derives an integrated inventory model for imperfect production/remanufacturing process with time varying demand, production and repair rates under inflationary environment. This inventory model deals with the joint manufacturing and remanufacturing options. There is a collection process devoted to collect used items with the aim to remanufacture them. Both production and repair runs generate imperfect items. The repair process remanufactures used and imperfect items. Further, it is also considered that the remanufactured item that is classified as good has exactly same quality as that of new one. Demand rate is supposed as time dependent. The production rate is assumed to be demand dependent and therefore it is also time dependent. The repair rate is supposed to be a function of time. All system costs are contemplated in uncertain environment. Therefore, the costs are considered as fuzzy nature. Theoretical results are illustrated thru a numerical example. Finally, a sensitivity analysis is performed in order to know the impact of different parameters on the optimal policy.

This paper determines the pricing, the replenishment cycle, and the number of shipments in a manufacturer–retailer supply chain of the deteriorating items. Generally speaking, deterioration items means products that their value is reduced over time. The relationship between the manufacturer and the retailer is analyzed by non-cooperative Stackelberg game, where the manufacturer is assumed to be the leader and retailer is the follower. It is assumed that inventory policy is non-delayed equal size shipments in which the manufacturer delivers shipments to the retailer in the production period. Also, the deterioration and demand rates are determined by probabilistic distribution function. First, an inventory control model for both the retailer and the manufacturer is formulated. Then, the conditions to obtain the optimal solution under non-cooperative Stackelberg equilibrium are derived. Next, a numerical example is extended by performing a sensitivity analysis and simulation of the model parameters and managerial insights are discussed. The main outcome of this paper is the optimal selling price and inventory control variables. Also, the results indicate that the conditions of inventory system determine the act of the manufacturer as a leader whether use its power against retailer as a follower or have a cooperation with the retailer. Moreover, the retailer’s total profit is more sensitive to the ordering costs than the other parameters and the decision variables of manufacturer significantly depend upon the manufacturer’s holding cost. In addition, the simulation results show the validation of the proposed model.