An optimal control of inventory under probablistic replenishment intervals and known price increase (original) (raw)
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This paper addresses the simultaneous determination of pricing and inventory replenishment strategies in the face of demand uncertainty. More specifically, we analyze the following single item, periodic review model. Demands in consecutive periods are independent, but their distributions depend on the item's price in accordance with general stochastic demand functions. The price charged in any given period can be specified dynamically as a function of the state of the system. A replenishment order may be placed at the beginning of some or all of the periods. Stockouts are fully backlogged. We address both finite and infinite horizon models, with the objective of maximizing total expected discounted profit or its time average value, assuming that prices can either be adjusted arbitrarily (upward or downward) or that they can only be decreased. We characterize the structure of an optimal combined pricing and inventory strategy for all of the above types of models. We also develop an efficient value iteration method to compute these optimal strategies. Finally, we report on an extensive numerical study that characterizes various qualitative properties of the optimal strategies and corresponding optimal profit values.
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KnE Life Sciences, 2020
Today many retailers face high competition, therefore they have to operate in an efficient way. One aspect of efficiency is inventory. Many research on inventory is conducted intensively to get more realistic inventory model. In this paper, an inventory model was developed by considering pricing. Many retailers try to increase their profit by setting the best price for a single item, especially for some items that have high price-dependent demand. The customer demand depends on the price such household items. In the other side, some retailers face supply problems. Supplier often cannot supply products when the products needed on time. There is delay time between customer demand and products arrive at retailer warehouse. The retailer should determine the optimal price and replenishment time. There are some assumptions are used for the model. The first assumption, the demand is known and has constant elasticity. Second, there is stochastic replenishment period and demand that are not ...
Analysis of an inventory system under supply uncertainty
International Journal of Production Economics, 1999
In this paper, we analyze a periodic review, single-item inventory model under supply uncertainty. The objective is to minimize expected holding and backorder costs over a finite planning horizon under the supply constraints. The uncertainty in supply is modeled using a three-point probability mass function. The supply is either completely available, partially available, or the supply is unavailable. Machine breakdowns, shortages in the capacity of the supplier, strikes, etc., are possible causes of uncertainty in supply. We demonstrate various properties of the expected cost function, and show the optimality of order-up-to type policies using a stochastic dynamic programming formulation. Under the assumption of a Bernoulli-type supply process, in which the supply is either completely available or unavailable, and when the demand is deterministic and dynamic, we provide a newsboy-like formula which explicitly characterizes the optimal order-up-to levels. An algorithm is given that computes the optimal inventory levels over the planning horizon. Extensions and computational analysis are presented for the case where the partial supply availability has positive probability of occurrence.
Mathematical Problems in Engineering, 2009
An inventory system for non-instantaneous deteriorating items with price-dependent demand is formulated and solved. A model is developed in which shortages are allowed and partially backlogged, where the backlogging rate is variable and dependent on the waiting time for the next replenishment. The major objective is to determine the optimal selling price, the length of time in which there is no inventory shortage, and the replenishment cycle time simultaneously such that the total profit per unit time has a maximum value. An algorithm is developed to find the optimal solution, and numerical examples are provided to illustrate the theoretical results. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.
Optimization of Inventory for Optimal Replenishment Policies and Lead-Time with Time Varying Demand
Advances in Logistics, Operations, and Management Science, 2016
Considering a single period inventory management problem used in the distribution channel to represent consumer demand for marketing/sales of a product, attempt is made to develop a deterministic inventory model with time-varying increasing demand that may be used to reflect sales in different phases of a product life cycle in the competitive market. We propose inventory model assuming replenishment cost is to be linearly dependent on lot size and purchasing cost per unit item is dependent on lead time. Lead time is taken as decision variable. Shortages are allowed to backlog and to lose partly. Our objective is to cumulatively evaluate optimal replenishment lot-size, order time and lead-time for maximization of total profit. Considering the complexities of the proposed model, we propose a heuristic solution approach by developing an ERCM Genetic Algorithm based on ranking section, elitism, whole arithmetic crossover and non-uniform mutation dependent on the age of the population. T...
Optimal Pricing and Replenishment Policy for Production System with Discrete Demand
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In the classical inventory models, it is assumed that the demand for production items is continue, however, there are various types of manufactured products that demand for their items is discrete and periodic. In this paper, an inventory control model for production systems is developed with discrete demand and interval time between two sequential demands is same. Also, assumed the demand is dependent to the price which demand decreases linearly with the increase in price. We suggest a mixed integer mathematical model and the purpose of this model is maximizing the profit by determining the optimal selling price and replenishment quantity. Mathematical theorems are developed to determine the optimal selling price and replenishment quantity for continue decision variable and then we purposed an algorithm for finding optimal discrete value for the number of periods of demand at the production time and optimal price selling. A numerical example is given to illustrate the theory.
Optimal Inventory Control with Advance Supply Information
Economic and Business Review
It has been shown in numerous situations that sharing information between the companies leads to improved performance of the supply chain. We study a positive lead time periodic-review inventory system of a retailer facing stochastic demand from his customer and stochastic limited supply capacity of the manufacturer supplying the products to him. The consequence of stochastic supply capacity is that the orders might not be delivered in full, and the exact size of the replenishment might not be known to the retailer. The manufacturer is willing to share the so-called advance supply information (ASI) about the actual replenishment of the retailer's pipeline order with the retailer. ASI is provided at a certain time after the orders have been placed and the retailer can now use this information to decrease the uncertainty of the supply, and thus improve its inventory policy. For this model, we develop a dynamic programming formulation, and characterize the optimal ordering policy as a state-dependent base-stock policy. In addition, we show some properties of the base-stock level. While the optimal policy is highly complex, we obtain some additional insights by comparing it to the state-dependent myopic inventory policy. We conduct the numerical analysis to estimate the influence of the system parameters on the value of ASI. While we show that the interaction between the parameters is relatively complex, the general insight is that due to increasing marginal returns, the majority of the benefits are gained only in the case of ull, or close to full, ASI visibility.
Replenishment Policy for Price Sensitive Demand
One can manipulate the price of items to generate the excess demand. This paper developed a dynamic pricing policy for growing market. The replenishment policy also has been suggested to inventory managers. It is shown that dynamic pricing policy outperform to static pricing policy for price sensitive demand in growing market. A numerical example is given to illustrate the proposed model.
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This paper is attempt to develop a stochastic inventory model with quadratic price-sensitive demand. Objective function is developed by incorporating promotional efforts to boost the market demand, preservation technology to reduce the rate of deterioration, proportionate shortage time and partial backloggings. The proposed work is to generalise the stochastic demand with different probability distributions and their comparisons. The objective is to find the optimal price, optimal replenishment, and optimal preservation technology investment while optimizing the total profit per unit time. In the case of partial backlogging and lost sale, we deduced the optimal replenishment schedules for respective price and preservation technology cost. Also, we shown analytically and graphically that the total profit per unit time is a concave function with respect to per unit time, price, and preservation cost. The theoretical implications have been validated by useful results and numericals. Al...
In this paper, we address an important practical situation, namely where the usual replenishment lead time (when the supplier's production facility is operating) is a random variable and the supplier shuts down for an interval of known duration (for maintenance, vacation, etc.) each year. The demand rate is constant and any demand when out of stock is assumed to be lost. Under such circumstances we develop a heuristic procedure to decide when to initiate replenishment as well as the associated order-up-to-levels. Through the use of simulation (which accurately estimates the average costs per unit time), the heuristic is shown to perform excellently in a selection of small size problems when one can find the optimal solution. For a large number of problems of more realistic size, the use of simulation reveals that the heuristic achieves substantial cost savings when compared with a simpler, baseline approach. The heuristic itself does not require the use of simulation. The sensitivity of total expected costs to various parameters (such as the length of the shutdown interval and characteristics of the lead time distribution) is discussed.