Optimal inventory policies with non-stationary supply disruptions and advance supply information (original) (raw)
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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.
Production-Inventory Systems with Imperfect Advance Demand Information and Updating
We consider a supplier with finite production capacity and stochastic production times. Customers provide advance demand information (ADI) to the supplier by announcing orders ahead of their due dates. However, this information is not perfect, and customers may request an order be fulfilled prior to or later than the expected due date. Customers update the status of their orders, but the time between consecutive updates is random. We formulate the production-control problem as a continuous-time Markov decision process and prove there is an optimal state-dependent base-stock policy, where the base-stock levels depend upon the numbers of orders at various stages of update. In addition, we derive results on the sensitivity of the state-dependent base-stock levels to the number of orders in each stage of update. In a numerical study, we examine the benefit of ADI, and find that it is most valuable to the supplier when the time between updates is moderate. We also consider the impact of holding and backorder costs, numbers of updates, and the fraction of customers that provide ADI. In addition, we find that while ADI is always beneficial to the supplier, this may not be the case for the customers who provide the ADI.
European Journal of Operational Research, 2006
This paper addresses the single-item, non-stationary stochastic demand inventory control problem under the nonstationary (R, S) policy. In non-stationary (R, S) policies two sets of control parameters-the review intervals, which are not necessarily equal, and the order-up-to-levels for replenishment periods-are fixed at the beginning of the planning horizon to minimize the expected total cost. It is assumed that the total cost is comprised of fixed ordering costs and proportional direct item, inventory holding and shortage costs. With the common assumption that the actual demand per period is a normally distributed random variable about some forecast value, a certainty equivalent mixed integer linear programming model is developed for computing policy parameters. The model is obtained by means of a piecewise linear approximation to the non-linear terms in the cost function. Numerical examples are provided. (S.A. Tarim). European Journal of Operational Research xxx (2005) xxx-xxx www.elsevier.com/locate/eor
Inventory models with uncertain supply
2016
An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic-review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state-dependent base-stock policy characterized by a base-stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient ...
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.
Analysis of an inventory system under supply uncertainty - Deterministic and Stochastic Models
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.
Optimal Inventory Policy with Two Suppliers
We analyze a periodic-review inventory model where the decision maker can buy from either of two suppliers. With the first supplier, the buyer incurs a high variable cost but negligible fixed cost; with the second supplier, the buyer incurs a lower variable cost but a substantial fixed cost. Consequently, ordering costs are piecewise linear and concave. We show that a reduced form of generalized s S policy is optimal for both finite and (discounted) infinite-horizon problems, provided that the demand density is log-concave. This condition on the distribution is much less restrictive than in previous models. In particular, it applies to the normal, truncated normal, gamma, and beta distributions, which were previously excluded. We concentrate on the situation in which sales are lost, but explain how the policy, cost assumptions, and proofs can be altered for the case where excess demand is backordered. In the lost sales case, the optimal policy will have one of three possible forms: a base stock policy for purchasing exclusively at the high variable cost (HVC) supplier; an s LVC S LVC policy for buying exclusively from the low variable cost (LVC) supplier; or a hybrid s S HVC S LVC policy for buying from both suppliers.
Inventory models of future supply uncertainty with single and multiple suppliers
Naval Research Logistics, 1996
We consider order-quantity / reorder-point inventory models where the availability of supply is subject to random fluctuations. We use concepts from renewal reward processes to develop average cost objective function models for single, two, and multiple suppliers. Identifying the regenerative cycle for each problem aids the development of the cost function. In the case of two suppliers, spectral theory is used to derive explicit expressions for the transient probabilities of a four-state continuous-time Markov chain representing the status of the system. These probabilities are used to compute the exact form of the average cost expression. For the multiple-supplier problem, assuming that all the suppliers have similar availability characteristics, we develop a simple model and show that as the number of suppliers becomes large, the model reduces to the classical EOQ model. 0
Optimal inventory policies under imperfect advance demand information
2004
We consider an inventory control problem where it is possible to collect some imperfect information on future demand. We refer to such information as imperfect Advance Demand Information (ADI), which may occur in different forms of applications. A simple example is a company that uses sales representatives to market its products, in which case the collection of sales representatives' information as to the number of customers interested in a product can generate an indication about the future sales of that product, hence it constitutes imperfect ADI. Other applications include internet retailing, Vendor Managed Inventory (VMI) applications and Collaborative Planning, Forecasting, and Replenishment (CPFR) environments. We develop a model that incorporates imperfect ADI with ordering decisions. Under our system settings, we show that the optimal policy is of order-up-to type, where the order level is a function of imperfect ADI. We also provide some characterizations of the optimal solution. We develop an expression for the expected cost benefits of imperfect ADI for the myopic problem. Our analytical and empirical findings reveal the conditions under which imperfect ADI is more valuable.
Inventory management under random supply disruptions and partial backorders
Naval Research Logistics, 1998
We explore the management of inventory for stochastic-demand systems, where the product's supply is randomly disrupted for periods of random duration, and demands that arrive when the inventory system is temporarily out of stock become a mix of backorders and lost sales. The stock is managed according to the following modified (s, S) policy: If the inventory level is at or below s and the supply is available, place an order to bring the inventory level up to S. Our analysis yields the optimal values of the policy parameters, and provides insight into the optimal inventory strategy when there are changes in the severity of supply disruptions or in the behavior of unfilled demands.