A periodic review inventory model with Markovian supply availability (original) (raw)

A Continuous Review Inventory System with Bulk Demand and Markov Dependent Replenishment Quantities

Calcutta Statistical Association Bulletin, 1991

The paper deals with a continuous review bulk demand (positive-integer valued) ( s, S) inventory system where the interarrival times of demands are independent and identically distributed random variables. We assume that the successive quantities demallded lie between a and b (0< a⩽ b; s- b+l⩾0) with pk, k= a, a+l, ... , b-1, b as the probability that k items are demanded by an arriving unit. The maximum capacity of the system is S units and as soon as the inventory level falls to the set A= { s- b + 1, s- b + 2, ... , s -1, s}, order is placed for a quantity S- i if the ordering level is i, i ε A. Our model assumes that the quantity replenished forms a Markov chain defined over thestatespace E={ c, c + l, ... , S - s} with c⩾ b. Lead time is zero and no shortage is permitted. The distribution of the on band inventory at arbitrary time point and also the limiting distributions are obtained. A numerical illustration associated with the model is also provided.

A periodic review inventory system with two supply modes

European Journal of Operational Research, 1996

We describe a periodic review inventory system in which there are two modes of resupply, namely a regular mode and an emergency mode. Orders placed through the emergency channel have a shorter supply lead time but are subject to higher ordering costs compared to orders placed through the regular channel. We analyze this problem within the framework of an order-up-to-R inventory control policy. At each review epoch, the inventory manager must decide which of the two supply modes to use and then order enough units to raise the inventory position to a level R. We show that given any non-negative order-up-to level, either only the regular supply mode is used, or there exists an indifference inventory level such that if the inventory position at the review epoch is below the indifference inventory level, the emergency supply mode is used. We also develop procedures for solving for the two policy parameters, i.e., the order-up-to level and the indifference inventory level.

Periodic-review inventory models with inventory-level-dependent demand

Naval Research Logistics, 1994

Demand for some items can depend on the inventory level on display, a phenomenon often exploited by marketing researchers and practitioners. The implications of this phenomenon have received scant attention in the context of periodic-review inventory control models. We develop an approach to model periodic-review production/inventory problems where the demand in any period depends randomly, in a very general form, on the starting inventory level. We first obtain a complete analytical solution for a singleperiod model. We then investigate two multiperiod models, one with lost sales and the other with backlogging, whose optimal policies turn out to be myopic. Some extensions are also discussed.

A Continuous Review Model for an Inventory System with Two Supply Modes

Management Science, 1988

In this paper we develop an approximate model of an inventory control system in which there exist two options for resupply, with one having a shorter lead time. Because the optimal policy appears to be extremely complex, we consider a reasonable extension of the standard (Q, R) policy to allow for two different lot sizes QI and Q2, and two different reorder levels, R I and R2. Expressions for the expected on hand inventory and the expected backorders are developed and a procedure for determining the policy parameters is given. The model is validated by simulation, and calculations are included which compare the average annual cost with and without emergency ordering. (INVENTORY PRODUCTION; OPERATING CHARACTERISTICS; LEADTIME POL-ICY; ORDERING POLICY; STOCHASTIC MODELS)

Model of Inventory Replenishment in Periodic Review Accounting for the Occurrence of Shortages

2014

Background: Despite the development of alternative concepts of goods flow management, the inventory management under conditions of random variations of demand is still an important issue, both from the point of view of inventory keeping and replenishment costs and the service level measured as the level of inventory availability. There is a number of inventory replenishment systems used in these conditions, but they are mostly developments of two basic systems: reorder point-based and periodic review-based. The paper deals with the latter system. Numerous researches indicate the need to improve the classical models describing that system, the reason being mainly the necessity to adapt the model better to the actual conditions. This allows a correct selection of parameters that control the used inventory replenishment system and as a result to obtain expected economic effects. Methods: This research aimed at building a model of the periodic review system to reflect the relations (obs...

Single item inventory control under periodic review and a minimum order quantity

International Journal of Production Economics, 2011

In this paper we study a periodic review single item single stage inventory system with stochastic demand. In each time period the system must order none or at least as much as a minimum order quantity Q min. Since the optimal structure of an ordering policy with a minimum order quantity is complicated, we propose an easy-to-use policy, which we call (R, S, Q min) policy. Assuming linear holding and backorder costs we determine the optimal numerical value of the level S using a Markov Chain approach. In addition, we derive simple news-vendor-type inequalities for near-optimal policy parameters, which can easily be implemented within spreadsheet applications. In a numerical study we compare our policy with others and test the performance of the approximation for three different demand distributions: Poisson, negative binomial, and a discretized version of the gamma distribution. Given the simplicity of the policy and its cost performance as well as the excellent performance of the approximation we advocate the application of the (R, S, Q min) policy in practice.

Exact accounting of inventory costs in stochastic periodic-review models

International Journal of Production Economics, 2015

Most stochastic periodic-review inventory models calculate inventory costs according to the inventory level at the end of the review cycle. However, in most cases, actual inventory costs accrue at different time-points over the course of the cycle, suggesting that the outputs of these models might be suboptimal. This work proposes a means of overcoming this deficiency by attributing inventory costs to their actual timing. Formulas are presented for the expected profit and for its corresponding optimality equation in various multi-period models that follow complete or partial backlogging, with or without spoilage, stationary or varying inventory costs within cycle, and immediate or postponed revenues. We show that the optimality equation of all these model-variants is a kind of "newsvendor formula" with modified demand distribution and cost parameters. A simple approximation formula and bounds on the optimal order quantity, which are based only on the demand distribution over the entire cycle, are presented and combined together into an improved approximation formula. Numerical examples of a Brownian motion demand process demonstrate the benefit of the proposed approximation in comparison to the simple approximation formula.