A Two-Commodity Continuous Review Inventory System with Substitutable Items (original) (raw)
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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 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)
Analysis of Two-Commodity Continuous Review Inventory System in Supply Chain
This paper considers a two commodity continuous review inventory system. Continuous review inventory control of a single item at a single location had been considered by many researchers in past. We extend this inventory control strategy to two-echelon system, which is a building block for serial supply chain. The inventory control system consists of two warehouse (WH i
Two-Commodity Perishable Inventory System with Bulk Demand for One Commodity
The South African Journal of Industrial Engineering, 2011
This article considers a two-commodity continuous review inventory system in which the arriving customers belong to any one of three types, such that type 1 customers demand a single item of the first commodity, type 2 customers demand bulk items of the second commodity, and type 3 customers demand one item of the first commodity and bulk items of the second commodity. The arrivals of all three types of customers are assumed to be a Markovian arrival process (MAP). It is also assumed that the number of items demanded for the second commodity is a random variable. The ordering policy is to place orders for both commodities when the inventory levels are below prefixed levels for both commodities. The lead time is assumed to have a phase type distribution, and the demands that occur during stock out period are assumed to be lost. The joint probability distribution for both commodities is obtained in the steady state case. Various measures of system performance and the total expected cost rate in the steady state are derived. The results are illustrated with numerical examples. OPSOMMING 'n Tweeprodukstelsel se voorraad vir klante word kontinu hersien. Die vraag na die produktipes word gekenmerk deur klantvoorkeure. Die versoektempo van klante vir voorraad word aanvaar as 'n Markovproses. Aannames word gemaak oor vraaghoeveelhede en aanlooptyd. Die resultate van die ondersoek word voorgehou via syfervoorbeelde.
A periodic review inventory model with Markovian supply availability
International Journal of Production Economics, 1995
Occasional unavailability of materials and products has an impact on inventory decisions of utility companies, manufacturers, wholesalers and retailers. The possibility of periods of supply unavailability that start and end at random times has been recognized by inventory researchers, and incorporated into continuous-review models. The goal of this work is to address a periodic-review setting, with setup costs, where the probability that an order placed now is filled in full, as opposed to not at all, depends on whether supply was available in the previous period. We prove that the optimal inventory policy is of an (s, S) type, where s depends on the state of the supplier in the last period, while S does not. Some other issues are briefly discussed.
IJERT-A Discrete Time Two Commodity Inventory System
International Journal of Engineering Research and Technology (IJERT), 2016
https://www.ijert.org/a-discrete-time-two-commodity-inventory-system https://www.ijert.org/research/a-discrete-time-two-commodity-inventory-system-IJERTV5IS010602.pdf In this article, we consider a two-commodity inventory system under discrete time review. The demands for each commodity-) 2 , 1 ( i i arrive according to a independent Bernoulli process. The maximum inventory level for the 1,2) = (i i th commodity is fixed as 1,2 = , i S i and the reorder level as 1,2 = , i s i. The ordering policy is defined as, when both the inventory levels are less than or equal to their respective reorder levels, we place an order for 1,2 =), (= i s S Q i i i units. The lead time distribution is assumed to be geometric. The demands that occur during the stock-out period are considered to be lost. Some system performance measures in the steady state are derived and the total expected cost rate under a suitable cost structure is calculated. The results are illustrated numerically.
Stochastic Review Inventory Systems with Deteriorating Items; A Steady-State Non-Linear Approach
Processes
The primary goal of business organization is optimally maximizing their productivity and profit whilst reducing the cost resulting from lost sales and services given to their customers, which can be achieved by exceeding the balance between the demand and supply. Analyzing real-world situations, including integrated queuing-inventory systems, such as M/M/1-systems and M/M/1/∞-systems, can help business organizations reach this goal. This research analyzes integrated queuing-inventory systems with lost sales validated under a deterministic and uniformly distributed order size scheme under continuous review. The limited integrated inventory-queuing M/M/1/N-1-system was chosen as subject of our interest due to its closeness to reality. Thus, this system with exponentially distributed deteriorating products and random planning time with lost sales was simulated. This research aimed to analyze customers’ sanctification by studying the addition of the deterioration parameter γ to the mode...
Markov Models of Systems with Demands of Two Types and Different Restocking Policies
Cybernetics and Systems Analysis, 2018
Markov models of queuing-inventory systems with demands of two types are proposed. In these systems, two restocking policies are used: policies with fixed and variable demand size. High-priority demands have no access constraints while low-priority demands are accepted if the total number of demands in the system is less than a given threshold. Methods are developed to calculate performance measures of the systems under study and problems of their optimization are solved. Results of the numerical experiments are shown.
Mathematics
The use of a Markovian inventory system is a critical part of inventory management. The purpose of this study is to examine the demand for two commodities in a Markovian inventory system, one of which is designated as a major item (Commodity-I) and the other as a complimentary item (Commodity-II). Demand arrives according to a Poisson process, and service time is exponential at a queue-dependent rate. We investigate a strategy of (s,Q) type control for commodity-I with a random lead time but instantaneous replenishment for commodity-II. If the waiting hall reaches its maximum capacity of N, any arriving primary client may enter an infinite capacity orbit with a specified ratio. For orbiting consumers, the classical retrial policy is used. In a steady-state setting, the joint probability distributions for commodities and the number of demands in the queue and the orbit, are derived. From this, we derive a waiting time analysis and a variety of system performance metrics in the steady...