A Multi-Server Heterogeneous Queuing-Inventory System with Class-Dependent Inventory Access

Abstract

In this paper, we consider a queuing inventory system with heterogeneous customers of K types arriving according to a marked Markovian arrival process. Each class of customers differs by nature of the service they seek and different priorities are assigned for each class resulting in different levels of inventory admitted to exhaust for customers of each class. A single service node is provided for each class with exponential services having class-dependent service rates. All classes of customers are served from a single source of inventory replenished according to (s,S) policy with exponentially distributed lead time. Stability condition and steady state probabilities are obtained by matrix-analytic method. Some important performance measures are also derived. Inventory recycle time was analyzed in detail. Useful cost function and numerical illustrations are also given. The optimization problem is interesting and can be solved in similar real scenario.

Double Sources Queuing-Inventory System with Hybrid Replenishment Policy

“…The values of the initial parameters of the model and the coefficients in the functional (22) are chosen as follows [54]:…”

“…Optimization problem is formulated as follows: it is required to find such pairs of optimal values (s * , r * ) in order to minimize the functional (22). This problem is formally written as (s * , r * ) = arg min…”

“…The developed Formulas ( 15)-( 21) allow us to calculate the expected total costs (TC) as follows: (22) where K i are the fixed costs of one order from Source-i; c r (i) are the procurement costs per unit inventory from Source-i, i = 1, 2; c c is the cost due to order cancellation from Source-1; c h is the holding cost of an inventory unit per unit time; c d is the cost due to damage per unit inventory; c l is the cost of losing a c-customer; c w is the waiting cost of a c-customer per unit time.…”

“…These days there are various important directions of development of QISs theory. Taking into account the features studied here QIS, the works devoted to systems with perishable inventory [10][11][12][13][14][15], systems with impatient customers [16][17][18][19][20][21], systems with multi-class customers [22][23][24][25][26][27][28][29][30], systems with retrial customers [31][32][33][34][35][36][37][38][39][40][41][42], and productioninventory systems [43][44][45][46][47][48] should be noted. Note that the classification of QIS models based on some specific feature (indicator) is not a simple problem since many of the above-indicated models simultaneously have many features.…”

Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System

“…The first type of customers can purchase the commodity whereas the second type can receive the service only. Rasmi et al [18] addressed a multi-server queuing-inventory system featuring diverse customer types (K in total) arriving in accordance with a marked Markovian arrival process. Each customer class seeks a distinct type of service and distinct priorities are allocated to each class.…”