Mehmet Murat Fadıloğlu

A dynamic rationing policy for continuous-review inventory systems

Stock rationing is an inventory policy that allows differential treatment of customer classes without using separate inventories. In this paper, we propose a dynamic rationing policy for continuous-review inventory systems, which utilizes the information on the status of the outstanding replenishment orders. For both backordering and lost sales environments, we conduct simulation studies to compare the performance of the dynamic policy with the static critical level and the common stock policies and quantify the gain obtained. We propose two new bounds on the optimum dynamic rationing policy that enables us to tell how much of the potential gain the proposed dynamic policy realizes. We discuss the conditions under which stock rationing - both dynamic and static - is beneficial and assess the value of the dynamic policy.

An embedded Markov chain approach to stock rationing

We propose a new method for the analysis of lot-per-lot inventory systems with backorders under rationing. We introduce an embedded Markov chain that approximates the state-transition probabilities. We provide a recursive procedure for generating these probabilities and obtain the steady-state distribution.

Supplier diversification under binomial yield

We consider supplier diversification in an EOQ type inventory setting with multiple suppliers and binomial yields. We characterize the optimal policy for the model and show that, in this case, it does not pay to diversify, in contrast to previous results in the random yield literature.

A discrete artificial bee colony algorithm for the economic lot scheduling problem

In this study we present a discrete artificial bee colony (DABC) algorithm to solve the economic lot scheduling problem (ELSP) under extended basic period (EBP) approach and power-of-two (PoT) policy. In specific, our algorithm provides a cyclic production schedule of n items to be produced on a single machine such that the production cycle of each item is an integer multiple of a fundamental cycle. All the integer multipliers are in the form of power-of-two, and under EBP approach feasibility is guaranteed with a constraint that checks if the items assigned in each period can be produced within the length of the period. For this problem, which is NP-hard, our DABC algorithm employs a multi-chromosome solution representation to encode power-of-two multipliers and the production positions separately. Both feasible and infeasible solutions are maintained in the population through the use of some sophisticated constraint handling methods. A variable neighborhood search (VNS) algorithm is also fused into DABC algorithm to further enhance the solution quality. The experimental results show that the proposed algorithm is very competitive to the best performing algorithms from the existing literature under the EBP and PoT policy.

Production control and stock rationing for a make-to-stock system with parallel production channels

This article considers the problem of production control and stock rationing in a make-to-stock production system with lost sales, multiple servers in parallel production channels, and several customer classes. It is assumed that independent stationary Poisson demand streams and exponential service times are in operation. At decision epochs, the control specifies whether or not to increase the number of active servers in conjunction with the stock allocation decision. Previously placed production orders cannot be cancelled. The system is modeled as an M/M/s make-to-stock queue, and properties of the optimal cost function and of the optimal production and rationing policies are characterized. It is shown that the optimal production policy is a state-dependent base-stock policy, and the optimal rationing policy is of threshold type. Furthermore, it is shown that the rationing levels are non-increasing in the number of active channels. It is also shown that the optimal ordering policy transforms into a bang-bang type policy when the model is relaxed by allowing order cancellations. Another model with partial order-cancellation flexibility is provided to fill the gap between the no-flexibility and the full-flexibility models. The additional gain that the optimal policy provides over the suboptimal base-stock policy proposed in the literature is qualified along with the value of the flexibility to cancel production orders.

Variance reduction techniques: Experimental comparison and analysis for single systems

We provide a thorough analysis of the effectiveness of different Variance Reduction Techniques (VRTs). We consider both stand-alone and combined applications of two input techniques, Antithetic Variates (AV) and Latin Hypercube Sampling (LHS), and two output techniques, Control Variates (CV) and Poststratified Sampling (PS). Previous research in the area mainly focuses on asymptotic variance reduction. In this experimental study, we measure the performance of VRTs under finite simulation run lengths and analyze their effects. Our findings show that the asymptotic variance reduction results do not readily apply to finite-length simulations. We consider three different types of systems (M/M/1, serial production line and (s, S) inventory control systems) and compare the VRTs under various experimental conditions. We observe that a variance reduction cannot be guaranteed for every instance a VRT is applied. Our results also indicate that the output VRTs (CV, PS) are better than input VRTs (AV, LHS) on the average for the single systems considered in this study. More interestingly, the less-sophisticated techniques (AV, CV) often perform better than the relatively more-complex techniques (LHS, PS). A comprehensive bibliography is also provided.

Models of production lines as quasi-birth-death processes

The aim of this work is to illustrate the suitability of quasi-birth-death processes (QBDs) for stochastic modelling of production lines. With this end in mind, first, an introduction to QBDs is made, so that the reader who may not be acquainted with this aspect of stochastic modelling may be introduced to the basics of the topic. Then, a formal definition of QBD is given and the QBDs are contrasted with the traditional birth-death processes. Later, examples of QBD models pertaining to production lines are presented. The rational of this exposition is to show how QBDs present themselves within the context of production lines and to show the kind of work that needs to be performed to fully specify the corresponding QBD. By compiling the aforementioned models, the strength of QBDs in modelling production lines is demonstrated.

A discrete harmony search algorithm for the economic lot scheduling problem with power of two policy

In this paper, we present a problem specific discrete harmony search (DHS) algorithms to solve the economic lot scheduling problem (ELSP) under the extended basic period (EBP) approach and power-of-two (PoT) policy. In particular, DHS algorithms generate a cyclic production schedule, consisting of n items to be produced on a single machine, where the production cycle of each item is an integer multiple of a fundamental cycle. All the integer multipliers take the form of PoT which restricts the search space but provides good solution qualities. Under the EBP approach, feasibility is guaranteed with a constraint checking whether or not the items assigned in each period can be produced within the length of the period. For this restricted problem, which is still NP-hard, the proposed DHS algorithms employ a multi-chromosome solution representation to encode power-of-two multipliers and the production positions separately. Both feasible and infeasible solutions are maintained in the population through the use of some sophisticated constraint handling methods. A variable neighborhood search (VNS) algorithm is also hybridized with DHS algorithms to further enhance the solution quality. The experimental results show that the proposed algorithms are very competitive to the best performing algorithms from the existing literature under the EBP and PoT policy.

A genetic algorithm for the economic lot scheduling problem under extended basic period approach and power-of-two policy

In this study, we propose a genetic algorithm (GA) for the economic lot scheduling problem (ELSP) under extended basic period (EBP) approach and power-of-two (PoT) policy. The proposed GA employs a multi-chromosome solution representation to encode PoT multipliers and the production positions separately. Both feasible and infeasible solutions are maintained in the population through the use of some sophisticated constraint handling methods. Furthermore, a variable neighborhood search (VNS) algorithm is also fused into GA to further enhance the solution quality. The experimental results show that the proposed GA is very competitive to the best performing algorithms from the existing literature under the EBP and PoT policy.

A general theory on spectral properties of state-homogeneous finite-state quasi-birth–death processes

Abstract In this paper a spectral theory pertaining to Quasi-Birth–Death Processes (QBDs) is presented. The QBD, which is a generalization of the birth–death process, is a powerful tool that can be utilized in modeling many stochastic phenomena. Our theory is based on the application of a matrix polynomial method to obtain the steady-state probabilities in state-homogeneous finite-state QBDs. The method is based on finding the eigenvalue–eigenvector pairs that solve a matrix polynomial equation. Since the computational effort in the solution procedure is independent of the cardinality of the counting set, it has an immediate advantage over other solution procedures. We present and prove different properties relating the quantities that arise in the solution procedure. By also compiling and formalizing the previously known properties, we present a formal unified theory on the spectral properties of QBDs, which furnishes a formal framework to embody much of the previous work. This framework carries the prospect of furthering our understanding of the behavior the modeled systems manifest.