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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.

An artificial bee colony algorithm for the economic lot scheduling problem

In this study, we present an artificial bee colony (ABC) algorithm for the economic lot scheduling problem modelled through the extended basic period (EBP) approach. We allow both power-of-two (PoT) and non-power-of-two multipliers in the solution representation. We develop mutation strategies to generate neighbouring food sources for the ABC algorithm and these strategies are also used to develop two different variable neighbourhood search algorithms to further enhance the solution quality. Our algorithm maintains both feasible and infeasible solutions in the population through the use of some sophisticated constraint handling methods. Experimental results show that the proposed algorithm succeeds to find the all the best-known EBP solutions for the high utilisation 10-item benchmark problems and improves the best known solutions for two of the six low utilisation 10-item benchmark problems. In addition, we develop a new problem instance with 50 items and run it at different utilisation levels ranging from 50 to 99% to see the effectiveness of the proposed algorithm on large instances. We show that the proposed ABC algorithm with mixed solution representation outperforms the ABC that is restricted only to PoT multipliers at almost all utilisation levels of the large instance.

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.

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 dynamic berth allocation problem with priority considerations under stochastic nature

Stochastic nature of vessel arrivals and handling times adds to the complexity of the well-known NP-hard berth allocation problem. To aid real decision-making under customer differentiations, a dynamic stochastic model designed to reflect different levels of vessel priorities is put forward. For exponential interarrival and handling times, a recursive procedure to calculate the objective function value is proposed. To reveal the characteristics of the model, numerical experiments based on heuristic approaches are conducted. Solution procedures based on artificial bee colony and genetic algorithms, covering both global and local search features, are launched to improve the solution quality. The practical inferences led by these approaches are shown to be helpful for container terminals faced with multifaceted priority considerations.

A discrete artificial bee colony algorithm for the assignment and parallel machine scheduling problem in DYO paint company

This paper presents a discrete artificial bee colony algorithm to solve the assignment and parallel machine scheduling problem in DYO paint company. The aim of this paper is to develop some algorithms to be employed in the DYO paint company by using their real-life data in the future. Currently, in the DYO paint company; there exist three types of filling machines groups. These are automatic, semiautomatic and manual machine groups, where there are several numbers of identical machines. The problem is to first assign the filling production orders (jobs) to machine groups. Then, filling production orders assigned to each machine group should be scheduled on identical parallel machines to minimize the sum of makespan and the total weighted tardiness. We also develop a traditional genetic algorithm to solve the same problem. The computational results show that the DABC algorithm outperforms the GA on set of benchmark problems we have generated.

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 discrete artificial bee colony algorithm for the Economic Lot Scheduling problem with returns

In this study, we model the Economic Lot Scheduling problem with returns (ELSPR) under the basic period (BP) policy with power-of-two (PoT) multipliers, and solve it with a discrete artificial bee colony (DABC) algorithm. Tang and Teunter [1] is the first to consider the well-known economic lot scheduling problem (ELSP) with return flows and remanufacturing opportunities. Teunter et al. [2] and Zanoni et al. [3] recently extended this first study by proposing heuristics for the common cycle policy and for a modified basic period policy, respectively. As Zanoni et al. [3], we restrict the study to consider independently managed serviceable inventory to test the performance of the proposed algorithm. Our study, to the best of our knowledge, is the first to solve ELSPR using a meta-heuristic. ABC is a swarm-intelligence-based meta-heuristic inspired by the intelligent foraging behaviors of honeybee swarms. In this study, we implement the ABC algorithm with some modifications to handle the discrete decision variables. In the algorithm, we employ two different constraint handling methods in order to have both feasible and infeasible solutions within the population. Our DABC is also enriched with a variable neighborhood search (VNS) algorithm to further improve the solutions. We test the performance of our algorithm on the two problem instances used in Zanoni et al. [3]. The numerical study depicts that the proposed algorithm performs well under the BP-PoT policy and it has the potential of improving the best known solutions when we relax BP, PoT and independently managed serviceable inventory restrictions in the future.