K. Skouri

Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate

In this paper, an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial backlogging of unsatisfied demand is considered. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The model is fairly general as the demand rate, up to the time point of its stabilization, is a general function of time. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The optimal replenishment policy for the model is derived for both the above mentioned policies.

An optimal replenishment policy for deteriorating items with time-varying demand and partial-exponential type - backlogging

We study a continuous review inventory model over a finite-planning horizon with deterministic varying demand and constant deterioration rate. The model allows for shortages, which are partially backlogged at a rate which varies exponentially with time. For this model an optimal replenishment policy is established.

An inventory model with deteriorating items, quantity discount, pricing and time-dependent partial backlogging

Abstract Wee (International Journal of Production Economics 59 (1999) 511), in his interesting paper presented a deterministic inventory model with the following characteristics. Quantity discount schemes for the unit cost, partial backlogging at a fixed rate, deterioration of stock in time and demand rate being a linear function of the selling price. In this article we generalize the work of Wee (1999). More specifically, we consider a model where the demand rate is a convex decreasing function of the selling price and the backlogging rate is a time-dependent function, which ensures that the rate of backlogged demand increases as the waiting time to the following replenishment point decreases.

Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging

Abstract Yan and Cheng (J. Operational Res. Soc. 49 (1998), 1288–1295) presented a general production–inventory model with production rate, product demand rate and deterioration rate, all considered as functions of the time. Their model allows for shortages and partial backlogging of the unsatisfied demand at a constant rate. In this paper, we extend the results of Yan and Cheng to cover the case where the backlogging rate is a time-dependent function and we propose an algorithm for the solution of this problem. We also propose some conditions which we believe to be necessary for the validity for some of Yans and Chengs statements. The paper closes with numerical examples which cover each one of the cases considered in the paper.

A continuous review inventory model, with deteriorating items, time-varying demand, linear replenishment cost, partially time-varying backlogging

Abstract In this paper we study a continuous review inventory model. Five costs are considered as significant: deterioration, holding, shortage, opportunity cost due to the lost sales and the replenishment cost per replenishment which is linear dependent on the lot size. The deterioration of items occurs at a fixed rate independent of time. Demand rate is described by any logconcave function of time, which satisfies very mild conditions. The model allows for partial backlogging. The backlogging rate is an exponentially decreasing, time-dependent function specified by a parameter. For this model we derive results, which ensure the existence of a unique optimal policy and we propose an algorithm to find it. Numerical examples are given to illustrate the application of the algorithm. This paper extends the model studied by Bhunia and Maiti [Appl. Math. Model. 23 (1999) 301] by considering a more general demand rate function, introducing partial backlogging and relaxing the condition of replenishment cycles of equal lengths.

Supply chain models for deteriorating products with ramp type demand rate under permissible delay in payments

In this paper an order level inventory model for deteriorating items with general ramp type demand rate under conditions of permissible delay in payments is proposed. In this model shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Its study requires exploring the feasible ordering relations between the time parameters appeared, which leads to three models. For each model the optimal replenishment policy is determined. The sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. Suitably selected numerical examples highlight the obtained results. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed.

Lot sizing for a single product recovery system with variable setup numbers

Inventory systems for joint remanufacturing and manufacturing have recently received considerable attention. In such systems, used products are collected from customers and are kept at the recoverable inventory warehouse for future remanufacturing. In this paper a production-remanufacturing inventory system is considered, where the demand can be satisfied by production and remanufacturing. The cost structure consists of the EOQ-type setup costs, holding costs and shortage costs. The model with no shortage case in serviceable inventory is first studied. The serviceable inventory shortage case is discussed next. Both models are considered for the case of variable setup numbers of equal sized batches for production and remanufacturing processes. For these two models sufficient conditions for the optimal type of policy, referring to the parameters of the models, are proposed.

Order Level Inventory Models for Deteriorating Seasonable/Fashionable Products with Time Dependent Demand and Shortages

An order level inventory model for seasonable/fashionable products subject to a period of increasing demand followed by a period of level demand and then by a period of decreasing demand rate (three branches ramp type demand rate) is considered. The unsatisfied demand is partially backlogged with a time dependent backlogging rate. In addition, the product deteriorates with a time dependent, namely, Weibull, deterioration rate. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The optimal replenishment policy for the model is derived for both the above mentioned policies.

Metaheuristic optimization for the Single-Item Dynamic Lot Sizing problem with returns and remanufacturing

We study the performance of Differential Evolution on the Lot Sizing with returns.The most promising variant of the algorithm is identified and further modified.Modifications in the formulation of the optimization problem are introduced.The algorithm is applied on an abundant test suite employed in previous studies.Its performance is compared with state-of-the-art heuristics and metaheuristics. The use of metaheuristics for solving the Single-Item Dynamic Lot Sizing problem with returns and remanufacturing has increasingly gained research interest. Recently, preliminary experiments with Particle Swarm Optimization revealed that population-based algorithms can be competitive with existing state-of-the-art approaches. In the current work, we thoroughly investigate the performance of a very popular population-based algorithm, namely Differential Evolution (DE), on the specific problem. The most promising variant of the algorithm is experimentally identified and properly modified to further enhance its performance. Also, necessary modifications in the formulation of the corresponding optimization problem are introduced. The algorithm is applied on an abundant test suite employed in previous studies. Its performance is analyzed and compared with a state-of-the-art approach as well as with a previously investigated metaheuristic algorithm. The results suggest that specific DE variants can be placed among the most efficient approaches, thereby enriching the available algorithmic artillery for tackling the specific type of problems.

Particle swarm optimization for tackling continuous review inventory models

We propose an alternative algorithm for solving continuous review inventory model problems for deteriorating items over a finite horizon. Our interest focuses on the case of time-dependent demand and backlogging rates, limited or infinite warehouse capacity and taking into account the time value of money. The algorithm is based on Particle Swarm Optimization and it is capable of computing the number of replenishment cycles as well as the corresponding shortage and replenishment instances concurrently, thereby alleviating the heavy computational burden posed by the analytical solution of the problem through the Kuhn-Tucker approach. The proposed technique does not require any gradient information but cost function values solely, while a penalty function is employed to address the cases of limited warehouse capacity. Experiments are conducted on models proposed in the relative literature, justifying the usefulness of the algorithm.