Sotirios Papachristos

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.

Economic ordering policy for an item with imperfect quality subject to the in-house inspection

This article considers a production/inventory system where each lot of items received or produced contains a random proportion of defective units, items of imperfect quality. The purchaser contacts a 100% inspection in order to identify the perfect (acceptable) quality items. The model examines the following two options for the imperfect quality items: sell them to a secondary market, as a single batch and at a price lower to that of new ones, or rework them at some cost and then use them as new ones to satisfy demand. After inspection, the good quality items are sent to the working inventory warehouse in batches of equal size. For both of these cases, the optimal ordering lot size and the optimal number of batches are obtained. A numerical example illustrates the solution procedure and sensitivity analysis results are reported.

Lot-sizing for a single-product recovery system with backordering

In this article, a single-product recovery system is studied. Used products are collected from customers and kept at the recoverable inventory warehouse for future recovery. The constant demand rate can be satisfied either by newly produced products or by recovered ones (serviceable inventory), which are regarded as perfectly as the new ones. Excess demand is completely backordered. Following an exact analytical approach, the optimal production and recovery policy is obtained. A numerical cost comparison of this model with the corresponding one without backordering is also performed. The results are general, as they were valid for finite and infinite production and recovery rates.

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.

Optimal policy and holding cost stability regions in a periodic review inventory system with manufacturing and remanufacturing options

In this paper a periodic review inventory model with finite horizon and remanufacturing, manufacturing options is studied. It is assumed that demand and cost parameters are constant and a sufficiently large quantity of used products is available at the beginning of the horizon. The model is studied within the class of policies with given remanufacturing and manufacturing set up and the optimal policy is obtained within this class. The policy specifies the period of switching from remanufacturing to manufacturing (switching period), the periods where remanufacturing and manufacturing activities take place and the corresponding lot sizes. An explicit formula for the cost function and some of its properties are established. Based on these, an algorithm which partitions the set of holding cost parameters into subsets, computes the optimal policy and constructs its corresponding stability regions on every such subset is proposed.

Note on: An optimal ordering and recovery policy for reusable items

This paper deals with a joint EOQ and EPQ model where the stationary demand can be satisfied by remanufactured and newly purchased products. The model assumes that a proportion of the already used products is collected from customers and later is recovered for reuse. The remanufactured products are regarded as perfect as new ones. For this model Koh et al. [Koh, S. -G., Hwang, H., Sohn, K. -I., & Ko, C. -S. (2002). An optimal ordering and recovery policy for reusable items. Computers and Industrial Engineering, 43, 59-73] found closed form expressions for the economic order quantity for new products and the optimal inventory level where the recovery process starts. Further they proposed a numerical procedure, which calculates the optimal number of set up in both recovery and ordering processes. In this paper, we revisit Koh et al.s paper and following a different analysis we obtain closed form expressions for both optimal number of set up in the recovery and the ordering processes. The approach is explained by an example.