A production lot size inventory model for deteriorating items and arbitrary production and demand rates

In this paper, we present a method for finding the optimal replenishment schedule for the production lot size model with deteriorating items, where demand and production are allowed to vary with time in an arbitrary way and in which shortages are allowed. The method is illustrated by a numerical example.     

Lost-sales inventory theory: A review

In classic inventory models it is common to assume that excess demand is backordered. However, studies analyzing customer behavior in practice show that most unfulfilled demand is lost or an alternative item/location is looked for in many retail environments. Inventory systems that include this lost-sales characteristic appear to be more difficult to analyze and to solve. Furthermore, lost-sales inventory systems require different replenishment policies to minimize costs compared to backorder systems. In this paper, we classify the models in the literature based on the characteristics of the inventory system and review the proposed replenishment policies. For each classification and type of replenishment policy we discuss the available models and their performance. Furthermore, directions for future research are proposed.     

Evaluating the effects of distribution centres on the performance of vendor-managed inventory systems

This paper evaluates the effects of the distribution centre (DC) in a vendor-managed inventory (VMI) system comprising one manufacturer, one DC and n retailers. Adopting the order-up-to-level (OUL) replenishment policy, the system aims to maximize the overall system profit. We propose a model to evaluate the system performance by considering the scale of the distribution network, influential cost factors, demand distribution, planning horizon, and facility locations. From the viewpoint of a supply chain, we examine the DC’s effects on the system in terms of net profit. Our findings reveal that the DC has effects on demand variance and system profit, and there are some dominant factors that affect the overall system performance. The DC may lead to different system performance under a variety of cost factors, and in some situations, the DC may negatively affect system performance. We also suggest some innovative uses of the DC’s location to help enhance system performance.     

The impact of production time variability on make-to-stock queue performance

In this paper, we exploit the distributional Little’s law to obtain the steady-state distribution of the number of customers in a GI/G/1 make-to-stock queueing system. Non-exponential service times in make-to-stock queue modeling are usually avoided or at best, considered in approximations due to difficulties in developing an exact method. By providing a numerical solution of the GI/G/1 make-to-stock queue, we observed the impact of production time variability on optimal inventory control policies. The numerical results prove the degree of errors in the results if an exponential service time distribution were assumed instead of the actual distribution.     

Note on the fill rate of single-stage general periodic review inventory systems

For base-stock policies, Zhang and Zhang [J. Zhang, J. Zhang, Fill rate of single-stage general periodic review inventory systems, Operations Research Letters 35 (2007) 503-509] derive the fill rate, defined as the long-run average fraction of demand satisfied immediately. We derive the same expression for the fill rate defined as the ratio of expected demand satisfied immediately to expected demand, and generalize to (R,Q) policies.     

The impact of preventive activities on the economics of production systems: Modeling and application

In this paper, the impact of preventive activities on the economics of production systems has been discussed. A defective production system has been used to evaluate the financial return of a system with and without preventive activity. A mathematical model has been developed to simulate the situation. A practical case in the automotive industry has been used to verify the model. According to this research, it has been found that preventive activities will affect the return of the production system, and the effect depends on the cost of the action that has been taken.     

Optimal design of unreliable production–inventory systems with variable production rate

In this article, we study an economic manufacturing quantity (EMQ) problem for an unreliable production facility where the production rate is treated as a decision variable. As the stress condition of the machine changes with the production rate, the failure rate of the machine is assumed to be dependent on the production rate. The unit production cost is also taken as a function of the production rate, as the machine can be operated at different production rates resulting in different unit production costs. The basic EMQ model is formulated under general failure and general repair time distributions and the optimal production policy is derived for specific failure and repair time distributions viz., exponential failure and exponential repair time distributions. Considering randomness of the time to machine failure and corrective repair time, the model is extended to the case where certain safety stocks in inventory may be useful to improve service level to customers. Optimal production policies of the proposed models are derived numerically and the sensitivity of the optimal results with respect to those parameters which directly influence the machine failure and repair rates is also examined.     

Fill rate of single-stage general periodic review inventory systems

This paper develops an exact formula for the fill rate of a single-stage inventory system that uses a general periodic-review base-stock policy. For normal demand, we present a fill-rate expression that uses the standard normal PDF and CDF, and develop two approximations for the fill rate.     

The shape of the yield and its impact on inventory decisions

We consider an inventory model with stochastic demand, positive lead time and random yield where ordering decisions are made according to a linear inflation rule. In case of a positive lead times the complexity of such inventory systems increases distinctly. Due to positive lead times, the inventory position contains no longer a term for outstanding orders but the estimated quantity of goods to be delivered after a known positive lead time period, which differ from the realized deliveries. Thus, a forecast error occurs in each period. In previous research this forecast error was assumed to be normally distributed which is not an appropriate assumption in case of symmetric yield. Since yield skewness can’t be neglected, we propose to fit a skew normal distribution or a generalized extreme value distribution on the forecast error to account for the yield skewness. A numerical study reveals that the proposed approaches are excellent and outperform existing ones.     

Predictive control of periodic-review production inventory systems with deteriorating items

In this paper a predictive control strategy is applied to a periodic-review dynamic inventory system with deteriorating items. Given the current inventory level, we determine the optimal production rates to be implemented at the beginning of each of the following periods over the control horizon. The effectiveness of this approach is the use of future information of the inventory target level and the desired production rate, which are available, along the fixed horizon. The deterioration coefficient may be known or unknown and both cases are considered. In the case where it is unknown, the self-tuning predictive control is applied. The proposed control algorithms are illustrated by simulations.     

The cohomology of the moduli space of controllable linear systems

In this paper we explicitly describe, by generators and relations, the cohomology ring of the manifold _n,m (F) of controllable linear systems having m inputs and state-space dimension n. It is shown that the cohomology ring of _n,m (F) is isomorphic to the invariant cohomology ring of a product of projective spaces. Estimates for the cup length of the cohomology ring are obtained.     

The impact of data collection on fill rate performance in the (R,s, Q) inventory model

In this paper we consider the determination of the reorder point s in an (R, s, Q) inventory model subject to a fill rate service level constraint. We assume that the underlying demand process is a compound renewal process. We then derive an approximation method to compute the reorder level such that a target service level is achieved. Restrictions on the input parameters are given, within which this method is applicable. Moreover, we will investigate the effects on the fill rate performance in case the underlying demand process is indeed a compound renewal process, while the demand process is modelled as a discrete-time demand process. That is, the time axis is divided in time units (for example, days) and demands per time unit are independent and identically distributed random variables. It will be shown that smooth and erratic behaviour of the inter-arrival times have different impacts on the performance of the fill rate when demand is modelled as a discrete-time process and in case the underlying demand process is a compound renewal process.     

A note on multi-item inventory systems with limited capacity

Functional relationships between the Lagrange multiplier and system parameters for multi-item inventory systems with one restriction are identified and used to establish tight bounds on the optimal multiplier value. A recursive process which rapidly converges to the optimal multiplier is also discussed. Finally, a comparative analysis of the new bounds in relation to existing bounds is presented.