An optimal critical level policy for inventory systems with two demand classes

We consider an inventory system under continuous review with two demand classes that are different in terms of service level required (or penalty cost incurred for backordering of demand). Prior literature has proposed the critical level rationing (CLR) policy under which the demand from the lower priority class is backordered once inventory falls below the critical level. While this reduces the penalty cost for the higher demand class, the fill rate achieved for the lower priority demand class gets compromised. In this study, we propose a new class of two‐bin (2B) policy for the problem. The proposed 2B policy assigns separate bins of inventory for the two demand classes. The demand for each class is fulfilled from its assigned bin. However, when the bin intended for the higher demand class is empty, the demand from the higher class can still be fulfilled with the inventory from the other bin. The advantage of the 2B policy is that better fill rates are achieved, especially for the lower demand class. Computational results show that the proposed policy is able to provide a much higher service level for the lower priority class demand without increasing the total cost too much and without affecting the service level for the higher priority class. When a service level constrained optimization problem is considered, the 2B policy dominates the CLR policy when the service level difference for the two classes is not too high or the service levels required for both the classes are relatively lower.

This paper analyzes the use of a constant critical level policy for fast-moving items, where rationing is used to provide differentiated service levels to two demand classes (high priority and low priority). The previous work on critical level models, with either a continuous or periodic review policy, has only considered slow-moving items with Poisson demand. In this work, we consider a continuous review (Q, r, C) policy with two demand classes that are modeled through continuous distributions, and the service levels are measured by the probability of satisfying the entire demand of each class during the lead time. We formulate a service level problem as an non-linear problem with chance constraints for which we optimally solve a relaxation obtaining a closed-form solution that can be computed easily. For instances, we tested, computational results show that our solution approach provides good-quality solutions that are on average $$0.3~\%$$0.3% from the optimal solution.

Joint optimization of inventory replenishment and rationing policies for an omnichannel store with both in-store and online demands

This paper discusses an inventory rationing system with a threshold in a relatively stable inventory demand environment. There are two different demand classes in this inventory system, prior demand and secondary demand, distinguished by different shortage cost. The inventory system functions as follow. When the inventory level is above the threshold, demands come from both classes are filled. Once the inventory level falls below the threshold, all demands come from secondary demand class are backordered, only prior demand would be served. Heuristic approach was used to solve the model in this paper, and the optimal order quantity, single inventory cycle time and inventory threshold were given. Compare between inventory system with and without inventory threshold shows the cost advantage of the first system. Sensitivity analysis was performed to give a better understanding of two crucial parameter, inventory threshold and cost saving rate.

Capacity flexibility allocation in an outsourced supply chain with reservation

The reliability of electrical energy networks depends on the quality and availability of electrical equipment like power transformers. Local failures inside their insulation may lead to catastrophic breakdowns and might cause high outage and penalty costs. To prevent these destructive events power transformers are e.g. tested for partial discharge (PD) activity before commissioning and currently also during service. The current work deals with the electromagnetic PD detection method, also known as UHF method. The disadvantage of the UHF method is still the missing possibility for a calibration or at least a verification of the sensitivity. The so-called Sensitivity Check might show in future a relation between unconventionally measured UHF quantities to the apparent charge level in pico Coulomb. An important aspect is the attenuation of UHF signals within power transformers which is investigated in this paper.

An inventory model for items with demands satisfied from stock or by special deliveries

To improve the inventory management system in spare-part business. The author studied how to improve inventory management in automotive spare-part business. Seven steps of inventory management system for this research are conducted to solve problems in ABC Company as poor storage space utilization, large number of stocks and high inventory costs. Warehouse management and inventory record system improvement are required for solving warehouse problems and more accuracy of stocks. Then, inventory policy is set to decide which part and when they should start to stocks. Trend of spare parts is another point to study trend of demand for demand forecasting. This research also presents how to select the suitable techniques for forecasting, and example of forecast demand in the next year. Optimal order quantity is also computed for appropriated replenishment order. Finally, dead stocks and sleeping stocks will be managed to improve storage space area and reduce inventory cost. From the proposed systems, the result for inventory management system involves total inventory costs reduction of the example spare parts around 64.7% from actual system with trends of spare part demands analysis and more storage space area is also benefit from the system.

Customer segmentation is an important marketing tool. Effective customer segmentation helps the enterprises increase profits and improve customer service level. On the other hand, due to possible detrimental consequences, supply disruptions have been receiving more and more attention. This paper aims to investigate the effect of customer segmentation on a single-product inventory system in the presence of supply disruptions. The concerned inventory system involves an unreliable supplier, a retailer, and customers. The retailer adopts a continuous-review (s, S) inventory policy. Partial backordering is considered when stockouts occur. This inventory system is simulated. Based on different customer backorder proportions, the effect of customer segmentation on the inventory system is studied under different scenarios about supply disruption severity. The experimental results show that supply disruption duration is an important factor in influencing the effect of customer segmentation on the inventory system. Some managerial insights are also derived from the results.

This paper considers an inventory control system with a constraint on the service level. We focus on a popular service target in practice, the time-window ready rate, which is defined as the percentage of periods in which demands are completely fulfilled within a pre-specified time window. We explore the cost impact of different time-window ready rate settings by proposing evaluation and optimization methods for a single-location single-item min-max (or (s, S)) inventory system. New optimization procedures have been developed because the existing methods, which are based on a Lagrangian multiplier, cannot generally handle the current problem. More specifically, in some cases the time-window ready rate is a complicated function of the re-order point s, which renders existing algorithms inapplicable. Our algorithms are based on the monotone properties of cost and service constraint functions, which allow us to search the optimal policy efficiently within an identified region of policy-parameter values. Numerical experiments show the non-linear trade-off between cost and service, and indicate that extending or shrinking the time window can have a significant impact on the inventory cost.

This paper presents a Markov decision process for managing inventory systems with Markovian customer demand and Markovian product returns. Employing functional analysis, we prove the existence of the optimal replenishment policies for the discounted-cost and average-cost problems when demand, returns, and cost functions are of polynomial growth. Our model generalizes literature results by integrating Markovian demand, Markovian returns, and positive replenishment lead times. In particular, the optimality of the reorder point, order-up-to policies is proved when the order cost consists of fixed setup and proportional cost components and the inventory surplus cost is convex. We then make model extensions to include different cost components and to differentiate returned products from new ones. Finally, we derive managerial insights for running integrated closed-loop supply chains. At the aggregate level, returns reduce effective demand while many structural characteristics of inventory models are intact. A simple heuristic for managing systems with returns is to still utilize literature results without returns, but effective demand is lower than customer demand.

We consider a spare parts inventory system controlled by a base-stock policy. We assume several demand classes, where the demands of each class follow a compound Poisson process, and a stochastic replenishment lead-time common to all classes. For this inventory system, we investigate two rationing policies that can be employed when the inventory level is critically low. The first policy is the reservation policy, where a part of the stock is reserved for high priority demand classes, whereas the second one is new, which we call a threshold policy, and accepts demands of a given class until the pipeline stock caused by the particular class (plus the amount of the incoming order) reaches a critical level. On average, for 8% (12%) of all instances, the threshold policy performs better than the reservation policy under the full (partial) lost sales case and when the objective is to minimise the average on-hand inventory subject to fill rate service requirements. Furthermore, in many cases where the reservation policy outperforms the threshold policy, the gap between the two policies is small under both service requirements and total cost minimisation criteria. This suggests that a trade-off between ‘fairness’ and ‘cost’ is required, and that when the performance of two policies are similar, the threshold policy is generally favoured.

We consider a continuous review inventory system with service facility and a single server. The customers arrive according to a Poisson process. Any arriving customer, who finds the waiting room is full, is considered to be lost. The individual customer's unit demand is satisfied after a random time of service which is distributed as exponential. After a customer is served, he/she will decide either to join the orbit, for another service or leave the system according to a Bernoulli trial. The service time for these feedback customers are assumed to be exponential distribution. The inventory is replenished according to an (s, S) inventory policy and the replenishing times are assumed to be exponential. We have carried out the busy period analysis of the system and the waiting time distribution for both primary and feedback customers. The sensitivity analysis has been carried out the effect of different parameters and costs rates.

In this paper, we simulate allocation policies for a two-stage inventory system that receives perfect advance demand information (ADI) from customers belonging to different demand classes. Demands for each customer class are generated by independent Poisson processes while the processing times are deterministic. All customers in the same class have the same demand lead time (the difference between the due date and the requested date) and back-ordering costs. Each stage in the inventory system follows order-base-stock-policies where the replenishment order is issued upon arrival of a customer order. The problem requires a fast and reliable method that determines the system performance under different policies and ADI. Thus, we employ discrete event simulation to obtain output parameters such as inventory costs, fill rates, waiting time, and order allocation times. A numerical analysis is conducted to identify a reasonable policy to use in this type of system.

PurposeThis study investigates the impacts of changing the length of review period on the performance of a periodic review system with lost sales under varying demand patterns by using simulation method.Design/methodology/approachThe simulation model has been built using a spreadsheet program and depicts a special case of several retailers supplied by a central warehouse. Simulation scenarios are created based on two factors: length of the review period, and product type in terms of the average and standard deviation of the corresponding product's demand distribution.FindingsResults obtained from the simulation model show that inventory performance is quite sensitive to the duration of review periods, and selecting the appropriate period length is largely dependent on the variability of demand. Specifically, relatively shorter review periods are required for products with high variable demand, while the inventory system can tolerate longer review periods if the product demand is less fluctuating.Originality/valueThe study provides some practical guidelines for the inventory managers regarding the selection of an appropriate length for a review period in a periodic review system with lost sales.