Michael Dreyfuss

Optimal spares allocation to an exchangeable-item repair system with tolerable wait

In a multi-location, exchangeable-item repair system with stochastic demand, the expected waiting time and the fill rate measures are oftentimes used as the optimization criteria for the spares allocation problem. These measures, however, do not take into account that customers will tolerate a reasonable delay and therefore, a firm does not incur reputation costs if customers wait less than their tolerable wait. Accordingly, we generalize the expected waiting time and fill rate measures to reflect customer patience. These generalized measures are termed the truncated waiting time and the window fill rate, respectively. We develop efficient algorithms to solve the problem for each of the criteria and demonstrate how incorporating customer patience provides considerable savings and profoundly affects the optimal spares allocation.

Optimizing Spare Battery Allocation in an Electric Vehicle Battery Swapping System

Electric vehicle battery swapping stations are suggested as an alternative to vehicle owners recharging their batteries themselves. To maximize the network’s performance spare batteries must be optimally allocated in these stations. In this paper, we consider the battery allocation problem where the criterion for optimality is the window fill rate, i.e., the probability that a customer that enters the swapping station will exit it within a certain time window. This time is set as the customer’s tolerable wait in the swapping station. In our derivation of the window fill rate formulae, we differ from previous research in that we assume that the swapping time itself is not negligible. We numerically analyse the battery allocation problem for a hypothetical countrywide application in Israel and demonstrate the importance of estimating correctly customers’ tolerable wait, the value of reducing battery swapping time and the unique features of the optimal battery allocation.

Determining Customer Delay in an MB/G/∞ Exchangeable Item Repair System with Spares

We consider an MB/G/∞ exchangeable-item repair system with spares and ample servers to which arriving customers bring groups of random size B identical items for repair. An exact formula for the waiting time distribution and a computationally efficient approximation are presented for this system. From this, we not only have the standard fillrate, but a practical extension of this concept to a ‘window fillrate’, which provides the probability of filling an order within a specified acceptable period of time. The model solution can be used not only for a one-echelon system, but for multi-echelon systems as well, where the waiting-time distribution obtained for any echelon k is used to calculate the repair-time distribution of lower echelon k-1, until the customer delay at level 1 (the window fillrate) is determined. Finally, some numerical examples are added to show the sensitivity of its various system parameters to variations in the number of spares for different forms of bulk size B.

Waiting Time Distribution for an Exchangeable Item Repair System with Two Failed Components

Models involving exchangeable component repair systems are widely treated in the literature. In such systems, a customer arrives at a repair queue with a failed component which is replaced from stocks of previously repaired components. Various strategies and service measures have been discussed. Customers who arrive with a single failed component type will be referred to the appropriate service queue which will exchange the failed component. The waiting time distribution for a single failed component has also been developed. The development of the waiting time distribution for a single queue servicing multiple component failures has been neglected. There are many instances where two distinct components are linked so that one failure will cause the failure of the second. Finding the waiting time distribution for the customer is important because it can lead to better facility planning and realistic service measures. For example, how many extra spares should be in the system so as to limit the probability of waiting more than an acceptable amount of time (the window fill rate). We limit our development to the case of two failed components; however, the ideas developed may be extendable to more than just two failed component.

A Risk Management Model for an Academic Institution's Information System

We develop and apply a two-step decision support model for investing in information technology security focusing on breaches that originate from system users. In the first step we map the risk level of each of the system’s components with the aim of identifying the subsystems that pose the highest risk. In the second step we determine how much to invest in various technological tools and workplace culture programs to enhance information security. We describe an application of this model to an information system in an academic institution in Israel. This system comprises ten subsystems and we identify the three that bear the most risk. We use these findings to determine the parameters of the investment allocation problem and find the optimal investment plan. The results of our application indicate that hacking for the purpose of cheating is a greater threat than other types of security issues. Additionally, we find support to the claim that information security officials tend to overinvest in security technological tools and underinvest in improving security workplace culture.

Optimal allocation of spares to maximize the window fill rate in a two-echelon exchangeable-item repair system

Abstract We solve the spares allocation problem in a two-echelon, exchangeable-item repair system in which the lower echelon comprises multiple locations and the higher echelon is a single depot. We assume that customers tolerate a certain wait and therefore the optimization criterion is the window fill rate, i.e., the expected portion of customers who are served within the tolerable wait. We develop two algorithms to solve this problem. The first algorithm (FTEA) is formula-based and is suboptimal. The second algorithm (HTEA) combines simulations into the first algorithm and obtains a higher degree of accuracy at the cost of extra running time. We characterize the near-optimal solution by its degree of pooling and concentration. Pooling happens when spares are allocated to the depot and are therefore shared by all the lower-echelon locations. Concentration takes place when spares are allocated to only a few lower-echelon locations whereas the other lower-echelon locations receive no spares. We use numerical examples to compare the algorithms and to illustrate how the budget, shipment time, local repair and customer patience affect the optimal solution and degree of pooling in varying ways. Using the numerical results, we propose a third algorithm (ETEA) that obtains HTEA’s output in 30% of the time.

An analytical approach to determine the window fill rate in a repair shop with cannibalization

Abstract We consider a repair shop in which each unit comprises multiple component types and cannibalization is allowed. The shop’s managers have a budget for purchasing spare components and need to decide how many spares of each component type to purchase. Customers arrive to the shop with a single unit of which at least one of its components has failed and expect to be served within a tolerable waiting time. Accordingly, the shop’s performance measure is the window fill rate, that is, the fraction of customers who are served within the tolerable wait. In our analysis, we develop exact formulas for the window fill rate that comprise multiple dependent Skellam random variables. We overcome the practical complexity of evaluating these formulas by using simulation to evaluate only the random elements. We discuss run-time considerations for solving the spares allocation problem and demonstrate how the optimal solution and the window fill rate depend on the tolerable wait, budget and the customer base using an illustrative numerical example.

Waiting time distribution for an exchangeable item repair system with up to two failed components

Models involving exchangeable component repair systems are widely treated in the literature. In such systems a customer arrives at a repair queue with a failed component which is replaced from stocks of previously repaired components and spares. Various strategies and service measures have been discussed. The waiting time distribution for a single failed component has also been developed. Most customers who arrive at a repair facility will arrive with a single failed component type. They will be referred to an appropriate service queue which will ultimately exchange that particular failed component. Due to its complexity the development of the waiting time distribution for a single queue servicing multiple simultaneous component failures has been generally neglected. In a previous paper we found the waiting time distribution for the case where an item arrives with exactly two simultaneously failed components. In this paper we will consider a much more general case where either one or both of the components have failed. Finding the waiting time distribution is important because it can lead to better facility planning and new realistic service measures. For example, how many extra spares should be allocated to the system so that the probability of waiting more than an acceptable amount of time (the window fill rate) could be kept to within a predefined limit?

Window Fill Rate in a Two-Echelon Exchangeable-Item Repair-System

The fill rate service measure describes the proportion of customers who commence service immediately upon arrival. Since, however, customers will usually tolerate a certain wait time, managers should consider the window fill rate in lieu of the fill rate. That is, the performance measure of interest is the probability that a customer is served within the tolerable wait time. In this paper, we develop approximation formulas for the window fill rate in a two-echelon, exchangeable-item repair system in which the upper echelon is a central depot and the lower echelon comprises multiple locations. We demonstrate the use of the formulas through a numerical example and measure the approximation error of the window fill rate formulas using simulation.

Window Fill Rate with Compound Arrival and Assembly Time

Exchangeable-item repair systems are inventory systems in which customers receive operable items in exchange of the failed items they brought. The failed items are not discarded, but instead, they are repaired on site. We consider such a system in which failed items arrival follows a Compound Poisson process and in which the item removal and installation times may be positive. For this system, we develop exact formulas for the window fill rate, that is, the probability that customers receive service within a specific time window. This service measure is appropriate in situations that customers tolerate a certain delay and therefore the system does not incur reputations costs if it completes service within this time window.