A comparison between the order and the volume fill rates for a base-stock inventory control system under a compound renewal demand process

The order fill rate is less commonly used than the volume fill rate (most often just denoted fill rate) as a performance measure for inventory control systems. However, in settings where the focus is on filling customer orders rather than total quantities, the order fill rate should be the preferred measure. In this paper we consider a continuous review, base-stock policy, where all replenishment orders have the same constant lead time and all unfilled demands are backordered. We develop exact mathematical expressions for the two fill-rate measures when demand follows a compound renewal process. We also elaborate on when the order fill rate can be interpreted as the (extended) ready rate. Furthermore, for the case when customer orders are generated by a negative binomial distribution, we show that it is the size of the shape parameter of this distribution that determines the relative magnitude of the two fill rates. In particular, we show that when customer orders are generated by a geometric distribution, the order fill rate and the volume fill rate are equal (though not equivalent when considering sample paths). For the case when customer inter-arrival times follow an Erlang distribution, we show how to compute the two fill rates.Backordering; continuous review; compound renewal process; inventory control; negative binomial distribution; service levels

An inventory control project in a major Danish company using compound renewal demand models

We describe the development of a framework to compute the optimal inventory policy for a large spare-parts’ distribution centre operation in the RA division of the Danfoss Group in Denmark. The RA division distributes spare parts worldwide for cooling and A/C systems. The warehouse logistics operation is highly automated. However, the procedures for estimating demands and the policies for the inventory control system that were in use at the beginning of the project did not fully match the sophisticated technological standard of the physical system. During the initial phase of the project development we focused on the fitting of suitable demand distributions for spare parts and on the estimation of demand parameters. Demand distributions were chosen from a class of compound renewal distributions. In the next phase, we designed models and algorithmic procedures for determining suitable inventory control variables based on the fitted demand distributions and a service level requirement stated in terms of an order fill rate. Finally, we validated the results of our models against the procedures that had been in use in the company. It was concluded that the new procedures were considerably more consistent with the actual demand processes and with the stated objectives for the distribution centre. We also initiated the implementation and integration of the new procedures into the company’s inventory management systemBase-stock policy; compound distribution; fill rate; inventory control; logistics; stochastic processes

On order policies with pre-specified order schedules for a perishable product in retail.

This paper studies a retail inventory system for a perishable product, based on a practical setting in Dutch retail. The product has a fixed shelf life of three days upon delivery at the store and product demand has a weekly pattern, which is stationary over the weeks, but varies over the days of the week. Items of varying age occur in stock. However, in retail practice, the age-distribution is often unknown, which complicates order decisions. Depending on the type of product or the size of the supermarket, replenishment cycle lengths may vary. We study a situation where a store is replenished either three or four times a week on pre-specified days. The research aim is to find practical and efficient order policies that can deal with the lack of information about the age distribution of items in stock, considering mixed LIFO and FIFO withdrawal. Reducing potential waste goes along with cost minimization, while the retailer aims at meeting a cycle service level requirement. We present four new heuristics that do not require knowledge of the inventory age-distribution. A heuristic, based on a constant order quantity for each order moment, often generates least waste and lowest costs. However, this requires a few minutes of computation time. A new base stock policy appears second best

Finite production rate model with backlogging, service level constraint, rework, and random breakdown

In most real-life production systems, both random machine breakdown and the production of nonconforming items are inevitable, and adopting a backlogging policy with a predetermined minimum acceptable service level can sometimes be an effective strategy to help the management reduce operating cost or smoothen the production schedule. With the aim of addressing the aforementioned practical situations in production, this study explores the optimal production runtime for the finite production rate (FPR) model with allowable backlogging and service level constraint, rework of defective products, and random machine breakdown. Mathematical modelling is employed along with optimization techniques to derive the optimal production runtime that minimizes the long-run average system costs for the proposed FPR model. The joint effects of the allowable backlogging with a planned service level, rework, and random machine breakdown on optimal runtime decision have been carefully investigated through a numerical example and sensitivity analysis. As a result, important insights regarding various system parameters are revealed in order to enable the management to better understand, plan, and control such a practical production system

Service Level Constrained Inventory Systems

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/151878/1/poms13060_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/151878/2/poms13060.pd

A simulation-optimization approach for a service-constrained multi-echelon distribution network

Academic research on (s,S) inventory policies for multi-echelon distribution networks with deterministic lead times, backordering, and fill rate constraints is limited. Inspired by a real-life Dutch food retail case we develop a simulation-optimization approach to optimize (s,S) inventory policies in such a setting. We compare the performance of a Nested Bisection Search (NBS) and a novel Scatter Search (SS) metaheuristic using 1280 instances from literature and we derive managerial implications from a real-life case. Results show that the SS outperforms the NBS on solution quality. Additionally, supply chain costs can be saved by allowing lower fill rates at upstream echelons

Applications of Chance Constrained Optimization in Operations Management

In this thesis we explore three applications of chance constrained optimization in operations management. We first investigate the effect of consumer demand estimation error on new product production planning. An inventory model is proposed, whereby demand is influenced by price and advertising. The effect of parameter misspecification of the demand model is empirically examined in relation to profit and service level feasibility, and conservative approaches to estimating their effect on consumer demand is determined. We next consider optimization in Internet advertising by introducing a chance constrained model for the fulfillment of guaranteed display Internet advertising campaigns. Lower and upper bounds using Monte Carlo sampling and convex approximations are presented, as well as a branching heuristic for sample approximation lower bounds and an iterative algorithm for improved convex approximation upper bounds. The final application is in risk management for parimutuel horse racing wagering. We develop a methodology to limit potential losing streaks with high probability to the given time horizon of a gambler. A proof of concept was conducted using one season of historical race data, where losing streaks were effectively contained within different time periods for superfecta betting