Modeling Stochastic Lead Times in Multi-Echelon Systems

In many multi-echelon inventory systems, the lead times are random variables. A common and reasonable assumption in most models is that replenishment orders do not cross, which implies that successive lead times are correlated. However, the process that generates such lead times is usually not well defined, which is especially a problem for simulation modeling. In this paper, we use results from queuing theory to define a set of simple lead time processes guaranteeing that (a) orders do not cross and (b) prespecified means and variances of all lead times in the multiechelon system are attained

Convexity Properties and Comparative Statics for M/M/S Queues with Balking and Reneging

We use sample path arguments to derive convexity properties of an M/M/S queue with impatient customers that balk and renege. First, assuming that the balking probability and reneging rate are increasing and concave in the total number of customers in the system (head-count), we prove that the expected head-count is convex decreasing in the capacity (service rate). Second, with linear reneging and balking, we show that the expected lost sales rate is convex decreasing in the capacity. Finally, we employ a sample-path sub-modularity approach to comparative statics. That is, we employ sample path arguments to show how the optimal capacity changes as we vary the parameters of customer demand and impatience. We find that the optimal capacity increases in the demand rate and decreases with the balking probability, but is not monotone in the reneging rate. This means, surprisingly, that failure to account for customersâ reneging may result in over-investment in capacity. Finally, we show that a seemingly minor change in system structure, customer commitment during service, produces qualitatively different convexity properties and comparative statics.Operations Management Working Papers Serie

An intelligent computational approach to the optimization of inventory policies for single company

This study develops and tests a computational approach for determining optimal inventory policies for single company. The computational approach generally comprises of two major components: a meta-heuristic optimizer and an event-driven inventory evaluation module. Meta-heuristic is a powerful search technique, under the intelligent computational paradigm. The approach is capable of determining optimal inventory policy under various demand patterns regardless their distribution for a variety of inventory items. Two prototypes of perishability are considered: (1) sudden deaths due to disasters and (2) outdating due to expirations. Since every theoretical model is specially designed for a certain type of inventory problem while the real world inventory problems are numerous, it is desirable for the newly proposed computational approach to cover as many inventory problems/models as possible. In a way, the proposed meta-heuristic based approach unifies many theoretical models into one and beyond. Experimental results showed that the proposed approach provides comparable results to the theoretical model when demand follows their assumption. For demands not well conformed to the assumption, the proposed approaches are able to handle it but the theoretical approaches do not. This makes the proposed computational approach advantageous in that it can handle various types of real world demand data without the need to derive new models. The main motivation for this work is to bridge the gap between theory and practice so as to deliver a user-friendly and flexible computational approach for rationalizing the inventory control system for single company

Performance Analysis of Multi-Echelon Inventory Systems.

A two-echelon inventory and distribution system consisting of a centralized warehouse and N stores is considered in this paper. The inventories of the warehouse as well as the stores are controlled by periodic review (s,S) ordering policies. The expected levels of capital investment, storage space needs, capacity requirements for delivery vehicles, and reliable customer service are issues of great importance to practitioners when considering the introduction of a central warehouse and transportation system. Helmut Schneider, Dan Rinks, and Peter Kelle have developed a methodology that has been shown to provide approximately optimal (s,S) policies under various demand conditions, and are easy to handle computationally. The approximations of Schneider et al., are used to generate ordering policies for the two-echelon system in order to observe the behavior of the aggregate inventories generated by the (s,S) policies using computer simulation. The simulation results are used to evaluate the accuracy of the analytic models in predicting the aggregate inventory behavior, and simple computational formulas are proposed to calculate confidence limits for aggregate inventory levels and for shipping volumes and weights

Piecewise linear approximations for the static-dynamic uncertainty strategy in stochastic lot-sizing

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models build on piecewise linear upper and lower bounds of the first order loss function. We discuss different formulations of the stochastic lot sizing problem, in which the quality of service is captured by means of backorder penalty costs, non-stockout probability, or fill rate constraints. These models can be easily adapted to operate in settings in which unmet demand is backordered or lost. The proposed approach has a number of advantages with respect to existing methods in the literature: it enables seamless modelling of different variants of the above problem, which have been previously tackled via ad-hoc solution methods; and it produces an accurate estimation of the expected total cost, expressed in terms of upper and lower bounds. Our computational study demonstrates the effectiveness and flexibility of our models.Comment: 38 pages, working draf

A replenishment policy for a perishable inventory system based on estimated aging and retrieval behavior

So far the literature on inventory control for perishable products has mainly focused on (near-) optimal replenishment policies for a stylized environment, assuming no leadtime, no lot-sizing, stationary demand, a first in first out retrieval policy and/or product life time equal to two periods. This literature has given fundamental insight in the behavior and the complexity of inventory systems for perishable products. In practice, many grocery retailers have recently automated the inventory replenishment for non-perishable products. They recognize they may need a different replenishment logic for perishable products, which takes into account e.g. the age of the inventory in the system. Due to new information technologies like RFID, it now also becomes more economically feasible to register this type of information. This paper suggests a replenishment policy for perishable products which takes into account the age of inventories and which requires only very simple calculations. It will be shown that in an environment, which contains important features of the real-life retail environment, this new policy leads to substantial cost reductions compared with a base policy that does not take into account the age of inventories

Joint Inventory and Fulfillment Decisions for Omnichannel Retail Networks

With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an omnichannel approach, which integrates inventories across multiple channels. We analyze the inventory optimization of three such omnichannel fulfillment systems for a retailer facing two demand streams (online and in-store). The systems differ in the level of fulfillment integration, ranging from no integration (separate fulfillment center for online orders), to partial integration (online orders fulfilled from nearest stores) and full integration (online orders fulfilled from nearest stores, but in case of stockouts, can be fulfilled from any store). We obtain optimal order-up-to quantities for the analytical models in the two-store, single-period setting. We then extend the models to a generalized multi-store setting, which includes a network of traditional brick-and-mortar stores, omnichannel stores and online fulfillment centers. We develop a simple heuristic for the fully-integrated model, which is near optimal in an asymptotic sense for a large number of omnichannel stores, with a constant approximation factor dependent on cost parameters. We augment our analytical results with a realistic numerical study for networks embedded in the mainland US, and find that our heuristic provides significant benefits compared to policies used in practice. Our heuristic achieves reduced cost, increased efficiency and reduced inventory imbalance, all of which alleviate common problems facing omnichannel retailing firms. Finally, for the multiperiod setting under lost sales, we show that a base-stock policy is optimal for the fully-integrated model.With e-commerce growing at a rapid pace compared to traditional retail, many brick-and-mortar firms are supporting their online growth through an omnichannel approach, which integrates inventories across multiple channels. We analyze the inventory optimization of three such omnichannel fulfillment systems for a retailer facing two demand streams (online and in-store). The systems differ in the level of fulfillment integration, ranging from no integration (separate fulfillment center for online orders), to partial integration (online orders fulfilled from nearest stores) and full integration (online orders fulfilled from nearest stores, but in case of stockouts, can be fulfilled from any store). We obtain optimal order-up-to quantities for the analytical models in the two-store, single-period setting. We then extend the models to a generalized multi-store setting, which includes a network of traditional brick-and-mortar stores, omnichannel stores and online fulfillment centers. We develop a simple heuristic for the fully-integrated model, which is near optimal in an asymptotic sense for a large number of omnichannel stores, with a constant approximation factor dependent on cost parameters. We augment our analytical results with a realistic numerical study for networks embedded in the mainland US, and find that our heuristic provides significant benefits compared to policies used in practice. Our heuristic achieves reduced cost, increased efficiency and reduced inventory imbalance, all of which alleviate common problems facing omnichannel retailing firms. Finally, for the multiperiod setting under lost sales, we show that a base-stock policy is optimal for the fully-integrated model.http://deepblue.lib.umich.edu/bitstream/2027.42/136157/1/1341_Govindarajan.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136157/4/1341_Govindarajan_Apr2017.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136157/6/1341_Govindarajan_Jan18.pdfDescription of 1341_Govindarajan_Apr2017.pdf : April 2017 revisionDescription of 1341_Govindarajan_Jan18.pdf : January 2018 revisio