A Continuous Review Inventory System with Lost Sales and Emergency Orders

We analyze a continuous review lost sales inventory system with two types of orders—regular and emergency. The regular order has a stochastic lead time and is placed with the cheapest acceptable supplier. The emergency order has a deterministic lead time is placed with a local supplier who has a higher price. The emergency order is not always filled since the supplier may not have the ability to provide the order on an emergency basis at all times. This emergency order has a higher cost per item and has a known probability of being filled. The total costs for this system are compared to a system without emergency placement of orders. This paper provides managers with a tool to assess when dual sourcing is cost optimal by comparing the single sourcing and dual sourcing models

Linear integrated location-inventory models for service parts logistics network design

We present two integrated network design and inventory control problems in service-parts logistics systems. Such models are complicated due to demand uncertainty and highly nonlinear time-based service level constraints. Exploiting unique properties of the nonlinear constraints, we provide an equivalent linear formulation under part-warehouse service requirements, and an approximate linear formulation under part service requirements. Computational results indicate the superiority of our approach over existing approaches in the literature

Impact of inventory inaccuracy on service-level quality: A simulation analysis

This article discusses the impact of inventory inaccuracy on service-level quality in (Q,R) continuous review, lost-sales inventory models. A simulation model is built to study the behaviour of this kind of model exposed to an inaccuracy in inventory records as well as demand variability. We have observed an unusual result which goes against certain empirical practices in the SMEs that consist in hiking the inventory level proportionally to the data inaccuracy rate. A nonmonotone function shows that at the outset, the service-level quality is lowered as the inaccuracy rate increases but when the inaccuracy rate becomes much higher this quality is conversely enhanced. This relation can equally be observed given that stocktaking commences as soon as the threshold of decline in the service-level rate has been reached and when demand consequently dwindles. Finally, another noteworthy result also shows the same phenomenon between the function involving a level of safety stock defined by the simulation and the function between the service-level quality and the inventory inaccuracy. These different observed results are discussed in terms of both contribution to the (Q,R) inventory management policies in SMEs and of the limitations to this study.Continuous review inventory system, inventory inaccuracy, continuous model, discrete-time simulation

Service and inventory models subject to a delay-limit

Abstract: This thesis is concerned with the mathematical analysis of situations where service must be provided to customers within a prespecified time after arrival, the delay-limit (e.g., due to a service contract). Customer arrivals are governed by a stochastic process, and customers can be served jointly to obtain economies of scale. In Part I a basic model is extensively analysed, using techniques from Markov decision theory and queueing theory. In Part II this model is extended to the context of the production of exchangeable items, leading to a general framework for inventory models with a delay-limit on backorders. Several models within this framework are then studied in detail, including lost-sales inventory models.

Inventory control for point-of-use locations in hospitals

Most inventory management systems at hospital departments are characterised by lost sales, periodic reviews with short lead times, and limited storage capacity. We develop two types of exact models that deal with all these characteristics. In a capacity model, the service level is maximised subject to a capacity restriction, and in a service model the required capacity is minimised subject to a service level restriction. We also formulate approximation models applicable for any lost-sales inventory system (cost objective, no lead time restrictions etc). For the capacity model, we develop a simple inventory rule to set the reorder levels and order quantities. Numerical results for this inventory rule show an average deviation of 1% from the optimal service levels. We also embed the single-item models in a multi-item system. Furthermore, we compare the performance of fixed order size replenishment policies and (R, s, S) policies

Retail inventory management with lost sales

The inventory control problem of traditional store-based grocery retailers has several challenging features. Demand for products is stochastic, and is typically lost when no inventory is available on the shelves. As the consumer behavior studies reveal, only a small percentage of customers are willing to wait when confronted with an out-of-stock situation, whereas the remaining majority will either buy a different product, visit another store, or entirely drop their demand. A store orders inventory on a periodic basis, and receives replenishment according to a fixed schedule. The ordered stock is typically delivered before the next ordering moment, which results in lead times shorter than the review period length. Order sizes are often constrained to integer multiples of a fixed batch size, the case packs, generally dictated by the manufacturer. Upon order receipt at the store, the stock is manually stacked on the shelves, to serve customer demand. Shelf space allocation of many products is limited, dictated by marketing constraints. Hence, surplus stock, which does not fit on the regular shelf, is temporarily stored in the store’s backroom, often a small place, poorly organized. The focus of this dissertation is on developing quantitative models and designing solution approaches for managing the inventory of a single item, under periodic review, when some or all of the following characteristics are taken into account: ?? Lost sales. Demand that occurs when no inventory is available is lost, rather than backordered. ?? Fractional lead time. Time between order placement and order delivery is shorter than the review period length. ?? Batch ordering. Order sizes are constrained to integer multiples of a fixed batch size. ?? Limited shelf space. Shelf space allocation is predetermined. The retailer’s inventory is split between the sales floor and the backroom, which is used to temporarily store surplus inventory not accommodated by the regular shelves. We consider optimal, as well as easy-to-understand inventory replenishment policies, where the objective is to minimize the long-run average cost of the system. Two types of costs are primarily recognized in the inventory models developed in this dissertation: ?? inventory related costs: for ordering, for holding products on stock, and penalty costs for not being able to satisfy end-customer demand, and ?? handling related costs: for shelf stacking, and for handling backroom stock. Despite empirical evidence on the dominance of handling costs in the store, remarkably little is reported in the academic literature on how to manage inventory in the presence of handling costs. A reason for this is that formal models of handling operations are still scarce. In this dissertation, we first formalize a model of shelf stacking costs, using insights from an empirical study. Then, we extend the traditional single-item lost-sales periodic-review inventory control model with several realistic dimensions of the replenishment practices of grocery retailers: batch ordering, handling costs, shelf space and backroom operations. The models we consider are too complex to lend themselves to straightforward analytical tractability. As a result, numerical solution methods based on stochastic dynamic programming are proposed in this dissertation, and near-optimal alternative replenishment policies are investigated. Chapter 2 addresses operational concerns regarding the shelf stacking process in grocery retail stores, and the key factors that influence the execution time of this common store operation. Shelf stacking represents the regular store process of manually refilling the shelves with products from new deliveries, which is typically time consuming and costly. We focus on products that are replenished in pre-packed form but presented to the end-customer in individual units. A motion and time study is executed, and the complete shelf stacking process is broken down into several sub-activities. The main time drivers for each activity are identified, relationships are established, tested and validated using real-life data collected at two European grocery retailers. A simple prediction model of the total stacking time per order line is then inferred, in terms of the number of case packs and consumer units. The model can be applied to estimate the workload and potential time savings in the stacking process. Implications of our empirical findings for inventory replenishment decisions are illustrated by a lot-sizing analysis in Chapter 2, and further explored in Chapter 3. Chapter 3 defines a single item stochastic lost sales inventory control model under periodic review, which is designed to handle fractional lead times, batch ordering and handling costs. We study the settings in which replenishment costs reflect shelf stacking costs and have an additive form with fixed and linear components, depending on the number of batches and units in the replenishment order. We explore the structure of optimal policies under the long-run average cost criterion and propose a new policy, referred to as the (s;QjS; nq) policy, which partially captures the optimal policy structure and shows close-to-optimal performance in many settings. In a numerical study, we compare the performance of the policy against the best (s; Q; nq) and (s; S; nq) policies, and demonstrate the relative improvements. Sensitivity analyses illustrate the impact of the different problem parameters, in particular the batch size and the handling cost parameters, on the optimal solutions and associated average costs. Managerial insights into the effect of ignoring handling costs in the optimization of replenishment decisions are also discussed. Chapter 4 extends the retail setting from Chapter 3 to situations in which there is a limited shelf space to display goods on the sales floor, and the retailer uses the store’s backroom to temporarily store surplus stock. As a result, the back stock is regularly transferred from the backroom to the sales floor to satisfy end-customer demand, which results in additional handling costs for the retailer. We investigate the effect of using the backroom on the inventory system performance, where performance is measured with respect to the optimal ordering decisions, and the long-run average cost of ordering, holding, lost-sales and merchandise handling. Two extensions of the inventory model with ample shelf space are proposed in Chapter 4, which include a (i) linear or (ii) fixed cost structure for additional handling operations. In a numerical study, we discuss several qualitative properties of the optimal solutions, illustrate the additional complexities of the second model, and compare the findings with those of the previous chapter. Furthermore, we build several managerial insights into the effect of problem parameters, in particular the shelf space capacity, on the system’s performance. Finally, we quantify the expected cost penalty the retailer may face by ignoring the additional handling costs in the optimization of inventory decisions, and illustrate the trade-off between the different cost components. Chapter 5 studies a variant of the traditional infinite-horizon, periodic-review, singleitem inventory system with random demands and lost sales, where we assume fractional lead times and batch ordering, and allow for ??xed non-negative ordering costs. We present a comparison of four situations: zero vs. positive setup costs, and unit vs. non-unit batch sizes. For all cases, the optimal policy structure is only partially known in general. We show in a numerical study that the optimal policy structure of the most general model is usually more complex than that of the models with positive setup cost, or batch ordering only. Based on the gained insights, we further test the performance of the near-optimal (s;QjS; nq) heuristic policy in the different cases, and demonstrate its effectiveness. Also, well-known inventory control policies of base-stock, or (s; S) type are extended to the case of batch ordering and studied in comparison with the new heuristic under several conditions

Value Iteration for Perishable Inventory Control

This thesis focuses on finding optimal order policies for perishable inventory in supermarkets. By means of value iteration (VI) and simulation, several inventory dynamics are compared. First, several cases were designed: three cases without taking perishability into account, and one case based on perishability. Case 1-3 have the following characteristics, respectively: 1) backlogging is possible, and costs should be minimized; 2) backlogging is not permitted, and profit should be maximized; 3) the customer service level (CSL) should be met, and costs should be minimized. The fourth case, 4) contains products which perish after one day, and the profit should be maximized. The calculation of an optimal order policy is performed by implementing a VI method. The optimal order quantity per inventory level calculated in VI, is used in the simulation. The four cases gave different optimal order-policies. The first three cases showed a lot of similarities, and had the characteristics of an (s; S)-policy. Case 4, containing perishable products, was highly influenced by the fixed order cost k. If the fixed order costs were low, an optimal order policy could be determined. This was not possible for high fixed order costs, the order moments and order quantities turned out to be periodic. For fixed costs which were too high, no orders were placed. The order policy for the low fixed costs did not match the policies in the inventory control chapter. In case 4, we had to deal with the curse of dimensionality. The limited shelf-life causes an increase in state space. To deal with this problem, we had to keep the elements per set of states low