Inventory Availability Research Articles

On the solution of large-scale mixed integer programming scheduling models

In this paper, we show how four recently developed modeling and solution methods can be integrated to address mixed integer programs for the scheduling of large-scale chemical production systems. The first method uses multiple discrete time grids. The second adds tightening constraints that lower bound the total production and number of batches for each task and material based on the customer demand, while the third generates upper bounding constraints based on inventory and resource availability. The final method is a reformulation that introduces a new integer variable representing the total number of batches of a task. We apply the aforementioned methods to large-scale problems with a variety of processing features, including variable conversion coefficients, changeovers, various storage policies, continuous processing tasks, setups, and utilities, using a discrete-time model. We illustrate how these methods lead to significant improvements in computational performance.

Single vehicle routing with predefined client sequence and multiple warehouse returns: the case of two warehouses

We examine three interesting cases of the single vehicle routing problem with a predefined client sequence and two load replenishment warehouses. Given the location and demand of the clients, we seek the minimal cost route, which includes optimal load replenishment visits to the warehouses in order to fully satisfy the client demand. The cases studied vary with respect to inventory availability at each warehouse and are of increasing complexity. We have developed solution algorithms that address this complexity, ranging from a standard dynamic programming algorithm for the simplest case, to labeling algorithms and a new partitioning heuristic. The efficiency of these algorithms has been studied by solving a wide range of problem instances, and by comparing the results with those obtained from a state-of-the-art MILP solver.

The role of physical distribution services as determinants of product returns in Internet retailing

Pressure continues to build on Internet retailers to squeeze out inefficiencies from their day-to-day operations. One major source of such inefficiencies is product returns. Indeed, product returns in Internet retailing have been shown to be, on average, as high as 22% of sales. Yet, most retailers accept them as a necessary cost of doing business. This is not surprising since many retailers do not have a clear understanding of the causes of product returns. While it is known that return policies of retailers, along with product attributes, are two important factors related to product return incidents, little is known about which aspects of the online retail transaction make such a purchase more return-prone. In the current study, we seek to address this issue. We use a large data set of customer purchases and returns to identify how process attributes in physical distribution service (PDS) influence product returns. The first attribute involves perceptions of scarcity conditions in inventory availability among consumers when retailers reveal to consumers information on inventory levels for the products that they intend to buy. Our results show that orders in which items are sold when these conditions are revealed to shoppers have a higher likelihood of being returned than orders in which these conditions are not revealed. While prior research has argued that inventory scarcity perceptions have an effect on purchases, our findings suggest that they are also related to the likelihood of these purchases being returned. The second attribute involves the reliability in the delivery of orders to consumers. We find that the likelihood of orders being returned depends on the consistency between retailer promises of timeliness in the delivery of orders and the actual delivery performance of the orders. Moreover, we find that the effect that consistency in the delivery has in the likelihood of returns, is stronger for orders that involve promises for expedited delivery than for orders with less expeditious promises. That is, although the occurrence of returns depends on the delays in the delivery of orders to consumers relative to the initial promises made by the retailers, this effect is more notable for orders that involve promises of fast delivery.

Integration of Online and Offline Channels in Retail: The Impact of Sharing Reliable Inventory Availability Information

Using a proprietary data set, we analyze the impact of the implementation of a “buy-online, pick-up-in-store” (BOPS) project. The implementation of this project is associated with a reduction in online sales and an increase in store sales and traffic. These results can be explained by two simultaneous phenomena: (1) additional store sales from customers who use the BOPS functionality and buy additional products in the stores (cross-selling effect) and (2) the shift of some customers from the online to the brick-and-mortar channel and the conversion of noncustomers into store customers (channel-shift effect). We explain these channel-shift patterns as an increase in “research online, purchase offline” behavior enabled by BOPS implementation, and we validate this explanation with evidence from the change of cart abandonment and conversion rates of the brick-and-mortar and online channels. We interpret these results in light of recent operations management literature that analyzes the impact of sharing inventory availability information. Our analysis illustrates the limitations of drawing conclusions about complex interventions using single-channel data. This paper was accepted by Alok Gupta, special issue on business analytics.

Exposure To ABO Compatible But Non-Group Identical Blood and In-Hospital Mortality

BackgroundTransfusions that are ABO compatible but not group identical (mismatched) are given for a variety of reasons including inventory availability, avoiding wastage from outdating, and clinical urgency. A recent observation at our centre suggested that patient outcome was different for those patients that received a transfusion of units with a compatible but mismatched ABO group compared to those receiving ABO group identical blood. Hence, we performed a retrospective hospital registry study to explore the association between mismatched blood and in-hospital mortality in transfused patients. Study DesignOur patient/blood utilization database included 35,487 transfused hospitalized patients from 3 acute care academic centres from April 1, 2002 to October 31, 2011. Information on transfused RBCs included duration of storage (days) and ABO type. Patient data included: sex; age; hemoglobin; creatinine; diagnosis; interventions; ABO blood group and hospital discharge status. Factors associated with mismatched blood and in-hospital mortality were examined using generalized estimating equations to account for the potential serial dependence over multiple transfusions. The effect of exposure to ABO mismatched blood on in-hospital death was examined through Cox regression with time-dependent strata defined by: year of first admission; disease group; and the cumulative number of units transfused (≤ 7 days of storage; > 7 days but ≤ 28 days storage; and, >28 days of storage); and, controlling for available baseline and time-varying characteristics. Results18,843 patients (blood groups A, B and AB), with complete covariates contributed to the analysis. Factors associated with transfusion of mismatched blood included: younger patient age (p<0.0001); lower hemoglobin (p<0.0001); higher creatinine (p<0.0001); intervention during hospitalization (OR=4.6, p<0.0001); and, patient ABO group whereby blood types A and B were much less likely to receive a mismatched unit compared to type AB patients (p<0.0001). There was a statistically significant interaction between patient blood type and the effect of receiving mismatched blood (p=0.034) with type A patients incurring a 79% higher risk of death (RR=1.79, 95% CI: 1.20, 2.67; p=0.0047); other patient blood types did not suggest increased risk. Similar results were observed when suspected trauma patients (≥ 6 units within 24 hours) were excluded from the analysis (Table 1).Table 1Multivariate Cox regression models for overall survival. Time Origin: from day of 1st transfusion; Stratified by: cumulative number of fresh blood transfused (≤7 days), cumulative number of middle age units transfused ( >7 days but ≤ 28 days), cumulative number of older units transfused (>28 days), year of first admission and comorbidities; Adjusted for: sex, age at admission (years), any intervention (time-varying), creatinine (μmol/L, time-varying) and hemoglobin (g/dL, time-varying).Full Cohort N=18,843Full Cohort excluding Trauma Patients (≥ 6 units in 24 hours) N=17,435RR95% CIpRR95% CIpABO Mismatch vs no mismatch1.220.92, 1.630.17321.140.84, 1.550.3999Mismatch by Patients ABO groupA: mismatch vs no mismatch1.791.20, 2.670.00471.681.08, 2.620.0216B: mismatch vs no mismatch0.640.30, 1.340.23190.720.34, 1.500.3793AB: mismatch vs no mismatch1.010.62, 1.650.96740.910.55, 1.510.7189Interaction test (2df)0.03400.0806 ConclusionControlling for known potential confounders through Cox regression yielded evidence of increased risk of in-hospital mortality among blood type A patients receiving group O red cells. This association remained after suspected trauma patients were excluded from the analyses. Further study of the association observed in this study is warranted. Disclosures:Cook:CIHR: Research Funding. Heddle:CIHR: Research Funding; Canadian Blood Services: Membership on an entity's Board of Directors or advisory committees, Research Funding; Health Canada: Research Funding. Eikelboom:CIHR: Research Funding.

An agent based model for the subsidized LPG with a closed distribution system

Purpose – This paper aims to explore major causes of the failure of the existing subsidized liquefied petroleum gas (LPG) distribution system and recommends alternative strategies. Design/methodology/approach – The analysis of subsidized LPG with a closed distribution system was carried out based on preliminary study, secondary data collection, and in-depth interviews to identify the root causes of the failure in achieving the desired service levels. In this research, agent based modeling and simulation was used to explain the phenomena occurred in the closed distribution system represented by three types of agents, namely selling agents, sub-selling agents, and end-users. Findings – Agent based modeling and simulation was successfully applied to describe the undesired symptoms in the closed distribution system. The simulation shows that the distribution system provides a service level of 81.61 percent by selling agents and 97.38 percent by sub-selling agents. The root cause analysis indicates that service and inventory levels in the LPG distribution system are strongly influenced by end-users demand variations, rationing system, and the occurrence of inventory leakage. To enhance the system quality, the Indonesian Government needs to implement the LPG with a closed distribution system using control card in real practice so that monitoring system can be significantly improved and ensure well-targeted subsidy. Research limitations/implications – This research is limited to the discussion of inventory level and availability. It does not include the issue of pricing, speculation, and targeting accuracy, because of the limitation of the existing data. Practical implications – This research will assist stakeholders involved in the distribution system such as selling agents and retailers to better understand the true potential of the LPG closed distribution system in preventing shortages. Originality/value – This paper describes that agent based modeling and simulation is very useful, especially to gain insights for improving the LPG closed distribution system.

Inventory System Design by Fuzzy Logic Control: A Case Study

Existing inventory lot-sizing models assume certain demand and sufficient supply, which are not practical for industry. Dynamic inventory models can serve uncertain demand, but supply is assumed to be available. However, in the real world situation, supply is not always offered. So, the method that can deal with both uncertain demand and supply should be developed. Fuzzy logic control is now being the effective methodology in many applications under uncertainty. Therefore, a fuzzy logic approach for solving the problem of inventory control under uncertainty was proposed for a case study factory. In the proposed Fuzzy Inventory System (FIS), both demand and availability of supply are described by linguistic terms. Then, the developed fuzzy rules are used to extract the fuzzy order quantity and the fuzzy reorder point continuously. The order quantity and reorder point are both adjusted according to the FIS system. In this research, the suitable ranges for the inputs of the FIS model are justified for the case study factory. Moreover, the effect of trend demands for both increase and decrease are also analyzed with the proposed range. Inventory costs of the proposed fuzzy inventory system are compared with the existing model based on historical data of the case study factory. It found that the proposed range can obtain lower cost than the previous research FIS lot-sizing model, which is better than conventional approaches.

A Study of Theory of Constraints Supply Chain Replenishment System

An effective inventory replenishment method implemented in the supply chain is one of the key success factors to achieve low inventory while maintaining high customer delivery performance. The Theory of Constraints (TOC) Supply Chain Replenishment System (TOC-SCRS) is one of the solutions to get this improvement in a multi-echelon supply chain. The TOC-SCRS is a replenishment method of the TOC supply chain solution. The TOC is a global managerial methodology that helps the manager to concentrate on the most critical issues. The TOC-SCRS is based on the following two strategies to decouple the bullwhip effect (or excess inventory in each node) and maintain the inventory availability to consumers (next nodes): (1) each node holds enough stock to cover demand during the time it takes to reliably replenish; (2) each node only needs to replenish what was sold. The TOC- SCRS is now being implemented by a growing number of companies. The performance reported by the implemented companies includes reduction of inventory level, lead-time and transportation costs and increasing forecast accuracy and customer service levels. However, the exploration of TOC-SCRS is lack in the literature. In this study, the concept and method of TOC-SCRS is first reviewed and modeled. A virtual supply chain case is secondly designed to show the behavior of the TOC-SCRS. A three factorial experiment, i.e., fluctuation of demand, time of replenishment and frequency of replenishment, is then presented to explore the feasibility and effectiveness of TOC-SCRS. A simulation model is designed to complete the experiment.

Blood supply management: experience and recommendations from the Netherlands

Sanquin Blood Supply is the only organization mandated to supply and deliver allogeneic blood products to all hospitals as requested. In the Netherlands two main responsible organizations can be distinguished, the blood establishment (Sanquin) and the hospitals. Sanquin monitors yearly the hospital demand for next years budget, the basis for the yearly collection plan with weekly steering based on the actual inventory levels. Blood supply management was developed recently to understand how nationally organized blood supply organizations have blood available for patients in need. An update was done of an analysis as recommended by the Council of Europe working party of the strength and weaknesses, opportunities and threats of the blood supply organisation in the Netherlands as described previously [http://dx.doi.org/10·1111/j.1423-0410·2009·1252.x]. The strengths are first the long standing commitment of voluntary blood donors. Donor commitment is high and research to understand motivation and retention to predict trends and developments in availability is important. This research has contributed to the EU co-funded DOMAINE project (Donor MAnagement IN Europe). The second strength is inventory management on a National level. The cooperation between blood supply and hospital transfusion laboratories is a third strength. A fourth strength is the national consensus on Blood Transfusion from experts in the whole transfusion chain that serves as national guideline. The transfusion trigger in the consensus resulted in a low 2011 transfusion rate of 31/1000 inhabitants as quality marker. Weaknesses are limited business hours for collection as result of efficiency aggravated by an ongoing decrease in demand. Further, inventory management has focused on minimizing the discard and less excess collection asks for flexible steering. Especially for Fresh Frozen Plasma steering effects are delayed by the 6 months quarantine period with risk of shortages by sudden increased demand or decreased collection levels. Another weakness is the challenge to get detailed clinical demand information. Opportunities of one virtual national inventory are the development of mathematical tools to support optimal inventory management. The increasing donor selection criteria may lead to less donor availability as a threat to the system. In the Netherlands the blood supply was centralized and with a national inventory availability is maintained and discard minimized. A national blood collection plan with weekly inventory review for RBC per blood type drives the operations. Mathematical models are used to optimize inventory management of platelets and developed for RBC. The EU co-funded DOMAINE manual describes donor management, while strict transfusion triggers resulted in moderate demand. This integrated system of donor and inventory management with moderate clinical use resulted in a reliable supply. Challenges encountered are delayed steering effect on fresh frozen plasma inventory levels, while safety measures and demographic changes can become a threat.

Review of SKUs in the Indian Paint Industry

A stock-keeping unit or SKU is a unique identifier for each distinct product that can be purchased. SKUs are used in data management, enabling the company to systematically track its inventory or product availability. Each SKU is attached to a Product, Shade and Pack Size. The Decorative or architectural segment (which constitutes upto 70% of the total paint market) involves a very wide choice in terms of products, shades and pack sizes. In addition to this, in order to offer innovative products, companies are continuously offering newer shades to match the colour of carpets/curtains etc. Initially, these shades are produced in anticipation and once the market accepts these shades, they are produced regularly. While Industrial Paints are available in bulk packs of 20lt and 200lt, decorative paints are available in 20lt, 10lt, 4lt, 1lt, 500ml, 200ml, 100ml and 50ml packs. Enamel category alone has got around 720 SKUs. The combination of different products, shades and packs sizes resulted in over 2500 SKUs for Asian Paints. Through a survey of paint dealers, effort has been made to analyze the reasons for accumulation of slow moving stock, and the solutions adopted by the dealers to liquidate these stocks. The paper concludes by suggesting remedies to deal with high inventory cost and a large number of SKUs.

Management Insights

Management Insights

Efficient formulations for pricing under attraction demand models

We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. Consumers' response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly.

Integration of Online and Offline Channels in Retail: The Impact of Sharing Reliable Inventory Availability Information

Using a proprietary dataset, we analyze the impact of the implementation of a “buy-online, pickup-in-store” (BOPS) project. The implementation of this project is associated with a reduction in online sales and an increase in store sales and traffic. These results can be explained by two simultaneous phenomena: (1) additional store sales from customers who use the BOPS functionality and buy additional products in the stores (cross-selling effect) and (2) the shift of some customers from the online to the brick-and-mortar channel and the conversion of noncustomers into store customers (channel-shift effect). We explain these channel shift patterns as an increase in “research online, purchase offline” (ROPO) behavior enabled by BOPS implementation, and we validate this explanation with evidence from the change of cart abandonment and conversion rates of the brick-and-mortar and online channels. We interpret these results in light of recent operations management literature that analyzes the impact of sharing inventory availability information. Our analysis illustrates the limitations of drawing conclusions about complex interventions using single-channel data.

Contingency planning for natural disasters

Contingency planning for natural disasters

Joint Dynamic Pricing of Multiple Perishable Products Under Consumer Choice

In response to competitive pressures, firms are increasingly adopting revenue management opportunities afforded by advances in information and communication technologies. Motivated by these revenue management initiatives in industry, we consider a dynamic pricing problem facing a firm that sells given initial inventories of multiple substitutable and perishable products over a finite selling horizon. Because the products are substitutable, individual product demands are linked through consumer choice processes. Hence, the seller must formulate a joint dynamic pricing strategy while explicitly incorporating consumer behavior. For an integrative model of consumer choice based on linear random consumer utilities, we model this multiproduct dynamic pricing problem as a stochastic dynamic program and analyze its optimal prices. The consumer choice model allows us to capture the linkage between product differentiation and consumer choice, and readily specializes to the cases of vertically and horizontally differentiated assortments. When products are vertically differentiated, our results show monotonicity properties (with respect to quality, inventory, and time) of the optimal prices and reveal that the optimal price of a product depends on higher quality product inventories only through their aggregate inventory rather than individual availabilities. Furthermore, we show that the price of a product can be decomposed into the price of its adjacent lower quality product and a markup over this price, with the markup depending solely on the aggregate inventory. We exploit these properties to develop a polynomial-time, exact algorithm for determining the optimal prices and the profit. For a horizontally differentiated assortment, we show that the profit function is unimodal in prices. We also show that individual, rather than aggregate, product inventory availability drives pricing. However, we find that monotonicity properties observed in vertically differentiated assortments do not hold.

Management Insights

Management Insights

Inventory Management of a Fast-Fashion Retail Network

Working in collaboration with Spain-based retailer Zara, we address the problem of distributing, over time, a limited amount of inventory across all the stores in a fast-fashion retail network. Challenges specific to that environment include very short product life cycles, and store policies whereby an article is removed from display whenever one of its key sizes stocks out. To solve this problem, we first formulate and analyze a stochastic model predicting the sales of an article in a single store during a replenishment period as a function of demand forecasts, the inventory of each size initially available, and the store inventory management policy just stated. We then formulate a mixed-integer program embedding a piecewise-linear approximation of the first model applied to every store in the network, allowing us to compute store shipment quantities maximizing overall predicted sales, subject to inventory availability and other constraints. We report the implementation of this optimization model by Zara to support its inventory distribution process, and the ensuing controlled pilot experiment performed to assess the model's impact relative to the prior procedure used to determine weekly shipment quantities. The results of that experiment suggest that the new allocation process increases sales by 3% to 4%, which is equivalent to $275 M in additional revenues for 2007, reduces transshipments, and increases the proportion of time that Zara's products spend on display within their life cycle. Zara is currently using this process for all of its products worldwide.

Optimal Commodity Trading with a Capacitated Storage Asset

This paper considers the so-called warehouse problem with both space and injection/withdrawal capacity limits. This is a foundational problem in the merchant management of assets for the storage of commodities, such as energy sources and natural resources. When the commodity spot price evolves according to an exogenous Markov process, this work shows that the optimal inventory-trading policy of a risk-neutral merchant is characterized by two stage and spot-price dependent basestock targets. Under some assumptions, these targets are monotone in the spot price and partition the available inventory and spot-price space in each stage into three regions, where it is, respectively, optimal to buy and inject, do nothing, and withdraw and sell. In some cases of practical importance, one can easily compute the optimal basestock targets. The structure of the optimal policy is nontrivial because in each stage the merchant's qualification of high (selling) and low (buying) commodity prices in general depends on the merchant's inventory availability. This is a consequence of the interplay between the capacity and space limits of the storage asset and brings to light the nontrivial nature of the interface between trading and operations. A computational analysis based on natural gas data shows that mismanaging this interface can yield significant value losses. Moreover, adapting the merchant's optimal trading policy to the spot-price stochastic evolution has substantial value. This value can be almost entirely generated by reacting to the unfolding of price uncertainty, that is, by sequentially reoptimizing a model that ignores this source of uncertainty.

Designing multi-echelon service parts networks with finite repair capacity

We propose an approach to model and solve the joint problem of facility location, inventory allocation and capacity investment in a two echelon, single-item, service parts supply chain with stochastic demand. The objective of the decision problem is to minimize the total expected costs associated with (1) opening repair facilities, (2) assigning each field service location to an opened facility, (3) determining capacity levels of the opened repair facilities, and (4) optimizing inventory allocation among the locations. Due to the size of the problem, computational efficiency is essential. The accuracy of the approximations and effectiveness of the approach are analyzed with two numerical studies. The approach provides optimal results in 90% of scenarios tested and was within 2% of optimal when it did not.We explore the impact of capacity utilization, inventory availability, and lead times on the performance of the approach. We show that including tactical considerations jointly with strategic network design resulted in additional cost savings from 3% to 12%. Our contribution is the development of a practical model and approach to support the decision making process of joint facility location and multi-echelon inventory optimization.

The Value to the Customer of RFID in Service Applications*

ABSTRACTThis article examines how customer value may be affected by deploying radio frequency identification (RFID) technologies within service environments. Business articles promote operational cost savings and improved inventory management as key benefits of deploying RFID. In response, service firms are using RFID to reengineer service transactions and customer touchpoints. Customers may view these RFID applications to offer both benefits and drawbacks. This article demonstrates that individuals will recognize far more value from RFID service applications than just cost savings and inventory availability. The article analyzes qualitative survey responses on the value gained from RFID to identify a broad list of value objectives—benefits and drawbacks—associated with RFID service applications. The article contributes to academic literature by providing salient value dimensions for return on investment models of service RFID applications and for future empirical analyses of means‐ends and value‐profit chain models. Managers can use the list of dimensions to develop rich business cases for evaluating the benefits and costs from enhancing service operations with RFID. The identified drawbacks also provide managers with a resource for understanding potential risks of RFID applications.