Mathematical modeling to optimize production planning and scheduling in a small foundry with multiple alternating furnaces

Purpose - This study presents an extension to a model in the literature for lot-sizing and scheduling in a small foundry with multiple alternate furnaces. The purpose of the model is to minimize delays and inventory costs. In addition, it determines the best use of the load capacity in the furnaces. Theoretical framework – Lot-sizing in foundries in the marketplace is a subject of academic interest due to its applicability and mathematical and computational complexity. Many papers address the production problem in foundries with a single furnace, however, few papers address the possibility of multiple furnaces. Design/methodology/approach - Mathematical modeling was used to represent the lot-sizing and scheduling problem in a small foundry. Data from the company's order books were collected and model validation questionnaires were applied. Findings - The extended model was able to generate good production plans at different planning horizons, with better performance than the current methods obtained by the company. Originality/value - the extension of the model contributes to the literature by addressing the existence of multiple non-simultaneous furnaces, a feature that has not been greatly explored. A comparison with other models is performed to indicate the most suitable model for actual application. Keywords: Alloys scheduling. Foundry. Lot size. Mixed integer programming.

The Use of Tranexamic Acid in Anterior Cruciate Ligament Reconstruction: A Systematic Review

Background: There are several papers that investigate the use of tranexamic acid (TXA) in anterior cruciate ligament reconstructions (ACLR) or other arthroscopic procedures that show favorable results and little to no complications. We aimed to perform a systematic review of all published randomized controlled trials (RCTs) that wanted to determine the effectiveness of intravenous use of TXA in ACLR. Methods: Data collection was performed independently by two authors via a previously created spreadsheet. They extracted information such as: first author name, publication year, lot size, TXA protocol, surgical protocol, outcome measures and follow-up duration. Results: After applying the screening process and the inclusion criteria, we were left with a total six RCTs. The selected studies included a total of 699 randomized patients. Statistical significance regarding a lower pain score (VAS) in the intervention groups was mostly reported for the early postoperative period (2 weeks). A statistically significant decrease in hemarthrosis grade was reported for the first 2–3 weeks. Conclusions: in our study, we show that TXA use in arthroscopic ACLR decreases postoperative blood loss and pain. Some evidence of improvement in functional scores was observed, but we believe that this needs to be addressed in specific long-term result studies.

Equality and Closure: The Paradox of Local Citizenship

In Bourgeois Utopias, a cultural history of suburbia in America, Robert Fishman states the fundamental paradox about the suburbs: “[H]ow can a form based on the principle of exclusion include every-one?” The promise of the American suburb was that every middle-class family would be able to own a home with a yard, but this egalitarian ideal was illusory because what made the suburbs appealing was precisely what it excluded, namely everything having to do with the city—its congestion, political corruption, and most importantly, its racial diversity. And so, as suburbia was mass-produced and made avail-able with cheap low-interest loans to white middle-class families, racial minorities were rigidly excluded. Although several waves of demographic change have reshaped the suburbs over the generations, this paradox remains evident today. Suburbs are becoming more dense and more diverse as many minorities have migrated from “inner cities” toward first-ring suburbs, and immigrants have found welcoming enclaves in the suburbs. But while suburbs have grown more diverse, they have also grown more segregated. High opportunity suburbs with plentiful jobs and good schools mandate low-density sprawl through zoning regulations, like mini-mum lot size and floor area requirements, parking mandates, and set-backs, that have the cumulative effect of making housing scarce and expensive. Only the very affluent or those lucky enough to have purchased a home years ago are welcome in these places. Racial minorities who, thanks to the earlier generation of suburban exclusion, have not had the opportunity to build the inter-generational wealth that is often a prerequisite to purchasing a home in the suburbs still find themselves locked out of the most desirable communities. The infra-structure of suburban communities, such as roads, sewers, and schools, are designed, perhaps deliberately, to completely collapse if the number of users increases by even a small amount, so these communities fiercely oppose any efforts to densify and permit more housing. Even modest attempts at densification are treated as calls to destroy suburban neighborhoods. But because our society has made a decision, undoubtedly questionable in retrospect, to treat suburban homeownership as the central tool for wealth building in this country, we cannot hope to meet our national aspirations for equality without opening up our suburbs to more housing. And so the question re-mains—how can a form based on the principle of exclusion include everyone?

Optimizing Inventory Replenishment for Seasonal Demand with Discrete Delivery Times

This study investigates replenishment planning in the case of discrete delivery time, where demand is seasonal. The study is motivated by a case study of a soft drinks company in Germany, where data concerning demand are obtained for a whole year. The investigation focused on one type of apple juice that experiences a peak in demand during the summer. The lot-sizing problem reduces the ordering and the total inventory holding costs using a mixed-integer programming (MIP) model. Both the lot size and cycle time are variable over the planning horizon. To obtain results faster, a dynamic programming (DP) model was developed, and run using R software. The model was run every week to update the plan according to the current inventory size. The DP model was run on a personal computer 35 times to represent dynamic planning. The CPU time was only a few seconds. Results showed that initial planning is difficult to follow, especially after week 30, and the service level was only 92%. Dynamic planning reached a higher service level of 100%. This study is the first to investigate discrete delivery times, opening the door for further investigations in the future in other industries.

An Inventory Model for Perishable Goods with Partial Backlogging of Shortages

This study illustrates inventory associated with deteriorating items. Nowadays the incident deterioration has a major impact on the preservation of goods in terms of handling inventory. The significant effect of deterioration has been observed on volatile liquids, fish, vegetables, etc. Here a mathematical model is presented incorporating the effect of deterioration. The model has been developed on an infinite time horizon. The shortage is allowed and backlogged partially. We aim to find out lot-size and back-ordered quantities in order to minimize the total average cost. In support of the proposed model, a numerical example has been provided. The stability of the solution of that example has been confirmed by performing a sensitivity analysis of key parameters. A graphical representation of cost function regarding decision variables has been displayed.

Parameter values for lot size and quality level via CAE simulation, statistical method, and mathematical programming

Because of the stochastic nature of production systems, it is necessary to first build an uncertainty model for subsequent real applications. Moreover, process parameter planning, quality design, and production inventory management are interdependent elements. In this research, a computer simulation model via computer-aided engineering (CAE) was developed to determine the optimal process parameters, lot size, and back order intervals for an integrated process design and inventory management system with simultaneous quality and cost considerations. Based on the estimated process time and costs obtained using CAE, the derived production rate and unit cost were then used for production inventory applications. In consideration of the uncertainty factor, the response surface method (RSM) was employed to analyze the output, namely the total costs incurred in employing the proposed approach, as well as the inputs, which include the cutting parameters, production quantity, and back order intervals. After the RSM was used to obtain the response functions, which represent the output of the collective interests, the mathematical programming (MP) was formulated based on the response functions to determine the optimal process parameters, process quality levels, production order quantities, and back order intervals. The total cost per set time unit was minimized by determining the required quality level, process parameter values, Economic Production Quantity (EPQ), and back order intervals. A cutting example was chosen to demonstrate the proposed approach. Two cases were used for comparison: the Integrated Case (the proposed approach herein) and the Disintegrated Case.

Optimal Price and Lot Size for an EOQ Model with Full Backordering under Power Price and Time Dependent Demand

In this paper, we address an inventory system where the demand rate multiplicatively combines the effects of time and selling price. It is assumed that the demand rate is the product of two power functions, one depending on the selling price and the other on the time elapsed since the last inventory replenishment. Shortages are allowed and fully backlogged. The aim is to obtain the lot sizing, the inventory cycle and the unit selling price that maximize the profit per unit time. To achieve this, two efficient algorithms are proposed to obtain the optimal solution to the inventory problem for all possible parameter values of the system. We solve several numerical examples to illustrate the theoretical results and the solution methodology. We also develop a numerical sensitivity analysis of the optimal inventory policy and the maximum profit with respect to the parameters of the demand function.

Lot-Size Models with Uncertain Demand Considering Its Skewness/Kurtosis and Stochastic Programming Applied to Hospital Pharmacy with Sensor-Related COVID-19 Data

Governments have been challenged to provide timely medical care to face the COVID-19 pandemic. Under this pandemic, the demand for pharmaceutical products has changed significantly. Some of these products are in high demand, while, for others, their demand falls sharply. These changes in the random demand patterns are connected with changes in the skewness (asymmetry) and kurtosis of their data distribution. Such changes are critical to determining optimal lots and inventory costs. The lot-size model helps to make decisions based on probabilistic demand when calculating the optimal costs of supply using two-stage stochastic programming. The objective of this study is to evaluate how the skewness and kurtosis of the distribution of demand data, collected through sensors, affect the modeling of inventories of hospital pharmacy products helpful to treat COVID-19. The use of stochastic programming allows us to obtain results under demand uncertainty that are closer to reality. We carry out a simulation study to evaluate the performance of our methodology under different demand scenarios with diverse degrees of skewness and kurtosis. A case study in the field of hospital pharmacy with sensor-related COVID-19 data is also provided. An algorithm that permits us to use sensors when submitting requests for supplying pharmaceutical products in the hospital treatment of COVID-19 is designed. We show that the coefficients of skewness and kurtosis impact the total costs of inventory that involve order, purchase, holding, and shortage. We conclude that the asymmetry and kurtosis of the demand statistical distribution do not seem to affect the first-stage lot-size decisions. However, demand patterns with high positive skewness are related to significant increases in expected inventories on hand and shortage, increasing the costs of second-stage decisions. Thus, demand distributions that are highly asymmetrical to the right and leptokurtic favor high total costs in probabilistic lot-size systems.