Optimal Deteriorating Inventory Models for Varies Supply Life Cycles

Agriculture items, such as fruits and vegetables, have different supply and demand characteristics during a harvest period. Fruits supply in the first and end of harvest time are not reliable so sometimes supply are not available when needed. Fruits demand is different during harvest season. In the first harvest season, demand depends on price and at the end of harvest time, the demand depends on presentation of the items. In this study, inventory deteriorating items models for the first and the end of the harvest season are developed. Since closed-form solutions cannot be derived from the models, a Genetic Algorithm and a heuristic method are used to solve the problems. A numerical example and sensitivity analysis are conducted to illustrate the model and get insights. The sensitivity analysis shows that the supplier will increase his price when supply is not reliable at the early harvest period.  The results show that the unreliable supply is susceptible to the total cost at the end of the harvest period

An optimal inventory pricing and ordering strategy subject to demand dependent on stock level and price

This article considers the deterministic singular optimal control problem of profit maximisation for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the product order rate and price are derived using the maximum principle. Several initial inventory regions are identified as potential inventory states for feasible profit optimisation. Bounds on the maximum price for maximising net profit or minimising loss are obtained. Numerical simulations accompanied by phase diagrams are performed to support the theoretical findings

Optimal ordering policy with non- increasing demand for time dependent deterioration under fixed life time production and permissible delay in payments

Most of the items in the universe deteriorate over time. Many items such as pharmaceuticals, high tech products and readymade food products also have their expiration dates. This paper developes an economic order quantity model for retailer in which demand rate is linearly time dependent and non increasing function of time, deterioration rate is time dependent having expiration dates under trade credits..We then show that the total average cost is sensitive with respect to the key parameters. Furthermore, we discuss several sub- special cases. Finally, numerical examples and sensitivity analysis is provided to illustrate the results. Mathematica 5.2 software is used to find numerical results

Degradation-based Optimal Swapping Policy.

Asset management is typically coupled with maintenance management as every system, machine, or tool is bound to degrade. In many disciplines, we are faced with a system of identical assets or components that are used differently. The difference in usage is attributed to the loading profile at which these assets are operating, or the frequency of their usage. With time, the degradation of the assets will reach a level, which can result in partial or complete loss of the system performance or functionality. This is usually met by maintenance actions (substitutions) performed on the degraded assets to restore the functionality of the system, which can be significantly costly. We propose a policy, denoted as the Degradation-based Optimal Swapping (DBOS) policy, which incorporates optimal implementation of swapping and substitution actions throughout a plan of finite time horizon to minimize projected maintenance costs. The swapping action refers to the inter-change in the placement of two assets from two different loading profiles. The substitution action refers to the replacement of the degraded assets with new ones. The degradation-informed resource allocation policy takes advantage of the different degradation rates in the assets' health states, due to the different loading conditions, achieving optimal placement at different time intervals throughout the plan horizon. For the primary application of the policy, the fleet-level battery utilization for electric or hybrid-electric fleet management, the policy is shown to establish substantial savings in the projected maintenance costs compared to other policies through promoted utilization of the highly costly and degradable Li-ion batteries. The policy is further developed to account for uncertain degradation estimation employing the Stochastic Dynamic Programming (SDP) and the Markov Decision Processes (MDP) framework. Finally, the policy is integrated with perishable spare parts inventory management to achieve simultaneous optimal fleet management and optimal replenishment.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99791/1/almuhtad_1.pd

An economic order quantity model for imperfect and deteriorating items with freshness and inventory level-dependent demand

Dissertation (MEng (Industrial Engineering))--University of Pretoria, 2023.Consumer purchasing behaviour is influenced by many factors. Depending on the circumstances, these factors may become relevant drivers of important supply chain decisions. Expiration dates have an influence on the purchasing decision of consumers for perishable goods. Another behavioural influence that stimulates demand is the volume of goods that are available on display as part of the purchase transaction. Furthermore, the fact that certain goods deteriorate over time must also be evaluated within the context of the study of perishable goods. The market is increasingly seeking goods that have no inherent defects or imperfections. This investigation seeks to determine the impact of imperfect quality, deterioration, freshness and inventory level and also, how those issues can be improved upon in workable situations. This paper proposes an inventory model that stipulates the demand as a function of freshness and the inventory level. In addition, the inventory depletes through both deterioration and demand, and the product quality is not always perfect. The objective of the inventory model is to maximise the system’s profit, hence the study has developed a theoretical mathematical model for imperfect and deteriorating items with freshness and inventory level-dependent demand. A numerical example was used to illustrate the practical application of the model in a real life environment. Sensitivity studies were conducted to determine the impact of changes or variations to the inputs that are used in the model. The findings were that the date of expiry, the elasticity of demand and the selling price of the perfect products are the main constituents that affect the profitability.Industrial and Systems EngineeringMEng (Industrial Engineering)Unrestricte

Modelos de Inventarios con Productos Perecederos: Revisión de la Literatura

This paper presents a review of the main characteristics of the mathematical modelsdeveloped by the scientific community in order to determine an optimal inventory policyfor deteriorating items. Thus, a classified bibliography of 390 articles published from2001 to 2014 in high-impact journals is submitted while considering the type of demandand deterioration, the integration of inventory and pricing decisions, the inclusionof shortage and/or the time value of money, the consideration of multiple items and/ormulti-echelon systems, and the incorporation of uncertain parameters other than demand.Finally, research questions not yet addressed by the research community in the field ofinventory control for deteriorating items are pointed out.En el presente artículo se lleva a cabo una revisión de las principales características estudiadas por la comunidad científica en el desarrollo de modelos matemáticos que buscan definir una política de inventario óptima para productos que se deterioran. De este modo, se referencian 390 artículos publicados a partir del año 2001 en revistas de gran impacto, teniendo en cuenta: el tipo de demanda y deterioro representado en los modelos matemáticos, el estudio de una política de precio óptima, la inclusión de faltantes y/o valor del dinero en el tiempo, el estudio de múltiples productos y/o dos o más eslabones de la cadena de suministro, y la utilización de parámetros o variables difusas. Finalmente, se identifican oportunidades de investigación que a la fecha no han sido abordadas por la comunidad científica en este campo del conocimiento

Application of Optimization in Production, Logistics, Inventory, Supply Chain Management and Block Chain

The evolution of industrial development since the 18th century is now experiencing the fourth industrial revolution. The effect of the development has propagated into almost every sector of the industry. From inventory to the circular economy, the effectiveness of technology has been fruitful for industry. The recent trends in research, with new ideas and methodologies, are included in this book. Several new ideas and business strategies are developed in the area of the supply chain management, logistics, optimization, and forecasting for the improvement of the economy of the society and the environment. The proposed technologies and ideas are either novel or help modify several other new ideas. Different real life problems with different dimensions are discussed in the book so that readers may connect with the recent issues in society and industry. The collection of the articles provides a glimpse into the new research trends in technology, business, and the environment

Shipment consolidation and distribution models in the international supply chain

With the increasing competition in global trade, buying and transporting items effectively in the international network are critical and challenging problems for many companies. The objective of this study is to design a cost-effective consolidation and distribution method to transport shipments in a global network. In the dissertation, we investigate an integrated consolidation problem in the international supply chain, where a US manufacturing company buys multiple items from China. A proactive order consolidation strategy is proposed. Different from current practices, our approach consolidates items in China considering inland transportation in US. This strategy is modeled to minimize the total costs by effectively loading items into an ocean container considering subsequent inland transportation cost and handling cost given container capacity and packing constraints. Two difficult combinatorial optimization problems, such as a mode selection problem and a three-dimensional bin packing problem, are combined into the model. Due to the problem complexity, approximation algorithms are proposed to solve the model. The basic model is extended to consider the inland multi-stop delivery and multi-period planning horizon. Several solution methodologies are developed and evaluated to solve large-scale problems. Based on the numerical results, it is observed that our proposed methods could achieve up to 30% cost savings compared with the current shipping practices. The algorithms we developed could obtain the good implementable solution in a reasonable time for real-world problems

Optimizing Block-Stacking Operations with Relocation

The focus of the dissertation is developing the optimization problem of finding the minimum-cost operational plan of block stacking with relocation as well as devising a solution procedure to solve practical-sized instances of the problem. Assuming changeable row depth instead of permanent row depth, this research is distinguished from conventional block stacking studies. The first contribution of the dissertation is the development of the optimization problem under the assumption of deterministic demand. The problem is modeled using integer programming as a variation of the unsplittable multi-commodity flow problem. To find a good feasible solution of practical-sized instances in reasonable time, we decompose the original problem into a series of generalized assignment problems. In addition, to establish a good lower bound on the optimal objective function value, we apply a relaxation based upon Lagrangean decomposition in which the relaxed problem separates into a set of shortest path problems and a set of binary knapsack problems. The second contribution of the dissertation is the development of the optimization problem under the assumption of stochastic demand. The problem is formulated as a discrete time finite horizon Markov decision process model, incorporating the recursive daily situation of determining the assignment of product lots to storage areas for a day based on uncertain daily demand and observed system information. To tackle computational intractability in solving practical-sized instances, we develop a heuristic solution approach taking an on-line manner by instantly determining an action for a single observed state rather than an off-line manner by predetermining an action for every state

Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling

In the last decade, the Industrial Revolution 4.0 brought flexible supply chains and flexible design projects to the forefront. Nevertheless, the recent pandemic, the accompanying economic problems, and the resulting supply problems have further increased the role of logistics and supply chains. Therefore, planning and scheduling procedures that can respond flexibly to changed circumstances have become more valuable both in logistics and projects. There are already several competing criteria of project and logistic process planning and scheduling that need to be reconciled. At the same time, the COVID-19 pandemic has shown that even more emphasis needs to be placed on taking potential risks into account. Flexibility and resilience are emphasized in all decision-making processes, including the scheduling of logistic processes, activities, and projects