Mathematical Programming Model Research Articles

Decision support for allocating farmed fish to customer orders using a bi-objective optimization model

Aquaculture is an important industry in certain coastal areas. Focusing on farming of salmon and trout, an operational planning problem arises with the goal of allocating supply of fish to demand expressed through customer orders. This paper provides a conceptual model of such a planning problem, defines a corresponding bi-objective mathematical programming model. The problem is novel with respect to the structure of the transportation of fish, and the rules for satisfying customer orders with respect to fish size, quality, certification, and health status. Computational experiments are conducted to gain further insights into the use of the provided model to provide support for planners involved in the operational decision making. Results indicate that the bi-objective optimization model can be useful in situations where supply is insufficient to cover all the demand within a given planning horizon.

Water Pricing and Quotas: A Quantitative Analysis from a Private and Social Perspective

AbstractThe current situation of structural water scarcity due to the rise in demand, the reduction in supply as a consequence of climate change, increasingly frequent drought periods, and overall quantitative pressure on water resources creates a need for economic instruments to reduce the amount of water used, especially in the agricultural sector. Thus, water pricing and allocation quotas (proportional reduction of allocations) may be suitable tools to reduce demand or allocate scarce water resources. For a comparative analysis of the performance of these two measures, a Positive Mathematical Programming model has been developed, using the Guadalquivir River Basin as a case study. Additionally, the analysis takes into account the revenue generated from water pricing and the marginal cost of public funds. The results indicate that, from the farmer’s perspective, quotas result in smaller losses than water pricing. However, when considering water pricing along with the revenue generated from this measure, this mechanism would be more beneficial for society as a whole, since the taxes collected could be used for other purposes, albeit with efficiency losses measured by the marginal cost of public funds and the excess burden of taxation.

The stimulating effects of international emission price fluctuations on bioenergy development of an energy-importing economy

An increase in emission price creates economic incentives because bioenergy producers could sell bioenergy and realize values attached to emission offset. Recently, the termination of the short-term goal of carbon neutrality in some European countries has skyrocketed, and demand for fossil energy has increased, as has the emission price. This situation brings challenges and opportunities to an energy-importing economy like Taiwan, which relies on fossil imports and is vulnerable to price distortions but also gets a chance to develop low-carbon energy domestically. This study proposes a mathematical programming model to investigate how such variations in emission price would affect bioenergy development from energy crops and how bioenergy producers with different production possibilities would behave in uncertain market conditions. Some insightful results are explored. First, bioenergy producers would change their production strategies from energy-focused technologies to emission-oriented ones because the gain from co-products would make emission offset more profitable. At a high emission price, biopower production declines from 11,492 GWh to about 3315 GWh. Still, more than 8.73 million tons of biochar is produced, and the total offset from bioenergy and biochar sequestration expands to 33.7 million tons of CO2. Second, the production pattern of energy crops varies substantially under market conditions. Energy crop plantation at low energy prices is 227,000–263,000 ha but expands to 638,000–798,000 ha when energy and emission prices increase. Third, reducing bioenergy production does not necessarily minimize social welfare because the gain from carbon sequestration may outweigh the loss from reduced bioenergy production at high emission prices. Potential policies that can be applied to adjust production strategies are also discussed in detail.

Agri-food supply chain optimization through a decentralized production process in the olive oil industry

A tactical/operational model is proposed to assist decision-making in harvest planning and olive oil production planning of the different producers in the rural sector, considering allocation and transportation decisions of the kilograms of olives to the production plant with temporary relocation decisions of the mobile olive oil mills through decentralized production activities in the agri-food supply chain. A Mixed Integer Linear Programming model is presented that maximizes the profit of small farmers in the production process of single-varietal extra virgin olive oil. The decisions are based on the geographical dispersion of the different olive growers and the oil concentration of the olive varieties in a certain period, which depends on the climatic conditions of each sector where the olives are cultivated. The mathematical programming model is applied in Coquimbo, Chile, using actual data collected from previous harvest seasons. The computational results of the optimization model indicate that transportation decisions impact olive harvesting and oil production decisions. It is concluded that cooperatives of small producers in the rural sector increase overall profits and reduce transportation costs and the number of kilometers traveled by at least 41% through a decentralized production process with mobile production plants.

Mathematical programming models for order picking in warehouses with decoupling of picker and cart

As a special Travelling Salesman Problem (TSP), the Single-Picker Routing Problem (SPRP) in warehouses is of important theoretical and practical significance. In manual order picking, the items are usually picked up by a picker with a cart. To speed up the picking process, the picker is allowed to stop the cart to pick up the items individually and return to the location of the cart. This paper proposes a mixed integer linear programming formulation for an order picking problem with the decoupling of the picker and the cart in a multi-block warehouse, where the picker capacity is at most four. And based on this model, order batching problem is also analysed. Through numerical experiments, the cost of above decoupling problems is computed under different settings of the speed ratio and the capacity of the picker while he/she is travelling alone. The results indicate how the decoupling of picker and cart leads to cost reduction. Our model shows good performance for orders of small and medium scale and hence has great potential to improve the order picking operation which is executed by decoupling containers and robots/vehicles in modern digital warehouse systems.

Data-Driven Heuristic Optimization for Complex Large-Scale Crude Oil Operation Scheduling

This paper addresses the challenging scheduling of crude oil operations (SCOO) problem, characterized by the intricate sequencing of activities involving discrete events and continuous variables. Given the NP-Hard nature of scheduling problems due to their combinatorial complexity, this study employs a data-driven optimization approach. Initially, historical operational data relevant to the SCOO are scrutinized; however, due to data limitations, small-scale instances are solved using a mathematical programming model to generate data. Subsequently, operational solution data are processed using the Apriori algorithm, a renowned data mining technique. The insights gained are translated into heuristic rules, laying the groundwork for a novel data-driven heuristic algorithm tailored for the SCOO problem. This algorithm is then applied to a 45-day scheduling scenario, demonstrating the efficacy of the proposed approach.

A robust optimization model for multi-objective blood supply chain network considering scenario analysis under uncertainty: a multi-objective approach

Annually, different regions of the world are affected by natural disasters such as floods and earthquakes, resulting in significant loss of lives and financial resources. These events necessitate rescue operations, including the provision and distribution of relief items like food and clothing. One of the most critical challenges in such crises is meeting the blood requirement, as an efficient and reliable blood supply chain is indispensable. The perishable nature of blood precludes the establishment of a reserve stock, making it essential to minimize shortages through effective approaches and designs. In this study, we develop a mathematical programming model to optimize supply chains in post-crisis scenarios using multiple objectives. Presented model allocates blood to various demand facilities based on their quantity and location, considering potential situations. We employ real data from a case study in Iran and a robust optimization approach to address the issue. The study identifies blood donation centers and medical facilities, as well as the number and locations of new facilities needed. We also conduct scenario analysis to enhance the realism of presented approach. Presented research demonstrates that with proper management, crises of this nature can be handled with minimal expense and deficiency.

Collaborative optimization of routing and storage strategy of multi-period multimodal transport in an uncertain environment

This study uses a storage service strategy to investigate a multiperiod multimodal transport routing and transit planning problem (MPMT-RTP). First, a mathematical integer programming model is used to describe the problem in a deterministic environment. Second, two robust optimization models are established to address the uncertainty of the freight rate fluctuations in each period and the storage space in the total set, thereby improving the solving efficiency of the model through a robust equation transformation. Subsequently, hybrid heuristics are proposed to solve the above problems, and a series of small-scale experiments are conducted to verify the accuracy of the model and effectiveness of the algorithm. Finally, this study conducts case experiments based on survey data. The results show that the total operating cost is reduced by 13.31 % via strategic multiperiod multimodal transport planning. A price fluctuation study shows that under different price fluctuations, the transportation and storage periods of some orders change accordingly, and under three specific price fluctuations, the operating costs are 1085100, 967330, and 948770, respectively. Therefore, the results of this study can provide theoretical guidance for enterprises to optimize their resource allocation paradigms and better adapt to freight rate fluctuations to minimize their operating costs.

Efficient approach to cyclic scheduling of high throughput screening systems for bioengineering

As a standard technology, high throughput screening (HTS) is widely applied for the analysis and detection of new biological substances and drugs in pharmaceutical industries and life science research. Efficient scheduling of HTS systems is a crucial issue for reducing the cost of their operations. As a typical application of high throughput screening, this work studies the scheduling problem of the enzyme-linked immunoassay (ELISA) processes in HTS systems. For this process, it requires a one-microplate cyclic schedule and a microplate visits some processing resources multiple times, making the process deadlock-prone such that its scheduling problem is very challenging. To tackle this problem, the process is modeled by a kind of Petri nets. Based on this model, by analyzing the dynamic properties of the process, it is able to directly deduce an activity sequence to form an optimal cyclic schedule. In this way, it not only efficiently solves the challenging scheduling problem without building a mathematical programming model, but also the obtained schedule is very easy to understand and implement.

Presenting a new model for evaluating the factors affecting equipment reliability using system dynamics

AbstractThis study examines reliability of equipment (RoE) through three approaches: equipment design reliability, human reliability (HR), and maintenance‐based reliability. HR plays a key role in minimizing human error (HE) and subsequently enhancing RoE. Given that equipment reliability is influenced by numerous factors, these technologies come with various constraints, multiple outputs, and inputs. Compared to mathematical programming and analytical models, simulation methods in the field of reliability are relatively limited. However, system dynamics (SD) modeling is well‐suited to capture dynamics and complexity of systems, making it a valuable tool for long‐term strategic decision‐making. In this study, a combination of SD and regression approaches has been employed to explore the relationship between reliability and key variables such as HE and profit. Initially, the variables influencing reliability are identified, and then SD is utilized to understand the processes and interactions among these variables. Furthermore, linear regression is employed to establish the relationship between affective variables, reliability, and HE. To validate the results obtained from the proposed method, a sensitivity analysis is conducted. The results demonstrate the effectiveness of the proposed model. Simulation results indicate that implementing policies such as employee training and preventive maintenance significantly enhances RoE, leading to increased sales and profits for the organization. Therefore, managers should prioritize these variables and allocate adequate attention and resources to them.

Socioeconomic impact of agricultural water reallocation policies in the Upper Litani Basin (Lebanon): a remote sensing and microeconomic ensemble forecasting approach

The integration of remote sensing and socio-economic data is crucial for policy making in regions suffering from water scarcity and climate change. We present a framework that combines remotely sensed estimates of biomass and water use from FAO’s Water Productivity Open-access portal (WaPOR) (V2) with an ensemble of calibrated mathematical programming models to assess the impact of water reallocations on rain-fed and irrigated land use and production in water-stressed basins. We evaluated our model in the Upper Litani Basin of Lebanon using two water reallocation policies: (i) quotas that progressively reduces water allocation for irrigation up to 100%, at 1% intervals and (ii) a pricing policy that increases the agricultural water price up to 0.25 USD/m3, at 0.0025 USD/m3 intervals. Our results reveal that 1) the impacts of water availability reductions due to quotas on profit and employment are less-than-proportional when water allocation is reduced by <50%, but abruptly increase when water allocation is reduced by >50%; 2) irrigators responses to prices are inelastic until a price increase of 0.03 USD/m3, become significantly more elastic afterwards, and again become inelastic above a price increase of 0.06 USD/m3; 3) higher water prices progressively reduce profit and labor, significantly reduce water use over the elastic interval (where irrigators cultivating low value-added crops shift to rainfed agriculture), and increase tariff revenue during the inelastic interval (where irrigators largely stick to their crop portfolios and pay the higher water prices). Our results reveal nontrivial uncertainties and tipping points, thus highlighting the value of combining reliable water use data with multi-model and multi-scenario ensembles in informing robust policies.

Circular closed-loop supply chain network design considering 3D printing and PET bottle waste

AbstractOne of the most critical pillars of Industry 4.0 (I4.0) is Additive Manufacturing (AM) or 3D Printing technology. This transformative technology has garnered substantial attention due to its capacity to streamline processes, save time, and enhance product quality. Simultaneously, environmental concerns are mounting, with the growing accumulation of plastic bottle waste, offering a potential source of recycled material for 3D printing. To thoroughly harness the potential of AM and address the challenge of plastic bottle waste, a robust supply chain network is essential. Such a network not only facilitates the reintegration of plastic bottle waste and 3D printing byproducts into the value chain but also delivers significant environmental, social, and economic benefits, aligning with the tenets of sustainable development and circular economy. To tackle this complex challenge, a Mixed-Integer Linear Programming (MILP) mathematical model is offered to configure a Closed-Loop Supply Chain (CLSC) network with a strong emphasis on circularity. Environmental considerations are integral, and the primary objective is to minimize the overall cost of the network. Three well-known metaheuristics of Simulated Annealing (SA), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO) are employed to treat the problem which are also efficiently adjusted by the Taguchi design technique. The efficacy of our solution methods is appraised across various problem instances. The findings reveal that the developed model, in conjunction with the fine-tuned metaheuristics, successfully optimizes the configuration of the desired circular CLSC network. In conclusion, this research represents a significant step toward the establishment of a circular supply chain that combines the strengths of 3D printing technology and the repurposing of plastic bottle waste. This innovative approach holds promise for not only reducing waste and enhancing sustainability but also fostering economic and social well-being.

Optimizing Sulfur Emission Control Areas for Shipping

The design of emission control areas (ECAs), including ECA width and sulfur limits, plays a central role in reducing sulfur emissions from shipping. To promote sustainable shipping, we investigate an ECA design problem that considers the response of liner shipping companies to ECA designs. We propose a mathematical programming model from the regulator’s perspective to optimize the ECA width and sulfur limit, with the aim of minimizing the total sulfur emissions. Embedded within this regulator’s model, we develop an internal model from the shipping liner’s perspective to determine the detoured voyage, sailing speed, and cargo transport volume with the aim of maximizing the liner’s profit. Then, we develop a tailored hybrid algorithm to solve the proposed models based on the variable neighborhood search meta-heuristic and a proposition. We validate the effectiveness of the proposed methodology through extensive numerical experiments and conduct sensitivity analyses to investigate the effect of important ECA design parameters on the final performance. The proposed methodology is then extended to incorporate heterogeneous settings for sulfur limits, which can help regulators to improve ECA design in the future. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72025103, 71831008, 72201163, 72071173, 72371221, 72394360, 72394362, 72361137001 and HKSAR RGC TRS T32-707/22-N]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0278 .

Multi-Stage Mathematical Programming Models and Their Applications in Agriculture

The article presents multi-stage parametric programming models, the characteristics of which depend on time and seasonality. The first model took into account the impact on the yield of agricultural crops of predecessors. In the second model, related to the distribution of sales of products by seasons, at the first stage, a point and interval forecast of the task parameters is carried out, at the second stage, optimal coefficients are determined that characterize the volume of sales of crop products depending on the season. Then, based on the obtained forecasts and optimal coefficients, the parametric programming problem is solved. The described tasks are implemented on real objects of the Irkutsk region. Logistic and asymptotic dependences are used to predict crop yields, and the price trend is a seasonal model. It should be noted that the presented models can be refined with the help of expert assessments, which will improve the adequacy of planning the activities of agricultural producers.

Design of a mathematical model for staff planning in an emergency department

The emergency department plays a fundamental role in hospitals and critically affects a hospital's overall efficiency. Inadequate staff planning in emergency departments generates high costs, overcrowding, and patient dissatisfaction due to long waiting times, possibly putting the patient's health and life at risk. This research designed two mixed integer linear programming mathematical models. The first determined the optimal number of physicians required per shift and weekday in an adult emergency department to minimize the deviation between available and required capacity. The results of the optimization model would reduce by 16.07 % the required medical office staff per week, from 56 physicians in the current situation to 47, reducing staffing costs without impacting waiting times. Moreover, the overall physician utilization would be 95.01 % compared to 77.79 % in the current situation, indicating an adequate distribution of physicians on each shift of each day according to patient demand. These results contribute to the problem of high medical staff costs and overcrowding without sacrificing timeliness and quality of care. In contrast, the second model that minimized the number of physicians considering capacity constraints would increase the staff by 7.14 % concerning the current situation. This research was based on a model presented in the literature, but the objective function included the deviation variables as unrestricted in sign and a constraint to ensure that they were positive. The first model designed is presented as a tool to support emergency department managers in the medium-term planning of medical staff, ensuring an optimal solution to this problem

Optimization of chemotherapy regimens using mathematical programming

Cancer is a leading cause of death and a cost burden on healthcare systems worldwide. The mainstay of treatment is chemotherapy which is most often administered empirically. Optimizing the frequency of drug administration would benefit patients by avoiding overtreatment and reducing costs. In this work, the optimization of chemotherapy regimens using mathematical programming techniques is demonstrated by developing a simple mathematical programming model for the administration of a fictitious drug. The question to be answered by the solution of the model is how often the drug should be administered so that the tumor size does not exceed a predefined size and the treatment cost reaches a minimum value. The proposed mathematical programming model is computer-implemented using a well-established mathematical programming system, thus keeping the cost and effort of obtaining the optimization results low. An example is used to demonstrate the superiority of the proposed optimization approach over the mainstay approach.

An Optimization Approach to Berth Allocation Problems

The berth allocation problem determining the berthing time and position for incoming vessels in port operations has garnered increased attention within the global transportation network. This study focuses on the berth allocation problem with a continuous quay and dynamic vessel arrivals. With the overarching goal of enhancing service quality and optimizing berth utilization rates, this article proposes a mathematical programming model that minimizes the total waiting time of vessels and the overall completion time of vessel service. The formulated model is a mixed-integer linear programming problem that deterministic optimization techniques can globally solve. For large-scale problems, this study develops a genetic algorithm optimization approach to improve computational efficiency in reaching a near-optimal solution. Several numerical experiments are conducted to demonstrate the effectiveness and efficiency of the proposed approach.

Optimisasi Portofolio Saham Syariah dengan Pendekatan Fuzzy Goal Programming

This study discusses about solving the problem of stock portfolio optimization. The portfolio optimization problem can be modeled as a multiobjective model with two objective functions, they are maximizing return and minimizing risk. This study uses the mean-variance Markowitz model to model the portfolio. The fuzzy goal programming approach is used to solve stock portfolio problems by converting a multi-objective model into a fuzzy mathematical programming model which is solved using a nonlinear programming method. The results of implementing the model on stocks listed on the Jakarta Islamic Index show that the best investment proportion forms an optimal portfolio according to the level of aspirations. Several different optimal portfolios can be formed using the fuzzy goal programming approach. The difference in the results of these portfolios depends on the level of aspiration of investors.

Enhancing production monitoring: A back allocation methodology to estimate Well flow rates and assist Well test scheduling

Production flow rates are crucial to make operational decisions, monitor, manage, and optimize oil and gas fields. Flow rates also have a financial importance to correctly allocate production to fiscal purposes required by regulatory agencies or to allocate production in fields owned by multiple operators. Despite its significance, usually only the total field production is measured in real time, which requires an alternative way to estimate wells’ production. To address these challenges, this work presents a back allocation methodology that leverages real-time instrumentation, simulations, algorithms, and mathematical programming modeling to enhance well monitoring and assist in well test scheduling. The methodology comprises four modules: simulation, classification, error calculation, and optimization. These modules work together to characterize the flowline, wellbore, and reservoir, verify simulation outputs, minimize errors, and calculate flow rates while honoring the total platform flow rate. The well status generated through the classification module provides valuable information about the current condition of each well (i.e. if the well is deviating from the latest well test parameters), aiding in decision-making for well testing scheduling and prioritizing. The effectiveness of the methodology is demonstrated through its application to a representative offshore oil field with 14 producing wells and two years of daily production data. The results highlight the robustness of the methodology in properly classifying the wells and obtaining flow rates that honor the total platform flow rate. Furthermore, the methodology supports well test scheduling and provides reliable indicators for well conditions. By utilizing real-time data and advanced modeling techniques, this methodology enhances production monitoring and facilitates informed operational decision-making in the oil and gas industry.

Data-Driven Optimization for Air Traffic Flow Management with Trajectory Preferences

In this paper, we present a novel data-driven optimization approach for trajectory-based air traffic flow management (ATFM). A key aspect of the proposed approach is the inclusion of airspace users’ trajectory preferences, which are computed from traffic data by combining clustering and classification techniques. Machine learning is also used to extract consistent trajectory options, whereas optimization is applied to resolve demand-capacity imbalances by means of a mathematical programming model that judiciously assigns a feasible four-dimensional trajectory and a possible ground delay to each flight. The methodology has been tested on instances extracted from the Eurocontrol data repository. With more than 32,000 flights considered, we solve the largest instances of the ATFM problem available in the literature in short computational times that are reasonable from the practical point of view. As a by-product, we highlight the trade-off between preferences and delays as well as the potential benefits. Indeed, computing efficient solutions to the problem facilitates a consensus between the network manager and airspace users. In view of the level of accuracy of the solutions and the excellent computational performance, we are optimistic that the proposed approach can make a significant contribution to the development of the next generation of air traffic flow management tools.