Multi-period Mixed-integer Programming Model Research Articles

Optimization on the multi-period empty container repositioning problem in regional port cluster based upon inventory control strategies

Within the area of regional port clusters, this paper establishes a multi-period mixed integer programming model to optimize the empty container repositioning between public hinterlands and ports, comprehensively considering the quantitative and periodic inventory control strategy. At the same time, this paper dynamically and heuristically determines the empty container inventory threshold (D, U) under quantitative strategy and S under periodical strategy at each port within the regional port clusters. On this basis, the empty container repositioning schemes between public hinterlands and ports are optimized by using Markov decision process combined with dynamic programming method. In addition, Liaoning coastal regional port cluster and its northeast hinterland are selected as the objects to solve this model and the results show that the total cost of shipping company can be saved by 14.16% and 11.92%, respectively, by the quantitative and periodical inventory control strategy. Selecting the quantity of public hinterland terminals, the empty container demand of public hinterland terminals and ports, the inventory threshold of empty containers and other factors, this paper carries on the sensitivity analysis. This paper validates inventory control strategy can weaken the shipping company in the influence of the external environment changes. And the quantitative inventory control strategy can reduce the total cost value to a greater extent and more effective in cost control than periodical strategy.

Sustainable renewable energy supply networks optimization – The gradual transition to a renewable energy system within the European Union by 2050

In order to achieve the goal of a carbon neutral EU by 2050 and meet the climate targets of the Paris Agreement, a sustainable, efficient, competitive and secure energy system needs to be developed. This paper presents the synthesis of sustainable renewable energy supply networks within the EU-27, proposing a stepwise energy transition in the transport and power sectors, achieving a carbon net neutral target by 2050. A multi-period mixed-integer programming model is developed, with the objective of maximizing sustainability net present value, considering different biomass and waste resources for the production of biofuels, renewable electricity, hydrogen, food and bioproducts, employing different types of technologies. The results show that, with further development of existing technologies, the goal of a carbon-neutral EU can be achieved without compromising food production. Wind farms have proven to be the most promising solution at present for the rapid expansion of electricity generation from renewable energy sources, while the importance of solar photovoltaics is increasing over the years, reaching the 43% share of electricity generation from RES in 2050. Moreover, the energy transition within the EU could have a significant positive impact on the economic, environmental and also social aspects of sustainability, with more than 1.5 million new job opportunities created across the EU over the next 30 years.

Multi-Period Mixed Integer Programming Model for Supply Chain Planning Under Safety Stock

Supply chain management philosophy has been adopted by enterprises due to the requirement of customer demand satisfaction in reasonable times under market competition. In case of rapid increase in product demands and/or occurrence of supply problems in materials, enterprises choose holding some amount of safety stock of several materials and products. In this study, a multi-period, multi-product supply chain with different suppliers, material storages, production plants, distribution centers and customers is modeled. To determine the optimal production, supply and storage plans at minimum cost, a mixed-integer programming model is proposed. Capacity, bill-of-materials structure of products and placement of safety stocks are taken into account within the proposed model. Solutions of a set of examples are also presented in order to test the model.

A multi-period ambulance location and allocation problem in the disaster

To achieve quick response in the disaster, this paper addresses the issue of ambulance location and allocation, as well as the location problem of temporary medical centers. Considering budget and capacity limitations, a multi-period mixed integer programming model is proposed and two hybrid heuristic algorithms are designed to solve this complex problem. The proposed model and algorithm are further verified in a real case study, and the numerical experiments demonstrate the effectiveness of our proposed model. Specifically, we obtain several findings based on the computational results: (1) The best locations of ambulance stations should change in each period because the demand rate changes over time. (2) Involving temporary medical centers is necessary to reduce the average waiting time of injured people. (3) It may not be optimal to allocate ambulances from the nearest ambulance stations because of potentially limited station capacity.

A multi-period mixed integer programming model on reconfigurable manufacturing cells

In general, the popular cell systems have two streams. One is the divided cell in Cellular Manufacturing (CM) and the other is the rotating cell in Cell Production Systems (CPS). Almost all manufacturing sites have these assembly lines separately. On the other hand, some advanced manufacturing sites have adopted both CM and CPS in order to absorb variability of demand and operators under the environment of limited multi-skilled operators. When the operators are replaced by robots in the real world, they are called robotic cells and focused as an important component of the cyber-physical system in the large number of recent papers. Therefore, this paper tackles to indicate a multi-period mixed integer programming model to solve simultaneously 2-type cell systems on reconfigurable manufacturing cells sustainably. Firstly, the traditional model is redefined by new parameters. Secondly, the proposed model is solved by 2-phase optimization problems. Finally, the proposed model is compared with the traditional model by using numerical experiments.

Production planning for stochastic manufacturing/remanufacturing system with demand substitution using a hybrid ant colony system algorithm

A hybrid manufacturing/remanufacturing system (HMRS) is an effective tool to address the global challenge of resource depletion and environmental deterioration. This paper aims to make an optimal production plan for a stochastic HMRS with demand substitution. To achieve the above objective, a multi-period mixed integer programming model was first constructed. An ant colony system algorithm with random sampling method (ACS-RSM) was proposed to minimize the total expected cost of the stochastic HMRS. Finally, the proposed model and ACS-RSM algorithm were applied to an auto alternator case. The effects of the used product recovery rate and batch sizes of new and remanufactured products on the total expected cost were analyzed. The research results showed that the ACS-RSM algorithm performed well regarding computational efficiency and solution quality. There were two major findings through the practical case study. The first finding was that with increase of recovery rate of used product, total expected cost of the HMRS declined dramatically until a certain point. When the recovery rate was greater than 91%, the total expected cost kept almost constant. The second finding was that when the batch sizes of the new product and remanufactured product rose, the total expected cost had an obvious increase and the running time of the ACS-RSM algorithm decreased monotonically. The study yields an effective decision-making tool for optimizing the production plan of the stochastic HMRS with demand substitution.

A Landscape-Scale Optimisation Model to Break the Hazardous Fuel Continuum While Maintaining Habitat Quality

Wildfires have demonstrated their destructive powers in several parts of the world in recent years. In an effort to mitigate the hazard of large catastrophic wildfires, a common practice is to reduce fuel loads in the landscape. This can be achieved through prescribed burning or mechanically. Prioritising areas to treat is a challenge for landscape managers. To help deal with this problem, we present a spatially explicit, multiperiod mixed integer programming model. The model is solved to yield a plan to generate a dynamic landscape mosaic that optimally fragments the hazardous fuel continuum while meeting ecosystem considerations. We demonstrate that such a multiperiod plan for fuel management is superior to a myopic strategy. We also show that a range of habitat quality values can be achieved without compromising the optimal fuel reduction objective. This suggests that fuel management plans should also strive to optimise habitat quality. We illustrate how our model can be used to achieve this even in the special case where a faunal species requires mature habitat that is also hazardous from a wildfire perspective. The challenging computational effort required to solve the model can be overcome with either a rolling horizon approach or lexicographically. Typical Australian heathland landscapes are used to illustrate the model but the approach can be implemented to prioritise treatments in any fire-prone landscape where preserving habitat connectivity is a critical constraint.

Achieving full connectivity of sites in the multiperiod reserve network design problem

The conservation reserve design problem is a challenge to solve because of the spatial and temporal nature of the problem, uncertainties in the decision process, and the possibility of alternative conservation actions for any given land parcel. Conservation agencies tasked with reserve design may benefit from a dynamic decision system that provides tactical guidance for short-term decision opportunities while maintaining focus on a long-term objective of assembling the best set of protected areas possible. To plan cost-effective conservation over time under time-varying action costs and budget, we propose a multi-period mixed integer programming model for the budget-constrained selection of fully connected sites. The objective is to maximize a summed conservation value over all network parcels at the end of the planning horizon. The originality of this work is in achieving full spatial connectivity of the selected sites during the schedule of conservation actions.

A multi-period mixed integer programming model for the problem of relocating a global manufacturing facility

In the recent years, changing business conditions have triggered labor-intensive global manufacturers to consider relocating out of the Pearl River Delta of China, known as “The World's Factory.” This article presents a multi-period mixed integer programming model for the problem of relocating a global manufacturing facility. The objective function of the model is to maximize total after-tax profit. The model addresses dynamic aspects of timing, including potential developments in business factors and the need for a gradual capacity transfer in order not to disrupt supply chain activities. The model application generates an optimal capacity transfer schedule and forecasts after-tax profits. In general, a stable exchange rate for the Chinese currency, renminbi (RMB), would make lower-cost areas of China more competitive. Also, a dramatic RMB appreciation would enhance the comparative advantage of Asian lower-cost countries. A rapid increase in oil prices would make locations near major markets more favorable in order to avoid high transportation costs.

A mathematical programming model for improvement planning in a semi-subsistence farm

In some semi-subsistence agriculture systems, long fallows have traditionally been used to maintain soil fertility, but fallow periods are often shortened because of increased pressure on land, resulting in reduced crop yields. In such cases crop yields can often be increased by adopting agricultural methods based on the use of new crop varieties, fertilisers and herbicides. These improved cultivation techniques must be introduced over a number of years, but the transition process has received little attention in evaluating improvement of semi-subsistence cultivation systems. In this paper a mathematical programming approach is developed for planning the introduction of improved cultivation systems in a semi-subsistence farm in northern Chiapas, Mexico. This new approach first uses a linear programming model to determine capital dependent steady state cultivation policies. Results from this steady model are then incorporated into a multiperiod mixed integer programming model for determining steady state policy and the associated improvement plan.

Modeling Norwegian petroleum productionand transportation

In the continental shelf off the coast of Norway, there are several petroleum fields containinga mixture of oil and gas. A multiperiod mixed integer programming model for investmentplanning for these fields has been used by The Norwegian Petroleum Directorate for morethan fifteen years. In practical use, the production from each field has mostly been declaredto follow profiles given by the user, but the user may also declare that the production canvary from the given profile. This paper describes the model and comments on some of thereal problems the model has been used to analyze and the modeling process involved.

A development planning model for deer farming

Abstract In existing methods for planning development of a livestock enterprise, the age-dependent population dynamics of the livestock are not fully considered, and both the planning horizon and the state of the enterprise at the end of this period must be specified. In this paper a mathematical programming approach, based on livestock population dynamics, is proposed for planning development of a deer farm. A steady state linear programming model is first used to determine the optimal steady state policy and herd structure for farms of specified sizes, and these results are incorporated in a multiperiod mixed integer programming model in which binary variables represent the discrete investments associated with farm development. This model is then used to determine the long-term steady state farm size and herd structure, together with the associated investment strategy and operating policy in each year before the steady state is reached.

Effect of the 1985 Farm Bill Provisions on Farmers' Soil Conservation Decisions

Abstract Conservation initiatives in the 1985 Farm Bill affected farmers' decisions regarding soil conservation. A farmer survey was conducted and a multi-period mixed-integer programming model was developed to determine an optimal farm plan with choices of crop-tillage combinations and land retirement Results indicate that farmers' incentives to reduce soil loss in the Sand Mountain region in Alabama are not substantially affected by provisions of the 1985 Farm Bill. The bid price for the Conservation Reserve Program will have to be considerably higher than 1988 levels to provide an incentive to remove land from production.

RADIOISOTOPE PRODUCTION SCHEDULING IN A NUCLEAR REACTOR

ABSTRACTA multiperiod mixed integer programming model has been developed for the production scheduling of several grades of a radioisotope in a nuclear reactor. Of special interest is the model's capability to evaluate possible future product “short falls” due to the acceptance of an unforecasted demand sales opportunity. The model is essential to decisions concerning reactor loading after an extended shutdown of several periods for modifications, maintenance, and upgrading.