Deterministic Mixed-integer Programming Model Research Articles

Optimisation of long-term quarry production scheduling under geological uncertainty to supply raw materials to a cement plant

ABSTRACT The success of a cement production project depends on the supply of raw materials. Long-term quarry production scheduling (LTQPS) based on resource models is essential to maintain a consistent supply to cement plants. Geological uncertainty is inherent due to sparse exploration data in resource models and significant risk factors for not achieving production targets. This research proposes a stochastic framework for LTQPS that considers the impact of geological uncertainty on raw material supply. A clustering algorithm uses multiple simulated deposit models to aggregate blocks into mining cuts. A new stochastic mixed-integer programming model is formulated with two objectives: to minimise the cost for developing the raw mix and the risk of not meeting production targets. The proposed framework is implemented successfully in a limestone deposit in Southern Vietnam, resulting in an increase of 5 million tons (Mt) and a 30% reduction in unit cost over the deterministic mixed-integer programming model.

Two-Stage Stochastic Programming for the Refined Oil Secondary Distribution With Uncertain Demand and Limited Inventory Capacity

In recent years, more and more oil companies adopt initiative delivery mode to make the refined oil secondary distribution scheme. In this work, we focus on the optimization problem of refined oil secondary distribution based on the initiative distribution mode considering stochastic demand and the limited inventory capacity of each petrol station. We present a two-stage stochastic programming model that determines the replenishment quantity of each petrol station based on its existing stock and the available supply quantity of each oil depot, as well as transportation schedule. When the uncertainty in demand can be captured via a finite set of scenarios, the two-stage stochastic programming model is transformed into an equivalent deterministic mixed integer programming model that can be efficiently solved by CPLEX solver. The effectiveness of the two-stage stochastic programming model is verified by simulation on extensive computer-generated instances. To solve practical problems with a large number of scenarios, we propose a method to reduce the problem scale by merging similar scenarios. We demonstrate that compared to the optimal solution obtained from the model with all scenarios, the gap corresponding to the model with merged scenarios is always less than 1%. The results of the sensitivity analysis show that an increase in the inventory capacity leads to a decrease in the total cost within a certain range. The results of this study can help companies making refined oil secondary distribution plan.

Inventory policies for humanitarian aid during hurricanes

In this work we present a stochastic programming model minimizing costs, to support the decision process of inventory policy which best satisfies the demand for food in shelters when hurricane winds are about to impact a town. In this model we consider perishable products as well as the first in first out (FIFO) system for their consumption. In order to make the model closer to reality ordering cost is time-varying and we add a penalty cost in case the shortage exceeds a known limit for two days in a row. Finally the cost to dispose of expired food is greater than the purchase cost of the product since throwing away food has ethical implications. Starting from a stochastic programming model, we present a procedure to transform it to a deterministic mixed integer programming model (MIP) with non-convex objective function over its entire domain, which closely states the situation in reality. Preliminary computational results and discussion are presented.

Optimal Policies for Crude Oil Selection

In this paper, we investigate the crude oil selection problem derived from the production of a large typical oil refinery. A deterministic mixed integer programming model for making purchasing decisions in the refinery is proposed in which practical transportation requirements are considered. The objective is to select the varieties of crude oil and determine the purchasing, production and inventory quantities under complicated material-balance constraints and capacity constraints for minimizing the sum of purchasing, order, inventory and transportation costs. A numerical example indicates the extensive application of the presented model.

Optimal Planning for Product Blending

This paper deals with the product blending problem originating from the production system of a large typical oil refinery. A deterministic mixed integer programming model is proposed. The objective is to make an effective production-inventory plan for product blending unit (PBU) in order to meet the demand of product oil with no backlogging allowed and minimize the total costs, that is, the sum of purchasing, production, inventory and setup costs. The constraints related to material balance, different capacities and different production schemes are considered. A numerical example is subsequently provided to illustrate the broad applicability of the proposed model.

Quantitative Modeling of the Capacitated Multi-Level Production-Inventory Problem in Petroleum Industry

This research deals with the multi-level capacitated lot-sizing problem originating from the production system of a large typical oil refinery. A deterministic mixed integer programming model based on the minimization of setup, production, transportation and inventory costs is formulated to determine the production, inventory and transportation quantities in each time period under complicated material-balance and capacity constraints. A numerical example is subsequently provided to illustrate the broad applicability of the proposed model.

A DESIGN STRATEGY FOR ALLOCATION OF FACILITIES IN AN ASSEMBLY LINE SYSTEM FOR THROUGHPUT MAXIMIZATION AND BOTTLENECK CONTROL

An optimal design strategy is developed to control the bottleneck problem, and for optimal utilization of a finite capacity integrated assembly line system (consisting of a set of tandem workstations, a set of inspection stations, a loading station and an unloading station, lined by a material handling system). To develop the proposed design strategy, a stochastic optimization model is presented to allocate flexible facilities amongst a set of workstations, such that the throughput rate from the system is maximized, while the resulting probability of finding either a workstation or a transporter station blocked will be sufficiently close to zero. The proposed stochastic optimization model is a non-linear channce constrained mixed integer programming model which is transformed into a deterministic mixed integer programming model, and is solved by a branch and bound algorithm.

A Dynamic Resource Allocation Model for A Machine Requirements Problem

Abstract This paper is concerned with the problem of determining the optimum number of machines to have in a production process. The problem is analyzed as a resource allocation problem involving the minimum cost allocation of limited floor space, capital budget, and available overtime among various types of machines. The dynamic nature of the problem is also included in the analysis. A deterministic mixed integer programming model is described. A numerical example is presented to illustrate the approach and its utility as an alternative way to address the machine requirements problem.