Semi-infinite Programming Model Research Articles

A robust multi-supplier multi-period inventory model with uncertain market demand and carbon emission constraint

The multi-period inventory management determines the optimal order quantity of products at the beginning of each period, which is an important research issue in supply chain management. In this paper, we propose a robust multi-supplier multi-period inventory model with uncertain market demand and uncertain unit carbon emission in transportation. We select product quality, ordering cost, service level, and emergency capacity as evaluation criteria for each supplier, employ analytic hierarchy process (AHP) technique to comprehensively evaluate and score each supplier. According to the evaluated score, the order weight for each supplier is obtained. In our model, we develop carbon emission constraint based on the carbon cap and carbon trading mechanism. As for uncertain market demand and uncertain unit carbon emission in transportation, we construct Box+Ball and Budget uncertainty sets to characterize various model uncertainties. The robust inventory model is a semi-infinite programming model, and cannot be solved directly. We transform the semi-infinite programming model into a mixed-integer second-order cone-programming (MISOCP) one via cone duality theory. Finally, the effectiveness of the proposed optimization method is illustrated by a case study.

Robust mechanism design and production structure for assembly systems with asymmetric cost information

We consider the design of a robust procurement mechanism for an assembler who must procure multiple complementary components under limited information regarding the unit production costs of the potential suppliers. We abandon the standard assumption that there exists a common prior distribution for the suppliers’ costs and we employ the max-min criterion in which we design a mechanism to maximize the assembler’s worst-case expected profit when only the means of the suppliers’ costs are known. We formulate this problem using a linear semi-infinite programming model and we apply a primal-dual approach to reduce the problem to a single joint optimization model. We characterize the optimal procurement mechanism (payments and ordering quantities) under the assumption of balanced ordering and uncertain end-customer demand. We use these results to compare the performance of component production, under which the components are sourced from separate suppliers, and integrated production, under which the components are sourced from the same supplier. We find that component production is preferred when the production costs of the components are heterogeneous. We also propose two heuristic mechanisms which are easier to compute and implement in practice, particularly when the number of components is large. Finally, we extend our analysis to the case in which the average and variance of the suppliers’ costs are known.

Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty

IPSIP model for used tire management and planning under uncertainty is developed.Flexible long-term purchasing, retreading, inventory and allocation plans are provided.The model can handle real-lif...

Interval-parameter semi-infinite programming model for used tire management and planning under uncertainty

In the European Union, approximately 3.6milliontonnes of used tires are generated annually. Because used tires are not biodegradable, there is strong motivation to successfully manage this fast-growing waste flow. One of the most popular approaches for sustainable environmental stewardship of used tires is retreading. The problem investigated in this paper is to identify optimized purchasing, retreading, and inventory planning schemes of used tires in multiple tire retreading plants as well as allocation patterns of retreaded, reusable, and end-of-life tires that secure maximized profit within a multi-period planning horizon and under multiple uncertainties. This paper proposes an interval-parameter semi-infinite programming model for used tire management and planning. The underlying difference between this model and those developed in previous research is its ability to consider the effects of external impact factors related to complicated economic, environmental, and social activities on used tire management systems. Moreover, it can successfully handle real-life uncertainties of the used tire management systems expressed as functional and crisp intervals. A numerical example is provided to demonstrate the usefulness of the developed model. Flexible long-term purchasing, retreading, inventory, and allocation plans, which are adjustable with variations of external impact factors, are obtained. The presented model has advantages in addressing the dynamic complexity of used tire management systems by introducing the functional interval parameters associated with the price of a new tire as well as electricity and gas prices and labor costs in waste management and transportation sectors. Compared with the available models, the resulting solutions are far more robust because they are able to satisfy all possible levels of external impact factors. The presented model is beneficial for the tire retreading industry, which processes millions of used tires annually.

Optimal joint distance and time toll for cordon-based congestion pricing

This paper addresses the optimal toll design problem for the cordon-based congestion pricing scheme, where both a time-toll and a nonlinear distance-toll (i.e., joint distance and time toll) are levied for each network user’s trip in a pricing cordon. The users’ route choice behaviour is assumed to follow the Logit-based stochastic user equilibrium (SUE). We first propose a link-based convex programming model for the Logit-based SUE problem with a joint distance and time toll pattern. A mathematical program with equilibrium constraints (MPEC) is developed to formulate the optimal joint distance and time toll design problem. The developed MPEC model is equivalently transformed into a semi-infinite programming (SIP) model. A global optimization method named Incremental Constraint Method (ICM) is designed for solving the SIP model. Finally, two numerical examples are used to assess the proposed methodology.

An immune-genetic algorithm for introduction planning of new products

The introduction planning problem of new products can be described as a semi-infinite programming model with infinite constraints. To solve complex constrained optimization problems, a new immune-genetic algorithm is proposed in this paper. In this approach, first of all, some antigens are randomly generated for the production and training of antibodies. Then, an efficient immune system with the capability to recognize self- and non-self-antigens is supported by these trained antibodies. The resulting immune system is built into genetic algorithms, and they can be used to identify and repair the illegal and infeasible chromosomes during the genetic iterations. The recommended algorithm can improve the performance of genetic algorithms particularly in complex constrained optimization problems. It has been achieved satisfactory results from the new product introduction problems.

Identification of Optimal Urban Solid Waste Flow Schemes under Impacts of Energy Prices

A large number of interval linear programming models were developed for urban solid waste management under uncertainty. Nevertheless, few of them can address the possible effects of energy prices on the identified waste management policies. This study proposes a fuzzy interval semi-infinite programming model by introducing the concept of a functional interval into the waste management problem. The model is applied to a case study and compared to the existing fuzzy interval linear programming (FILP) and interval semi-infinite programming (ISIP) models to illustrate the differences in producing associated waste management polices. Results reveal that the energy prices do have impacts on the optimal waste flow patterns, net system benefit, and satisfactory degree. In contrast to FILP, the FISIP model can produce a policy with low risk of system failure (or high satisfactory degree), and has better adaptability to the energy price fluctuations. In addition, the FISIP model has the advantages over the ISIP model in that it can (1) simultaneously deal with multiple types of parameter uncertainties, (2) allow for the existence of tolerance intervals for each of the constraints, (3) reflect what extent the constrains would not be violated, and (4) provide flexible patterns for cost-effectively transporting the urban solid waste.

New product introduction planning using a 0–1 semi-infinite programming model

A quantitative approach to screen products to the market was proposed. Product life cycles describe the whole process from new products introduction through trial production to the point when it is phased out. In theory, product life cycles go though four stages including introduction, growth, maturity and decline. However, there are very few practical products following such a prescriptive cycle. Based on product family analysis, the characteristics of new products can be classed into four categories with respective benefit curves and parameters. The curve parameters of each type can be determined according to the data derived from market prediction. A 0–1 semi-infinite programming (0–1 SIP) model was presented to describe the problem of new products introduction. An inexact approach to 0–1 semi-infinite programming was recommended for the model solution. Examples with numerical results indicate the potential industrial applications of the proposed approach.

A semi-infinite programming model for earliness/tardiness production planning with simulated annealing

To describe the earliness/tardiness production planning problems in the JIT environment, a nonlinear semi-infinite programming model was proposed in [1]. Due to a nonconvex objective function and infinitely many constraints, the model is difficult to solve by traditional methods. In this paper, simulated annealing method combined with a heuristic and the steepest descent method is developed. Numerical results shows that the present approach is very efficient. In theory, the developed method is an attempt to solve a continuous domain problem by simulated annealing.

A semi-infinite programming model for earliness/tardiness production planning with a genetic algorithm

To closely describe the earliness/tardiness production planning problems in the JIT environment, a nonlinear semi-infinite programming model is proposed. Due to the issues of non-convexivity and having infinitely many constraints, instead of applying traditional optimization approaches, a specially designed genetic algorithm with mutation along the negative gradient direction is developed. The proposed algorithm is a combination of the steepest descent method with the stochastic sampling algorithm. Some numerical results are included to show its potential for industrial applications.