Tarik Aouam

Fuzzy MADM: An outranking method

Abstract Multi-attribute decision making forms an important part of the decision process for both the small (an individual) and the large (an organization) problems. When available information is precise, many methods exist to solve this problem. But the uncertainty and fuzziness inherent in the structure of information make rigorous mathematical models inappropriate for solving this type of problems. This paper incorporates the fuzzy set theory and the basic nature of subjectivity due to the ambiguity to achieve a flexible decision approach suitable for uncertain and fuzzy environment. The proposed method can take both crisp and fuzzy inputs. An outranking intensity is introduced to determine the degree of overall outranking between competing alternatives, which are represented by fuzzy numbers. The comparison of these degrees is made through the concept of overall existence ranking index. A numerical example is given to illustrate the approach.

An evolutionary programming approach for solving the capacitated facility location problem with risk pooling

In this paper, we propose a genetic algorithm as an alternative technique for solving the capacitated facility location problem with risk pooling (CLMRP). The CLMRP is a joint location-inventory problem involving a single supplier and multiple retailers that face stochastic demand. Due to the stochasticity of demand associated with each retailer, risk pooling may be achieved by allowing some retailers to serve as distribution centres (DCs). This is a combinatorial optimisation problem that has been shown to be NP-hard. A genetic algorithm that is computationally very efficient is developed to solve the problem. A computational experiment is conducted to test the performance of the developed technique and computational results are reported. The algorithm can easily find optimal or near optimal solutions for benchmark test problems from the literature, where the Lagrangian relaxation approach was used.

Integrated production planning and order acceptance under uncertainty: A robust optimization approach

The aim of this paper is to formulate a model that integrates production planning and order acceptance decisions while taking into account demand uncertainty and capturing the effects of congestion. Orders/customers are classified into classes based on their marginal revenue and their level of variability in order quantity (demand variance). The proposed integrated model provides the flexibility to decide on the fraction of demand to be satisfied from each customer class, giving the planner the choice of selecting among the highly profitable yet risky orders or less profitable but possibly more stable orders. Furthermore, when the production stage exceeds a critical utilization level, it suffers the consequences of congestion via elongated lead-times which results in backorders and erodes the firm’s revenue. Through order acceptance decisions, the planner can maintain a reasonable level of utilization and hence avoid increasing delays in production lead times. A robust optimization (RO) approach is adapted to model demand uncertainty and non-linear clearing functions characterize the relationship between throughput and workload to reflect the effects of congestion on production lead times. Illustrative simulation and numerical experiments show characteristics of the integrated model, the effects of congestion and variability, and the value of integrating production planning and order acceptance decisions.

Modelling and solving the multiperiod inventory-routing problem with stochastic stationary demand rates

The inventory-routing problem (IRP) is a typical logistics optimisation problem that supply chains, implementing vendor managed inventory (VMI), are confronted with. It combines inventory control and vehicle routing. The main objective of the IRP is to jointly determine optimal quantities of the product to be delivered to the retailers, delivery periods and optimal vehicle routes for the shipment of these quantities. This paper considers a multiperiod inventory-routing problem with stochastic stationary demand rates (MP-SIRP). The problem is first formulated as a linear mixed-integer stochastic program for which we propose a deterministic equivalent approximation model (MP-DAIRP). This latter model can be decomposed into two well-know subproblems: an inventory allocation subproblem and a vehicle routing subproblem. The stochastic aspect of the demand is accounted for in the inventory allocation subproblem. The vehicle routing subproblem is solved as a deterministic mixed-integer problem. Lagrangian relaxation is used to determine close to optimal feasible solutions for the MP-DAIRP. Results of the proposed Lagrangian relaxation approach on some numerical examples are reported and thoroughly discussed.

A benchmark based AHP model for credit evaluation

In this work, a credit assessment and decision-making model is developed for financial institutions to evaluate the credibility of potential borrowers. Typically, financial institutions keep records of individuals and enterprises that have been evaluated as credible based on multiple internal criteria and were granted a loan. Among these borrowers, some turn out to be solvent, i.e., they are able to repay their debts on time and others insolvent. The present paper proposes a two-stage procedure for development banks to evaluate and assess credit risk of local communes in Morocco. In the first stage, a benchmark based analytical hierarchy process (AHP) is developed to represent subjective decisions based on knowledge and experience of decision-makers. The benchmark is a small yet representative and diversified set of solvent communes selected by the decision-maker against which a potential borrower can be compared, according to a set of qualitative and quantitative criteria. Once a potential borrower has been evaluated as acceptable, the second stage applies a discriminant analysis (DA) model to classify the borrower as either solvent, in which case the loan is granted or insolvent. The proposed model is applied and validated using a real case study from a Moroccan development bank.

Robust strategies for natural gas procurement

In order to serve their customers, natural gas local distribution companies (LDCs) can select from a variety of financial and non-financial contracts. The present paper is concerned with the choice of an appropriate portfolio of natural gas purchases that would allow a LDC to satisfy its demand with a minimum tradeoff between cost and risk, while taking into account risk associated with modeling error. We propose two types of strategies for natural gas procurement. Dynamic strategies model the procurement problem as a mean-risk stochastic program with various risk measures. Naive strategies hedge a fixed fraction of winter demand. The hedge is allocated equally between storage, futures and options. We propose a simulation framework to evaluate the proposed strategies and show that: (i) when the appropriate model for spot prices and its derivatives is used, dynamic strategies provide cheaper gas with low risk compared to naive strategies. (ii) In the presence of a modeling error, dynamic strategies are unable to control the variance of the procurement cost though they provide cheaper cost on average. Based on these results, we define robust strategies as convex combinations of dynamic and naive strategies. The weight of each strategy represents the fraction of demand to be satisfied following this strategy. A mean-variance problem is then solved to obtain optimal weights and construct an efficient frontier of robust strategies that take advantage of the diversification effect.

Chance-Constraint-Based Heuristics for Production Planning in the Face of Stochastic Demand and Workload-Dependent Lead Times

While the problem of planning production in the face of uncertain demand has been studied in various forms for decades, there is still no completely satisfactory solution approach. In this chapter we propose several heuristics based on chance-constrained models for a simple single stage single product system with workload-dependent lead times, which we compare to two-stage and multi-stage stochastic programing formulations. Exploratory computational experiments show promising performance for the heuristics, and raise a number of interesting issues that arise in comparing solutions obtained by the different approaches.

Multi-item production routing problem with backordering: a MILP approach

The aim of this paper is to present mixed integer linear programming formulations for the production routing problem with backordering (PRP-B) and a new hybrid heuristic to solve the problem. The PRP-B is considered in the context of a supply chain consisting of a production facility with limited production and storage capacities and geographically dispersed points of sale with limited storage capacities. The PRP-B integrates multiple item lot sizing decisions and vehicle routing decisions to the points of sale, where backordering of end customer demands is allowed at a penalty. Two integrated mixed integer programming models are formulated and a solution procedure consisting of a relax-and-fix heuristic combined with a local search algorithm is proposed. The numerical results show that this hybrid heuristic outperforms a state-of-the-art MIP commercial solver, in terms of solution quality and CPU times.

Traffic analysis for GSM networks

When GSM was introduced in the early 90s, it was considered an over specified system. Nowadays, it is obvious that the whole range of services is widely in use. In addition, performance is degrading due to the rapidly increasing number of mobile subscribers, numbering over 2.9 billion subscribers around the world. The performance of cellular networks is the most important issue concerning their operators. The main goal is to keep subscribers satisfied with the delivered quality of service (QoS). In order to achieve the best performance, service providers have to monitor and optimize their network continuously. A Network Management System (NMS) with an online database is responsible for the collection of data on live networks. For greater effectiveness, operators install systems that do a lot more than collect and store raw data. These systems are easier to use and take advantage of all the data provided by the NMS. In this paper, we summarize measurements that were carried out on an operative GSM-1900 network to evaluate the performance of the GSMs Air-Interface (Um), during eight months. In this paper we have established statistically the following facts: (i) The peak hour in North America is between 4:00 and 5:00 PM. (ii) During week days the duration of calls increases from Monday through Friday. (iii) Weekend traffic is different from week-days traffic. Using a regression analysis we forecast traffic over time. The presented KPIs along with the derived statistical facts are crucial for operators who are concerned with maintaining a reliable and stable network, while maintaining an acceptable QoS.

Zero-order production planning models with stochastic demand and workload-dependent lead times

We present three different formulations of a simple production planning problem that treat workload-dependent lead times, limited capacity and stochastic demand in an integrated fashion. We compare chance-constrained models, two-stage stochastic programming and robust optimisation using computational experiments. Our results show that the robust optimisation approach is promising, but all the different models face different but challenging issues in addressing this complex problem. We also conclude that successful approximations to this difficult problem with the potential for practical implementation can be developed.