Jamal Ouenniche

A heuristic for the pickup and delivery traveling salesman problem

Abstract This paper deals with the pickup and delivery traveling salesman problem. First we show how to adapt some classical traveling salesman heuristics to solve this problem, then we propose a new and efficient composite heuristic. The proposed heuristic is composed of two phases: a solution construction phase including a local optimization component and a deletion and re-insertion improvement phase. To evaluate its performance, the proposed heuristic was compared to the only available heuristic specially designed to solve this problem, to an adaptation of the most efficient heuristic designed to solve the traveling salesman problem with backhaul, to an adaptation of the farthest as well as to an adaptation of the cheapest insertion methods. Each of these heuristics was followed by our deletion and re-insertion procedure which considerably improved their performance. Results based on a new set of test problems show that the proposed heuristic outperforms all these reinforced heuristics. Scope and purpose In several physical distribution problems, goods must be picked at an origin and delivered to a destination. Examples include the transportation of handicapped persons, the pickup and delivery of fast courier, of some medical supplies, etc. This problem differs from classical transportation problems because we have to deal with precedence constraints between the customers to be visited. This article describes a powerful heuristic for this difficult problem.

A general unconstrained model for transfer pricing in multinational supply chains

Multinational supply chains operate in more than one country or tax jurisdiction and face decision problems concerned with trade flows of resources, products and services, transfer prices, and allocation of transport costs between their divisions. These decisions must consider, for the sake of optimality, corporate and governmental parameters such as the payment of dividends and royalties, ownership of and control over subsidiaries, income taxes differentials, duties and quotas, etc. In this paper, we generalize and extend the Theory of the Multinational Firm to the case of multinational supply chains. We propose a model that is more general and comprehensive than the previous ones proposed in the literature. To be more specific, our model integrates many of the previous research factors and includes new ones, such as transport costs and duty drawbacks, which are critical for supply chains that operate under international trade regulations. Under the maximization of the repatriated earnings objective, we study the optimality conditions of the corporate decision variables to derive managerial guidelines and to determine how decisions regarding trade quantities, transfer prices, and transport cost allocations affect the amount of taxes to be paid to host governments as well as the total after tax repatriated earnings of the corporation.

The two-group heuristic to solve the multi-product, economic lot sizing and scheduling problem in flow shops

Abstract This paper presents a new and efficient heuristic to solve the multi-product, economic lot sizing and scheduling problem in flow shops. The problem addressed is that of making sequencing, lot sizing and scheduling decisions for a number of products so as to minimize the sum of setup costs, work-in-process inventory holding costs and final-products inventory holding costs while a given demand is fulfilled without backlogging. The proposed heuristic, called the two-group method (TG), assumes that the cycle time of each product is an integer multiple of a basic period and restricts these multiples to take either the value 1 or K where K is a positive integer. The products to be produced once each K basic period are then partitioned into K sub-groups and each sub-group is assigned to one and only one of the K basic periods of the global cycle. This method first determines a value for K and a feasible partition. Then, a production sequence is determined for each sub-group of products and a non-linear program is solved to determine lot sizes and a feasible schedule. We also show how to adapt our method to the case of batch streaming (transportation of sub-batches from one machine to the next). To evaluate its performance, the TG method was compared to both the common cycle method and a reinforced version of El-Najdawi’s job-splitting heuristic. Numerical results show that the TG method outperforms both of these methods.

The multi-product, economic lot-sizing problem in flow shops: the powers-of-two heuristic

Abstract This paper presents a new and efficient heuristic to solve the multi-product, multi-stage, economic lot-sizing problem. The proposed heuristic, called the powers-of-two method, first determines sequencing decisions then lot sizing and scheduling decisions are determined. This method assumes that cycle times are integer multiples of a basic period and restricts these multiples to the powers of two. Once time multiples are chosen, we determine for each basic period of the global cycle the set of products to be produced and the production sequence to be used. Then a non-linear program is solved to simultaneously determine lot sizes and a feasible production schedule. To evaluate its performance, the powers-of-two method was compared to both the common cycle method and a reinforced version of the job-splitting heuristic. Numerical results show that the powers-of-two method outperforms both of these methods. Scope and purpose The multi-product, multi-stage, economic lot-sizing problem studied in this paper is the problem of making sequencing, lot-sizing and scheduling decisions for several products manufactured through several stages in a flow shop environment so as to minimize the sum of setup and inventory holding costs while a given demand is fulfilled without backlogging. This problem and similar problems are met in many different industries like the food canning industry, the appliance assembly facilities or in beverage bottling companies. The most commonly used approach to deal with this problem is the common cycle approach where a lot of each product is produced each cycle. A few other approaches are also proposed. In this paper we propose a new and more efficient solution approach that assigns different cycle times to different products.

The impact of sequencing decisions on multi-item lot sizing and scheduling in flow shops

The problem of sequencing, lot sizing and scheduling a number of products in flow shops has been studied by several authors. It has been reported by some of them that the sequence to be used has a negligible impact on total cost. Consequently, little attention was given to the sequencing sub-problem. The purpose of this paper is to study the impact of sequencing decisions and to suggest some methods to determine the sequence to be used. We propose a mathematical programming based heuristic as well as some construction and local search heuristics. The proposed heuristics are compared and computational results for 360 test problems are reported. These results reveal that sequencing decisions may have a non-negligible impact on total cost and may allow us to identify the best among the heuristics tested.

The finite horizon economic lot sizing problem in job shops: The multiple cycle approach

This paper addresses the multi-product, finite horizon, static demand, sequencing, lot sizing and scheduling problem in a job shop environment where the planning horizon length is finite and fixed by management. The objective pursued is to minimize the sum of setup costs, and work-in-process and finished products inventory holding costs while demand is fulfilled without backlogging. We propose a new and efficient cyclic scheduling solution framework, called the multiple cycle (MC) method, based on the assumption that the cycle time of each product is an integer multiple of a basic period. This method relies on a decomposition approach which decomposes the problem into an assignment sub-problem, a sequencing sub-problem and a lot sizing and scheduling sub-problem. To evaluate its performance, the MC method was compared to the common cycle method and numerical results show that it performs better, as expected. However, the magnitude of improvement varies between 4% and 8% depending on the structure of the problems.

Index Policies for the Admission Control and Routing of Impatient Customers to Heterogeneous Service Stations

We propose a general Markovian model for the optimal control of admissions and subsequent routing of customers for service provided by a collection of heterogeneous stations. Queue-length information is available to inform all decisions. Admitted customers will abandon the system if required to wait too long for service. The optimisation goal is the maximisation of reward rate earned from service completions, net of the penalties paid whenever admission is denied, and the costs incurred upon every customer loss through impatience. We show that the system is indexable under mild conditions on model parameters and give an explicit construction of an index policy for admission control and routing founded on a proposal of Whittle for restless bandits. We are able to gain insights regarding the strength of performance of the index policy from the nature of solutions to the Lagrangian relaxation used to develop the indices. These insights are strengthened by the development of performance bounds. Although we are able to assert the optimality of the index heuristic in a range of asymptotic regimes, the performance bounds are also able to identify instances where its performance is relatively weak. Numerical studies are used to illustrate and support the theoretical analyses.

The G-Group Heuristic to Solve the Multi-Product, Sequencing, Lot Sizing and Scheduling Problem in Flow Shops

This paper presents a new heuristic to solve the problem of making sequencing, lot sizing and scheduling decisions for a number of products manufactured in a flow shop environment, so as to minimize the sum of setup and inventory holding costs while a given demand is fulfilled without backlogging. The proposed solution method first determines sequencing decisions then lot sizing and scheduling decisions are simultaneously determined. This heuristic, called the G-group method, divides the set of products into G groups and requires that products belonging to the same group have the same cycle time. Also, the cycle time of each group is restricted to be an integer multiple of a basic period. For each basic period of the global cycle, the products to be produced during this period and the production sequence to be used are chosen. Then, a non-linear program is solved to determine lot sizes and to construct a feasible production schedule. To evaluate its performance, the G-group method was compared to four other methods. Numerical results show that the proposed heuristic outperforms all these methods.

Performance evaluation of competing forecasting models: A multidimensional framework based on MCDA

So far, competing forecasting models are compared to each other using a single criterion at a time, which often leads to different rankings for different criteria - a situation where one cannot make an informed decision as to which model performs best overall; that is, taking all performance criteria into account. To overcome this methodological problem, we propose to use a Multi-Criteria Decision Analysis (MCDA) based framework and discuss how one might adapt it to address the problem of relative performance evaluation of competing forecasting models. Three outranking methods have been used in our empirical experiments to rank order competing forecasting models of crude oil prices; namely, ELECTRE III, PROMETHEE I, and PROMETHEE II. Our empirical results reveal that the multidimensional framework provides a valuable tool to apprehend the true nature of the relative performance of competing forecasting models. In addition, as far as the evaluation of the relative performance of the forecasting models considered in this study is concerned, the rankings of the best and the worst performing models do not seem to be sensitive to the choice of importance weights or outranking methods, which suggest that the ranks of these models are robust.

A multidimensional framework for performance evaluation of forecasting models: context-dependent DEA

The performance evaluation of competing forecasting models is generally restricted to their ranking by criterion, which generally leads to several inconsistent rankings for different criteria. The purpose of this article is to propose a multidimensional framework; namely, Data Envelopment Analysis (DEA), to overcome this problem by determining a single ranking that takes account of multiple criteria. In order to operationalize this framework, we survey the literature on forecasting criteria and measures, propose a new classification of criteria, and discuss how one might measure them. We use forecasting models of crude oil prices to illustrate the use of the proposed multidimensional performance evaluation framework. Our empirical results suggest that both the best and the worst forecasting models with respect to most performance criteria and their measures tend to maintain their unidimensional ranking positions when assessed in a multidimensional setting; however, the multidimensional ranking of some models could be substantially different from their unidimensional rankings, which highlights the importance of the proposed performance evaluation tool.