Serpil Sayın

Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming

Abstract.One way of solving multiple objective mathematical programming problems is finding discrete representations of the efficient set. A modified goal of finding good discrete representations of the efficient set would contribute to the practicality of vector maximization algorithms. We define coverage, uniformity and cardinality as the three attributes of quality of discrete representations and introduce a framework that includes these attributes in which discrete representations can be evaluated, compared to each other, and judged satisfactory or unsatisfactory by a Decision Maker. We provide simple mathematical programming formulations that can be used to compute the coverage error of a given discrete representation. Our formulations are practically implementable when the problem under study is a multiobjective linear programming problem. We believe that the interactive algorithms along with the vector maximization methods can make use of our framework and its tools.

Assembly line balancing in a mixed-model sequencing environment with synchronous transfers

Abstract We consider the assembly line balancing problem in a mixed-model line which is operated under a cyclic sequencing approach. We specifically study the problem in an assembly line environment with synchronous transfer of parts between the stations. We formulate the assembly line balancing problem with the objective of minimizing total cycle time by incorporating the cyclic sequencing information. We show that the solution of a mathematical model that combines multiple models into a single one by adding up operation times constitutes a lower bound for this formulation. As an approximate solution to the original problem, we propose an alternative formulation that suggests to minimize the maximum subcycle time. We also develop a simple heuristic approach for this alternative problem. We provide computational results that compare the various approaches we discuss.

Towards finding global representations of the efficient set in multiple objective mathematical programming

We propose and justify the proposition that finding truly global representations of the efficient sets of multiple objective mathematical programs is a worthy goal. We summarize the essential elements of a general global shooting procedure that seeks such representations. This procedure illustrates the potential benefits to be gained from procedures for globally representing efficient sets in multiple objective mathematical programming.

A bicriteria approach to the two-machine flow shop scheduling problem

In this paper we address the problem of minimizing makespan and sum of completion times simultaneously in a two-machine flow shop environment. We formulate the problem as a bicriteria scheduling problem, and develop a branch-and-bound procedure that iteratively solves restricted single objective scheduling problems until the set of efficient solutions is completely enumerated. We report computational results, and explore certain properties of the set of efficient solutions. We then discuss their implications for the Decision Maker.

A mixed-integer programming approach to the clustering problem with an application in customer segmentation

Abstract This paper presents a mathematical programming based clustering approach that is applied to a digital platform company’s customer segmentation problem involving demographic and transactional attributes related to the customers. The clustering problem is formulated as a mixed-integer programming problem with the objective of minimizing the maximum cluster diameter among all clusters. In order to overcome issues related to computational complexity of the problem, we developed a heuristic approach that improves computational times dramatically without compromising from optimality in most of the cases that we tested. The performance of this approach is tested on a real problem. The analysis of our results indicates that our approach is computationally efficient and creates meaningful segmentation of data.

A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems

Most real-life decision-making activities require more than one objective to be considered. Therefore, several studies have been presented in the literature that use multiple objectives in decision models. In a mathematical programming context, the majority of these studies deal with two objective functions known as bicriteria optimization, while few of them consider more than two objective functions. In this study, a new algorithm is proposed to generate all nondominated solutions for multiobjective discrete optimization problems with any number of objective functions. In this algorithm, the search is managed over (p−1)-dimensional rectangles where p represents the number of objectives in the problem and for each rectangle two-stage optimization problems are solved. The algorithm is motivated by the well-known e-constraint scalarization and its contribution lies in the way rectangles are defined and tracked. The algorithm is compared with former studies on multiobjective knapsack and multiobjective assignment problem instances. The method is highly competitive in terms of solution time and the number of optimization models solved.

Assigning cross-trained workers to departments: A two-stage optimization model to maximize utility and skill improvement

Abstract We develop a general framework that is applicable in both manufacturing and service settings for assigning cross-trained workers across departments. The framework consists of a two-stage optimization model where two objective functions, departmental utility and skill improvement, are considered sequentially. Departmental utility is a function of departmental labor shortage and the first-stage optimization model maximizes total departmental utility subject to typical assignment constraints. The second stage model seeks to maximize total skill improvement, which is quantified by a hyperbolic learning curve, while trying not to deviate from the utility level obtained during the first stage optimization. Our computational experiments suggest that incorporating the skill improvement function explicitly in the model results in significant improvement in the total skill level of the workforce and thus leads to more effective worker assignments.

SKU demand forecasting in the presence of promotions

Promotions and shorter life cycles make grocery sales forecasting more difficult, requiring more complicated models. We identify methods of increasing complexity and data preparation cost yielding increasing improvements in forecasting accuracy, by varying the forecasting technique, the input features and model scope on an extensive SKU-store level sales and promotion time series from a European grocery retailer. At the high end of data and technique complexity, we propose using regression trees with explicit features constructed from sales and promotion time series of the focal and related SKU-store combinations. We observe that data pooling almost always improves model performance. The results indicate that simple time series techniques perform very well for periods without promotions. However, for periods with promotions, regression trees with explicit features improve accuracy substantially. More sophisticated input is only beneficial when advanced techniques are used. We believe that our approach and findings shed light into certain questions that arise while building a grocery sales forecasting system.

The Multiobjective Discrete Optimization Problem: A Weighted Min-Max Two-Stage Optimization Approach and a Bicriteria Algorithm

We study the multiple objective discrete optimization (MODO) problem and propose two-stage optimization problems as subproblems to be solved to obtain efficient solutions. The mathematical structure of the first level subproblem has similarities to both Tchebycheff type of approaches and a generalization of the lexicographic max-ordering problem that are applicable to multiple objective optimization. We present some results that enable us to develop an algorithm to solve the bicriteria discrete optimization problem for the entire efficient set. We also propose a modification of the algorithm that generates a sample of efficient solutions that satisfies a prespecified quality guarantee. We apply the algorithm to solve the bicriteria knapsack problem. Our computational results on this particular problem demonstrate that our algorithm performs significantly better than an equivalent Tchebycheff counterpart. Moreover, the computational behavior of the sampling version is quite promising.

Single-supplier/multiple-buyer supply chain coordination : Incorporating buyers' expectations under vertical information sharing

Abstract We address the coordination problem in a single-supplier/multiple-buyer supply chain. The supplier wishes to coordinate the supply chain by offering quantity discounts. To obtain their complete cost information, the supplier exchanges his own cost parameters with buyers leading to vertical information sharing. The supplier thinks that the buyers, as they have access to supplier’s setup and holding cost information, may demand a portion of the anticipated coordination savings based on the partial information they hold about the cost structure of the entire supply chain. We model each buyer’s expectations based on her limited view of the entire supply chain which consists of herself and the supplier only. These expectations are then incorporated into the modeling of the supply chain, which results in a generalization of the traditional Stackelberg type models. We discuss alternative efficiency sharing mechanisms, and propose methods to design the associated discount schemes that take buyers’ expectations into account. In designing the discount schemes, we consider both price discriminatory and non-price discriminatory approaches. The study adds to the existing body of work by incorporating buyers’ expectations into a constrained Stackelberg structure, and by achieving coordination without forcing buyers to explicitly comply with the supplier’s replenishment period in choosing their order quantities. The numerical analysis of the coordination efficiency and allocation of the net savings of the proposed discount schemes shows that the supplier is still able to coordinate the supply chain with high efficiency levels, and retain a significant portion of the net savings.