Application of interactive possibilistic linear programming to aggregate production planning with multiple imprecise objectives

Aggregate production planning (APP) addresses matching supply to forecast demand, with varying customer orders over the intermediate planning horizon. In real-world APP problems, input data and related parameters are commonly imprecise because information is incomplete or unavailable, and the decision maker (DM) must simultaneously consider conflicting objectives. This study develops an interactive possibilistic linear programming (i-PLP) approach to solve multi-product and multi-time period APP problems with multiple imprecise objectives and cost coefficients by triangular possibility distributions in uncertain environments. The imprecise multi-objective APP model designed here seeks to minimise total production costs and changes in work-force level with reference to imprecise demand, cost coefficients, available resources and capacity. Additionally, the proposed i-PLP approach provides a systematic framework that helps the decision-making process to solve fuzzy multi-objective APP problems, enabling a DM to interactively modify the imprecise data and parameters until a set of satisfactory solutions is derived. An industrial case demonstrates the feasibility of applying the proposed approach to a practical multi-objective APP problem.     

Multi-site aggregate production planning with multiple objectives: A goal programming approach

This paper addresses the problem of aggregate production planning (APP) for a multinational lingerie company in Hong Kong. The multi-site production planning problem considers the production loading plans among manufacturing factories subject to certain restrictions, such as production import/export quotas imposed by regulatory requirements of different nations, the use of manufacturing factories/locations with regard to customers' preferences, as well as production capacity, workforce level, storage space and resource conditions of the factories. In this paper, a multi-objective model is developed to solve the production planning problems, in which the profit is maximized but production penalties resulting from going over/under quotas and the change in workforce level are minimized. To enhance the practical implications of the proposed model, different managerial production loading plans are evaluated according to changes in future policy and situation. Numerical results demonstrate the robustness and effectiveness of the developed model.     

On linear bilevel problems with multiple objectives at the lower level

Bilevel programming problems provide a framework to deal with decision processes involving two decision makers with a hierarchical structure. They are characterized by the existence of two optimization problems in which the constraint region of the upper level problem is implicitly determined by the lower level optimization problem. This paper focuses on bilevel problems for which the lower level problem is a linear multiobjective program and constraints at both levels define polyhedra. This bilevel problem is reformulated as an optimization problem over a nonconvex region given by a union of faces of the polyhedron defined by all constraints. This reformulation is obtained when dealing with efficient solutions as well as weakly efficient solutions for the lower level problem. Assuming that the upper level objective function is quasiconcave, then an extreme point exists which solves the problem. An exact and a metaheuristic algorithm are developed and their performance is analyzed and compared.     

Congestion games with mixed objectives

We study a new class of games which generalizes congestion games and its bottleneck variant. We introduce congestion games with mixed objectives to model network scenarios in which players seek to optimize for latency and bandwidths alike. We characterize the (non-)existence of pure Nash equilibria (PNE), the convergence of improvement dynamics, the quality of equilibria and show the complexity of the decision problem. For games that do not possess PNE we give bounds on the approximation ratio of approximate pure Nash equilibria.     

Planning with multiple objectives

Planning any task that is characterised by the presence of multiple objectives presents the decision maker with a set of special considerations which are not present in the case of decision making with one unique objective. The paper outlines the stages in the formulation of a dynamic multiple-objective objective function and introduces the criterion complex as a decision making construct particularly suited to formulating and solving problems with multiple objectives. The paper then considers some of the mathematical properties of the alternative formulations of criterion complex.     

Experiments in mixed integer linear programming in a manufacturing system

This paper reports on a Manufacturing System and two Mixed Integer Programming (MIP) applications concurrent to it. The System is made up of four integrated modules designed to address problems of Strategic, Tactical and Operational Planning. The MIP applications concern problems of plant site selection and production planning. Optimization is done via the IBM's MPSX/370 Mathematical Programming Software.     

An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming

In this paper, we present an aggregate production planning (APP) model applied to a Portuguese firm that produces construction materials. A multiple criteria mixed integer linear programming (MCMILP) model is developed with the following performance criteria: (1) maximize profit, (2) minimize late orders, and (3) minimize work force level changes. It includes certain operational features such as partial inflexibility of the work force, legal restrictions on workload, work force size (workers to be hired and downsized), workers in training, and production and inventory capacity. The purpose is to determine the number of workers for each worker type, the number of overtime hours, the inventory level for each product category, and the level of subcontracting in order to meet the forecasted demand for a planning period of 12 months. Additionally, a decision support system (DSS) based on the MCMILP model is proposed. It will help practitioners find the “best” solution for an APP problem without having to familiarize themselves with the mathematical complexities associated with the model. An example to illustrate the use of the DSS is also included.     

An application of multiple objective linear programming to media selection

A multiple objective linear programming (MOLP) method utilizing interval criterion weights is applied to the problem of media selection. Using this technique, it is possible to analyze a problem more explicitly in terms of the several objectives inherent in many media selection situations. In order to illustrate the interval criterion weights approach, a multiple objective hierarchical media selection model is presented and its computer results discussed. In addition to being able to deal more directly with different decision criteria, a distinguishing feature of the mathematical analysis applied here is that its output enables the media-planner to be presented with a small cluster of candidate media schedules (rather than just one). Then, from this list, the media-planner should be in a position to qualitatively make a final choice as a close approximation to his optimal solution.     

A process for hierarchical decision making with multiple objectives

This research was motivated by a recurring management problem of a large service organization in Philadelphia. The problem concerns the contraction of service facilities. Typically, management decisions of this type and magnitude affect the entire management hierarchy. Each manager in the hierarchy may have several objectives with respect to the problem. The perspective of each manager can contribute to the decision-making process by providing additional insight into both (a) what should be done and (b) the resistance to implementation which may result. Thus the output of this research is not a solution to a particular problem but rather a process for providing critical information for decisions of this type. This paper generalizes the information gathering process and presents the results of eliciting objectives from managers, formalizing objectives into measurable attributes, and interacting with the decision makers to use their implicit preference relationships over the set of Pareto-optimal alternatives. Intuitively, the procedure is appealing as it is flexible enough to allow formal input from all pertinent decision makers in the organization, it is hierarchically consistent, it is politically acceptable, and it is not cumbersome to apply.     

Production planning with linear programming: From textbook to factory

A case study explores the application of linear programming (LP) to the medium-term planning of a factory's production. The case appears to be the only non-oil company application of LP for medium-term production planning in the region. Details of the application are presented. Conclusions about implementation and utility of LP models for production planning are reached.     

Hard and soft constraints in linear programming

The linear programme and its constraints are split into two parts. The first consists of the traditional structure, the second being akin to goal programming. SOFT constraints are weighted relative to each other and then approximately weighted relative to the HARD constraints. The LP is run four times giving different emphasis to the SOFT and HARD constraints. The manager requesting the LP has then to decide which gives the most appropriate solution.     

A production planning system based on linear programming

This paper describes the production planning system developed for the chemicals division of the Boliden Company Ltd., Sweden. The major elements of the production planning system are a linear programming model, a cost model, a scheduling program and a program to forecast the economic outcome. A special organization was established to implement the plans.     

Media selection via multiple objective integer programming

Multiple Objective Integer Linear Programming (MOILP) is presented as an aid to media selection. A MOILP analysis approach recognizes the lack of infinite division in media choices and provides the decisionmaker with an efficient set of alternatives. The decisionmaker may then utilize non-quantifiable criteria to make the final media selection or may use the efficient set developed by the MOILP procedure as a screening mechanism. These screened solutions would then be submitted to further analysis to consider interaction effects, non-linearity and so on. The approach is outlined and an illustrative example using somewhat standard data is provided.     

Two-stage stochastic mixed-integer linear programming: The conditional scenario approach

In this paper we consider the two-stage stochastic mixed-integer linear programming problem with recourse, which we call the RP problem. A common way to approximate the RP problem, which is usually formulated in terms of scenarios, is to formulate the so-called Expected Value (EV) problem, which only considers the expectation of the random parameters of the RP problem. In this paper we introduce the Conditional Scenario (CS) problem which represents a midpoint between the RP and the EV problems regarding computational tractability and ability to deal with uncertainty. In the theoretical section we have analyzed some useful bounds related to the RP, EV and CS problems. In the numerical example here presented, the CS problem has outperformed both the EV problem in terms of solution quality, and the RP problem with the same number of scenarios as in the CS problem, in terms of solution time.     

Modified linear programming and class 0 bounds for graph pebbling

Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move removes two pebbles from some vertex and places one pebble on an adjacent vertex. The pebbling number of a graph G is the smallest integer k such that for each vertex v and each configuration of k pebbles on G there is a sequence of pebbling moves that places at least one pebble on v. First, we improve on results of Hurlbert, who introduced a linear optimization technique for graph pebbling. In particular, we use a different set of weight functions, based on graphs more general than trees. We apply this new idea to some graphs from Hurlbert’s paper to give improved bounds on their pebbling numbers. Second, we investigate the structure of Class 0 graphs with few edges. We show that every n-vertex Class 0 graph has at least \(\frac{5}{3}n - \frac{11}{3}\) edges. This disproves a conjecture of Blasiak et al. For diameter 2 graphs, we strengthen this lower bound to \(2n - 5\), which is best possible. Further, we characterize the graphs where the bound holds with equality and extend the argument to obtain an identical bound for diameter 2 graphs with no cut-vertex.     

The use of edge-directions and linear programming to enumerate vertices

Given a list of vectors that contains directions of the edges of a given polytope ℘ and the availability of an algorithm that solves linear programs over ℘, we describe a method for enumerating the vertices of ℘; in particular, the method is adaptable to polytopes which are presented as (linear) projections of polytopes having linear inequality representation. Polynomial complexity bounds under both the real and the binary computation models are derived when the dimension of the polytope is fixed and the given LP algorithm is polynomial. Dedicated to Professor Frank K. Hwang on the occasion of his sixty fifth birthday. Supported in part by a grant from ISF—the Israel Science Foundation, by a VPR grant at the Technion and by the Fund for the Promotion of Research at the Technion.