Multi-product production planning: A goal programming approach

Cost minimization multi-product production problems with static production resource usage and internal product flow requirements have been solved by linear programming (LP) with input/output analysis. If the problem is complicated by interval resource estimates, interval linear programming (ILP) can be used. The solution of realistic problems by the above method is cumbersome. This paper suggests that linear goal programming (LGP) can be used to model a multi-product production system. LGP's unique modeling capabilities are used to solve a production planning problem with variable resource parameters. Input/output analysis is used to determine the technological coefficients for the goal constraints and is also used to derive an information sub-model that is used to reduce the number of variable resource goal constraints. Preliminary findings suggest that the LGP approach is more cost-efficient (in terms of CPU time) and in addition provides valuable information for aggregate planning.     

Strategic financial management in a multinational financial conglomerate: A multiple goal stochastic programming approach

The paper discusses a multi-stage stochastic programming approach to the strategic financial management of a multi-company financial conglomerate. The planning system creates a comprehensive strategy which simultaneously covers a number of future scenarios within a multi-period planning horizon. Multiple conflicting goals may be specified for the group level, company level or individual business area level, and the decision maker’s preferences are allowed to change over time to reflect changing operating conditions and trade-off relationships between the goals. Special features include, among other things, full market valuation throughout the model, integrated treatment of different types of risks, explicit modelling of various types of intra-group transactions and relationships, extensive structures to deal with distressed assets and the covering of losses within the group, as well as consideration of potential portfolio effects of a diversified group structure on the cost of funding.     

A fuzzy goal programming approach for mid-term assortment planning in supermarkets

We develop a fuzzy mixed integer non-linear goal programming model for the mid-term assortment planning of supermarkets in which three conflicting objectives namely profitability, customer service, and space utilization are incorporated. The items and brands in a supermarket compete to obtain more space and better shelf level. This model offers different service levels to loyal and disloyal customers, applies joint replenishment policy, and accounts for the holding time limitation of perishable items. We propose a fuzzy approach due to the imprecise nature of the goals’ target levels and priorities as well as critical data. A heuristic method inspiring by the problem-specific rules is developed to solve this complex model approximately within a reasonable time. Finally, the proposed approach is validated through several numerical examples and results are reported.     

A chance constraints goal programming model for the advertising planning problem

This paper presents a model which has been designed to decide the number of advertisement in different advertising media and the optimal allocation of the budget assigned to the different media. The main objective of this problem is to maximize the reach to the desired section of people for different media within their maximum allowable budget without violating the max and min number of advertisement goals. The media have been considered as different newspapers and different channels in Televisions. Here in this article the model has been formulated in such a way that the advertisement should reach to those who are suitable for the product instead of going to those section who are not considered suitable for the product as well. A chance constrained goal programming model has been designed after considering the parameter corresponding to reach for different media as random variables. The random variables in this case has been considered as values which have known mean and standard deviations. A case for an upcoming institution who are interested to advertise for its two years Post Graduate Diploma in Management (PGDM) programme to the different newspapers and television channels has been designed to illustrate the solution methodology.     

Earliness–tardiness production planning for just-in-time manufacturing: A unifying approach by goal programming

With popularity of the just-in-time (JIT) philosophy, researchers have started to seek the integration of Manufacturing Resource Planning (MRP-II) and JIT methodologies. This paper deals with the master production planning problem for a mass manufacturing system in the JIT environment, an earliness–tardiness production planning (ETPP) problem. The objective is to determine the optimum production rate for each product so that the total penalties imposed on the early and tardy production for all production periods be minimized. A goal programming (GP) approach is proposed to formulate the ETPP problem in a more generalized form, which includes several existing models in one unifying model. Moreover, the proposed GP algorithm ensures a global optimum solution, while the existing ones did not. In addition, it also possesses the advantages over others, such as easier to comprehend, easier to solve, and easier to extend it to the problem of multiple goals.     

A weighted goal programming approach for replenishment planning and space allocation in a supermarket

We propose a mixed integer non-linear goal programming model for replenishment planning and space allocation in a supermarket in which some constraints on budget, space, holding times of perishable items, and number of replenishments are considered and weighted deviations from two conflicting objectives, namely profitability and customer service level, are minimized. We apply a minimum–maximum approach to introduce demand where the maximum demand is a function of price change and allocated space. Each item is presented in the form of multiple brands, probably exposed to price changes, competing to obtain more space. In addition to inventory investment costs, replenishment costs, and inventory holding costs we also include costs related to non-productive use of space. The order quantity, the amount of allocated showroom and backroom spaces, and the cycle time of joint replenishments are key decision variables. We also propose an extended model in which price is a decision variable. Finally we solve the model using LINGO software and provide computational results.     

A generalized stochastic goal programming model

In this paper we show how one can get stochastic solutions of Stochastic Multi-objective Problem (SMOP) using goal programming models. In literature it is well known that one can reduce a SMOP to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems. The first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique. In the second part we try to go more in depth on notion of SMOP solution and we suppose that it has to be a random variable. We will present stochastic goal programming model for finding stochastic solutions of SMOP. Our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs (which depend on the number of experiments to be run) needed to be solved. On the other hand, since in our approach we suppose that a SMOP solution is a random variable, according to the Central Limit Theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a SMOP solution. The developed model will be illustrated through numerical examples.     

A goal programming approach to energy forecasting

Goal programming besides, being a broadly used decision tool, is shown in this paper to be a powerful forecasting device too. It is used as the main component of an energy demand forecasting system, performing a function of an integrator of information on the future growth of energy demand. This information comes from a variety of sources. The most important is a set of econometric models, based on different approaches, which explain past behaviour of the energy demand system. Other sources of information used are statements on government energy policy, feasibility or technical reports and, finally, the forecaster's guess. Thus GP is intended to relax many of the assumptions of conventional econometric forecasting, which render it inadequate under the prevailing conditions of quickly changing energy structures.An implementation of the system on the Greek economy is also described in this paper. Four scenarios of energy demand growth up to 1990 are studied. The levels of energy requirements in these scenarios vary as a consequence of the patterns of economic development and rates of increase in the price of oil.     

A mathematical programming approach to clusterwise regression model and its extensions

The clusterwise regression model is used to perform cluster analysis within a regression framework. While the traditional regression model assumes the regression coefficient (β) to be identical for all subjects in the sample, the clusterwise regression model allows β to vary with subjects of different clusters. Since the cluster membership is unknown, the estimation of the clusterwise regression is a tough combinatorial optimization problem. In this research, we propose a “Generalized Clusterwise Regression Model” which is formulated as a mathematical programming (MP) problem. A nonlinear programming procedure (with linear constraints) is proposed to solve the combinatorial problem and to estimate the cluster membership and β simultaneously. Moreover, by integrating the cluster analysis with the discriminant analysis, a clusterwise discriminant model is developed to incorporate parameter heterogeneity into the traditional discriminant analysis. The cluster membership and discriminant parameters are estimated simultaneously by another nonlinear programming model.     

A new approach for generating efficient solutions within the goal programming model

This paper deals with the issue of efficiency in the Goal Programming (GP) model. A general approach for the determination of an efficient solution of GP is presented. An efficiency test for the GP solution is developed; moreover, when this solution is not efficient, an efficient solution that dominates it is determined.     

An interactive fuzzy goal programming approach for multi-period multi-product production planning problem

This study addresses an interactive multiple fuzzy goal programming (FGP) approach to the multi-period multi-product (MPMP) production planning problem in an imprecise environment. The proposed model attempts to simultaneously minimize total production costs, rates of changes in labor levels, and maximizing machine utilization, while considering individual production routes of parts, inventory levels, labor levels, machine capacity, warehouse space, and the time value of money. Piecewise linear membership functions are utilized to represent decision maker’s (DM’s) overall satisfaction levels. A numerical example demonstrates the feasibility of applying the proposed model to the MPMP problem. Furthermore, the proposed interactive approach facilitates the DM with a systematic framework of decision making process which enables DM to modify the search direction to reach the most satisfactory results during solving process.     

A fuzzy goal programming approach to portfolio selection

Portfolio selection is a usual multiobjective problem. This paper will try to deal with the optimum portfolio for a private investor, taking into account three criteria: return, risk and liquidity. These objectives, in general, are not crisp from the point of view of the investor, so we will deal with them in fuzzy terms. The problem formulation is a goal programming (G.P.) one, where the goals and the constraints are fuzzy. We will apply a fuzzy G.P. approach to the above problem to obtain a solution. Then, we will offer the investor help in handling the results.     

Applying stochastic goal programming: A case study on water use planning

A decision support model to help public water agencies allocate surface water among farmers and authorize the use of groundwater for irrigation (especially in Mediterranean dry regions) is developed. This is a stochastic goal programming approach with two goals, the first concerning farm management while the other concerns environmental impact. Targets for both goals are established by the agency. This model yields three reduction factors to decide the different reductions in available surface water, standard groundwater and complementary groundwater that the agency should grant/authorize for irrigation, this depending on if it is a dry or wet year. In drought periods, the model recommends using more groundwater (in percentage) than in wet periods. A case study using year-to-year statistical information on available water over the period 1941–2005 is developed through numerical tables. A step-by-step computational process is presented in detail.     

Fuzzy goal programming for inventory management: A bacterial foraging approach

An efficient inventory planning approach in today’s global trading regime is necessary not only for increasing the profit margin, but also to maintain system flexibility for achieving higher customer satisfaction. Such an approach should hence be comprised of a prudent inventory policy and clear satisfaction of stakeholder’s goals. Relative significance given to various objectives in a supply chain network varies with product as well as time. In this paper, a model is proposed to fill this void for a single product inventory control of a supply chain consisting of three echelons. A generic modification proposed to the membership functions of the fuzzy goal-programming approach is used to mathematically map the aspiration levels of the decision maker. The bacterial foraging algorithm has been modified with enhancement of the algorithms’ capability to map integer solution spaces and utilised to solve resulting fuzzy multi-objective function. An illustrative example comprehensively covers various decision scenarios and highlights the underlying managerial insights.     

Least squares/ridge regression and goal programming/constrained regression alternatives

Ridge regression has been extensively reviewed in the literature of applied statistics as a method for dealing with problems of collinearity in least squares regressions. In this paper, ordinary least squares and least squares combined with ridge regressions are examined and compared with ordinary goal programming and goal programming combined with constraints on regressand values that admissible statistical estimates must satisfy. The comparisons are effected by means of an example in chemical processing that has been extensively treated in the ridge regression literature.     

A goal programming approach to simple U-line balancing problem

In this paper, a goal programming model for the simple U-line balancing (ULB) problem is developed. The model is based on the integer programming formulation developed by Urban [Urban, Note: Optimal balancing of U-shaped assembly lines, Management Science 44(5) (1998) 738–741] for the ULB problem and the goal model of Deckro and Rangachari [Deckro, Rangachari, A goal approach to assembly line balancing, Computers and Operations Research 17 (1990) 509–521] developed for the traditional single model assembly line balancing (ALB) problem. The proposed model which is the first multi-criteria decision making approach to the U-line version provides increased flexibility to the decision maker since several conflicting goals can be simultaneously considered.     

Product life cycle analysis: a goal programming approach

This paper considers the role of Life-Cycle Costing (LCC), Time-Based Competition (TBC), and other relevant goals at the three planning-horizon levels of strategic, intermediate, and tactical with respect to time and cost of products to market in a concurrent engineering environment. A conceptual framework has been developed in which the general areas of LCC and TBC are delineated. Based on the conceptual framework, the specific components of LCC and TBC at each level of planning are developed and presented. Subsequently, a Preemptive Goal Programming (PGP) model is developed. This model uses the components of LCC, TBC, and other relevant goals as the decision variables. Then, a case study of a company that has developed LCC and TBC is considered. The PGP model is then applied to the company's operations by using the actual data obtained from the company in order to capture the essence of the conceptual framework. This example explains and validates the PGP model in practice and provides managerial implications of the solution. Finally, a set of conclusions and an assessment of the results are presented.     

A modified goal programming model for piecewise linear functions

Piecewise linear function (PLF) is an important technique for solving polynomial and/or posynomial programming problems since the problems can be approximately represented by the PLF. The PLF can also be solved using the goal programming (GP) technique by adding appropriate linearization constraints. This paper proposes a modified GP technique to solve PLF with n terms. The proposed method requires only one additional constraint, which is more efficient than some well-known methods such as those proposed by Charnes and Cooper's, and Li. Furthermore, the proposed model (PM) can easily be applied to general polynomial and/or posynomial programming problems.     

A mixed-integer goal programming model for nursing service budgeting

This paper presents a mixed-integer goal programming model for expense budgeting in a hospital nursing department. The model incorporates several different objectives based upon such considerations as cost containment and providing appropriate nursing hours for delivering quality nursing care. Also considered are possible trade-offs among full-time, part-time and overtime nurses on weekdays as well as weekends. The budget includes vacation, sick leave, holiday, and seniority policies of a hospital and various constraints on a hospital nursing service imposed by nursing unions. The results are based upon data from a study hospital and indicate that the model is practical for budgeting in a hospital nursing department.     

A goal programming model for bank assets and liabilities management

Assets and liabilities management is one of the most important issues in bank strategic planning. In the past, this problem has often been addressed through conventional mathematical programming, i.e. linear programming.However, bank management typically involves several conflicting goals, such as the maximisation of returns, minimisation of risk, expansion of deposits and loans, etc. The complexity of this problem can be captured more adequately by multiobjective mathematical programming. This paper discusses the construction and application at the Commercial Bank of Greece of a goal programming model that takes into account the essential institutional, financial, legal and bank policy considerations.