Integer Programming Models for Sales Territory Alignment to Maximize Profit

1976 ◽  
Vol 13 (4) ◽  
pp. 426-430 ◽  
Author(s):  
Andris A. Zoltners
Keyword(s):  
Integer Programming ◽  
Mathematical Programming ◽  
Recent Article ◽  
Programming Model ◽  
Solution Procedure ◽  
Programming Models ◽  
Mathematical Programming Model ◽  
Heuristic Solution ◽  
Linear Integer Programming

A recent article described a mathematical programming model and heuristic solution procedure to realign sales territories. This report presents two linear integer programming models for sales territory alignment to maximize profit. Emphasis is placed on the development of models which are easy to implement.

Sales Territory Alignment to Maximize Profit

1975 ◽  
Vol 12 (1) ◽  
pp. 30-36 ◽  
Author(s):  
Leonard M. Lodish
Keyword(s):  
Mathematical Programming ◽  
Objective Function ◽  
Travel Time ◽  
Programming Model ◽  
Solution Procedure ◽  
Sales Force ◽  
Mathematical Programming Model ◽  
Heuristic Solution ◽  
Frequency Determination ◽  
Unique Model

A mathematical programming model and heuristic solution procedure are developed to realign sales territories. Unique model aspects are: (1) the objective function is the anticipated profit generated by the sales force; (2) the interrelated problem of account specific call frequency determination is simultaneously considered; (3) travel time is considered, including combining calls on accounts into trips.

An Empirical Study on Port Choice Behaviors of Shippers in a Multiple-Port Region

2009 ◽  
Vol 43 (3) ◽  
pp. 71-77 ◽  
Author(s):  
Chien-Chang Chou
Keyword(s):  
International Trade ◽  
Mathematical Programming ◽  
Empirical Study ◽  
Programming Model ◽  
Transportation Costs ◽  
Programming Models ◽  
Mathematical Programming Model ◽  
Logistics System ◽  
Mathematical Programming Models ◽  
Port Choice

AbstractIn the international trade cargo logistics system, the port choice of the shipper is seen to depend not only on transportation costs, but also on the value of the cargoes being shipped. In many previous studies, researchers have assumed that the ultimate aim of shippers when making port choices was to minimize inland freight costs. They then used that assumption to develop mathematical programming models for port choices. In practice, however, when making decisions about port choices, shippers always focus on total logistics costs. In other words, shippers not only aim to minimize the inland freight costs but also consider the frequency of ship callings. Thus, in this paper, a mathematical programming model for port choice of shippers, which not only considers inland freight costs but also takes into account the frequency of ship callings, is proposed and tested using a Taiwanese port case. The results show that the model proposed in this paper can be used to explain the actual port choice behaviors of Taiwanese shippers accurately.

scholarly journals A Mathematical Programming Model for Vegetable Rotations

1985 ◽  
Vol 17 (1) ◽  
pp. 169-176 ◽  
Author(s):  
Wesley N. Musser ◽  
Vickie J. Alexander ◽  
Bernard V. Tew ◽  
Doyle A. Smittle
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Crop Production ◽  
Programming Model ◽  
Crop Rotations ◽  
Programming Models ◽  
Vegetable Production ◽  
Model Design ◽  
Mathematical Programming Model ◽  
Large Numbers

AbstractRotations have historically been used to alleviate pest problems in crop production. This paper considers methods of modeling rotations in linear programming models for Southeastern vegetable production. In such models, entering each possible crop rotation as a separate activity can be burdensome because of the large numbers of possible rotational alternatives. Conventional methodology for double crop rotations reduces the number of activities but must be adapted to accommodate triple crop rotational requirements in vegetable production. This paper demonstrates these methods both for a simple example and an empirical problem with numerous rotation alternatives. While the methods presented in this paper may have computational disadvantages compared to entering each rotation as a separate activity, they do have advantages in model design and data management.

Temporal and spatial harvesting of irregular systems of parcels

1996 ◽  
Vol 26 (6) ◽  
pp. 1079-1088 ◽  
Author(s):  
Stephanie Snyder ◽  
Charles ReVelle
Keyword(s):  
Integer Programming ◽  
Spatial Data ◽  
Programming Model ◽  
The United States ◽  
Simplex Algorithm ◽  
Programming Models ◽  
Mixed Integer ◽  
Central Position ◽  
Private Lands ◽  
Heuristic Solution

Spatial management issues have assumed a central position in planning for forest ecosystems in the United States on both public and private lands. The arrangement of management activities, especially harvesting activities, can often have adverse impacts on other neighboring areas of the forest. Thus, spatially explicit programming models, which can account for or prevent certain arrangements of activities or land allocations through the use of harvest adjacency constraints, have received considerable attention in the literature. The need for spatial specificity in programming models has led to the development of integer programming or mixed integer programming models. Given that integer programming problems are often viewed as a difficult class of problems to solve, heuristic solution methods have most often been used to solve spatially constrained forest management models. In this paper, a discrete (0–1) integer programming model that maximizes harvested timber volume over a multiperiod time horizon subject to harvest adjacency constraints is developed and tested for irregular, realistic systems of parcels. This model performed well computationally for many example configurations and was solved exactly using the simplex algorithm and limited branching and bounding. Certain spatial configurations with long time horizons did, however, require a nontrivial amount of branching and bounding. The model was tested using both contrived and real spatial data sets.

A mathematical programming approach for walking-worker assembly systems

2014 ◽  
Vol 34 (1) ◽  
pp. 56-68 ◽  
Author(s):  
Emre Cevikcan
Keyword(s):  
Mathematical Programming ◽  
Task Allocation ◽  
Programming Model ◽  
Programming Models ◽  
Assembly System ◽  
Programming Approach ◽  
Assembly Systems ◽  
Mathematical Programming Model ◽  
Content Type ◽  
Mathematical Programming Approach

Purpose – It has become increasingly critical to design and maintain flexible and rapid assembly systems due to unpredictable and varying market conditions. The first stage of developing such systems is to restructure the existing assembly system. After designing the manufacturing system, efforts should be made for capacity adjustments to meet the demand in terms of allocating tasks to workers. Walking-worker assembly systems can be regarded as an effective method to achieve flexibility and agility via rabbit chase (RC) approach in which workers follow each other around the assembly cell or line and perform each task in sequence. In this paper, a novel mathematical programming approach is developed with the aim of integrating RC in assembly processes. Therefore, this study is thought to add value to industrial assembly systems in terms of effectively raising engineering control for task allocation activities. Design/methodology/approach – Two consecutive mathematical models are developed, since such a hierarchical approach provides computational convenience for the problem. The initial mathematical programming model determines the number of workers in each RC loop for each segment. In addition, the number of stations and the distribution of station times in the segments is essential. Therefore, the succeeding mathematical programming model generates stations in each segment and provides convenience for the workflow in RC loops. The output of mathematical programming models are the parameters of simulation model for performance assessment. Findings – The effectiveness of the proposed approach was validated by an application in a real-life chair production system. The application resulted in performance improvements for labour requirement (12.5 per cent) and production lead time (9.6 per cent) when compared to a classical assembly system design (CASD) where one stationary worker exists in each station. In addition, it is worth to note that RC leads to a reduced number of workers for a considerable number (39.4 per cent) of test problems. What is more, input as well as output factors have been determined via discriminant analysis and their impacts to the utilization of RC were analyzed for different levels. Practical implications – This study is thought to add value to the industry in terms of effectively providing convenience during production planning and task allocation in assembly lines and cells. Originality/value – To the best knowledge of the author, optimization models for RC considering a real industrial application have not yet been developed. In this context, this paper presents an approach which models RC by the use of mathematical programming in manual assembly processes to address this research gap. The contribution of the paper to the relevant literature is the development of hierarchical mixed integer linear programming models to solve RC problem for the first time.

scholarly journals Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model

2020 ◽  
Vol 5 (6) ◽  
pp. 1249-1269
Author(s):  
Ali Al-Hasani ◽  
Masar Al-Rabeeah ◽  
Santosh Kumar ◽  
Andrew Eberhard
Keyword(s):  
Integer Programming ◽  
Mathematical Programming ◽  
Programming Model ◽  
Optimal Solution ◽  
Optimal Solutions ◽  
Mathematical Programming Model ◽  
Integer Programming Model ◽  
Multi Objective ◽  
Solution Methods ◽  
Single Objective

For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal solutions and based on them a new rank-based solution method (RBSM) is outlined to identify non-dominated points set of a multi-objective integer programming model. Each method is illustrated by a numerical example, and for each approach, we have discussed its limitations, advantages and computational complexity.

Assigning Salesmen to Accounts to Maximize Profit

1976 ◽  
Vol 13 (4) ◽  
pp. 440-444 ◽  
Author(s):  
Leonard M. Lodish
Keyword(s):  
Linear Programming ◽  
Mathematical Programming ◽  
Programming Model ◽  
Solution Procedure ◽  
Marketing Mix ◽  
Mathematical Programming Model ◽  
Geographic Locations ◽  
Programming Solution ◽  
Linear Programming Solution

A mathematical programming model and linear programming solution procedure are developed to assign salesmen to accounts and simultaneously to determine appropriate time allocations to the accounts. The model is useful for sales situations in which geographic locations of accounts are close and the interaction of the salesman with the account is relatively important in the marketing mix. An implementation example is discussed.

scholarly journals Effective Optimisation of the Patient Circuits of an Oncology Day Hospital: Mathematical Programming Models and Case Study

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 62
Author(s):  
Adrián González-Maestro ◽  
Elena Brozos-Vázquez ◽  
Balbina Casas-Méndez ◽  
Rafael López-López ◽  
Rosa López-Rodríguez ◽  
...  
Keyword(s):  
Mathematical Programming ◽  
Programming Model ◽  
Stochastic Approach ◽  
Programming Models ◽  
Day Hospital ◽  
Mathematical Programming Model ◽  
Waiting Room ◽  
Mathematical Programming Models

In this paper, we first use the information we have on the patients of an oncology day hospital to distribute the treatment schedules they have in each of the visits to this centre. To do this, we propose a deterministic mathematical programming model in such a way that we minimise the duration of the waiting room stays of the total set of patients and taking into account the restrictions of the circuit. Secondly, we will look for a solution to the same problem under a stochastic approach. This model will explicitly consider the existing uncertainty in terms of the different times involved in the circuit, and this model also allows the reorganisation of the schedules of medical appointments with oncologists. The models are complemented by a tool that solves the problem of assigning nurses to patients. The work is motivated by the particular characteristics of a real hospital and the models are used and compared with data from this case.

scholarly journals A Mathematical Programming Model to Determine Objective Weights for the Interval Extension of TOPSIS

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Hai Shen ◽  
Lingyu Hu ◽  
Kin Keung Lai
Keyword(s):  
Mathematical Programming ◽  
Input Data ◽  
Programming Model ◽  
Multiple Criteria Decision Making ◽  
Decision Makers ◽  
Mathematical Programming Model ◽  
Topsis Method ◽  
Data Set ◽  
Interval Extension ◽  
Interval Valued

Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method has been extended in previous literature to consider the situation with interval input data. However, the weights associated with criteria are still subjectively assigned by decision makers. This paper develops a mathematical programming model to determine objective weights for the implementation of interval extension of TOPSIS. Our method not only takes into account the optimization of interval-valued Multiple Criteria Decision Making (MCDM) problems, but also determines the weights only based upon the data set itself. An illustrative example is performed to compare our results with that of existing literature.

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