Transshipment Model Research Articles

A Generalized Transshipment Model for Cash Management Decisions

Cash Management involves the optimal financing of net cash outflows and investing net inflows of a firm, while simultaneously determining payment schedules for existing liabilities. We formulate this as a generalized transshipment model to minimize the total cost of allocating sources of funds to existing uses, while retaining the flexibility of transshipping cash among existing sources. Utilizing a numerical example of Orgler, which is solved using Linear Programming, we compare our model with its ordinary transshipment reformulation by Srinivasan. We provide a richer formulation than earlier formulations in the literature for two reasons. First, due to our model flexibility, we can provide a unique shadow price for each source-use possibility which is not available in Orgler. Second, we can address and capture the time value of money in both directions which is not possible in Srinivasan's model. Extensions of our methodology for post-optimal and sensitivity analysis, minimum cash balance requirements and other institutional constraints are outlined in our computationally efficient model formulation. Other applications are identified in the conclusion.

A Generalized Transshipment Model for Cash Management Decisions

A Generalized Transshipment Model for Cash Management Decisions

Improved optimization strategies for automated heat exchanger network synthesis through physical insights

A heuristic approach to improving current automatic heat exchanger network synthesis (HENS) methods is presented, where the various sets of matches that all achieve the minimum or a specified number of units are rated according to their potential for being able to transfer heat vertically between the composite curves, and thus give minimum total area in the corresponding network. For cases where the film heat transfer coefficients for the streams are significantly different, the requirement of strict vertical heat transfer should be relaxed, and this is done in the model by introducing stream individual contributions to Δ T min. Most published work on HENS to date, including the pinch design method, use a single global minimum approach temperature (Δ T min), not only to set the level of heat recovery, but also as a basic design parameter for the heat exchanger network. It is shown in this paper that relaxing this assumption by using the heat recovery approach temperature (HRAT) only to set the level of heat recovery and allow the exchanger minimum approach temperature to be set at any value (EMAT < HRAT) when designing the heat exchanger network, will result in designs that have lower total annual cost, use less total area for a given (small) number of units and/or require fewer number of units. This is the case even when the streams have identical heat transfer coefficients. Reduced network complexity is another benefit. A new procedure for HENS is presented that uses the heat recovery approach temperature (HRAT) and the number of units ( U) as the two basic optimization variables. The set of matches is found by a new vertical MILP transshipment model, where the exchanger minimum approach temperature (EMAT) can either be completely relaxed (zero) or set to a lower value by the engineer.

Processing center location analysis for multiple branch banks

Recently banks in the United States and Great Britain have acquired large numbers of branch offices. These banks have just begun to recognize that the operations arm of their business must be restructured and consolidated to take advantage of the economies of scale possible with a multibranch system. This entails the identification of the appropriate number and location of regional check processing centers and the assignment of individual branches to each center. A network transshipment model (or netform) has been developed to aid management in this critical, strategic decision. Used in conjunction with a simulation model which analyzes the minute by minute flow of work, the transshipment model suggests preferred processing sites and branch assignments. Using data collected from a bank recently involved in the process, the use of the model is illustrated.

Structure of the U.S. soybean processing industry in the 1990s

A transshipment model was used to derive the existing and projected optimal structure of the US soybean processing industry. Analyses of model results for various time periods indicate that the potential exists for significant cost reductions on a national basis, if processing plants could be more optimally sized and located. It was also found that present processing capacity was in excess of present needs in most regions of the US; however, by the year 2000, almost all regions would need more plants or greater capacities than currently exist.

Studies in the heat integration of chemical process plants

AbstractA method for solving the problem of heat exchanger network synthesis in chemical process plants is presented based on the use of the out‐of‐kilter algorithm. The method represents an extension of previous approaches based on network flow problem formulations. A new approach to overcome the constraints in forbidden‐match problems, termed the dual stream approach, has been developed based on the use of a stream as both a hot and a cold stream. This approach results in considerable savings in utility costs in certain forbidden‐match problems. An algorithm to deal with heating or cooling utilities that undergo temperature changes, termed non‐point‐temperature utilities, is presented using the transshipment model. The new algorithm determines the utility mass flow rates and pinch points accurately.

Spatial Organization of Marketing Facilities in Developing Countries: A Case Study of Oilseeds in Sudan

AbstractLittle attention has been devoted to the study of spatial organization of marketing facilities in developing countries, even though such studies would be most useful for a wide range of marketing problems. The results of such studies could be valuable to private and public decision‐makers in developing countries whose policies and decisions determine the number, size and location of marketing facilities. The spatial organization model developed in this paper for application to the oilseeds industry in Sudan demonstrates the relevance of this research technique for developing country studies of marketing facilities. A linear programming transshipment model is utilized to determine the optimal spatial organization of oilseeds in Sudan when the costs of oilseed assembly, processing and distribution of oil and cake to final destinations are considered simultaneously. The optimal spatial organization of oilseed processing plants was determined for six alternative solutions. Model results indicate that the optimal organization of processing plants would be obtained with fewer and larger plants, resulting in lower transportation costs.

Spatial organization of marketing facilities in developing countries: A case study of oilseeds in Sudan

Little attention has been devoted to the study of spatial organization of marketing facilities in developing countries, even though such studies would be most useful for a wide range of marketing problems. The results of such studies could be valuable to private and public decision-makers in developing countries whose policies and decisions determine the number, size and location of marketing facilities. The spatial organization model developed in this paper for application to the oilseeds industry in Sudan demonstrates the relevance of this research technique for developing country studies of marketing facilities. A linear programming transshipment model is utilized to determine the optimal spatial organization of oilseeds in Sudan when the costs of oilseed assembly, processing and distribution of oil and cake to final destinations are considered simultaneously. The optimal spatial organization of oilseed processing plants was determined for six alternative solutions. Model results indicate that the optimal organization of processing plants would be obtained with fewer and larger plants, resulting in lower transportation costs.

Effects of increased transportation costs on spatial price differences and optimum locations of cattle feeding and slaughter

A least-cost multiproduct transshipment model is developed to evaluate the impact of changes in interregional relationships in the cattle feeding/fed-beef economy as a result of increased transportation costs. Results indicate that Southern and Central Plains and Corn Belt cattle feeders would continue to account for nearly 85% of all cattle fed in the US in the short run. Slaughter generally was shown to remain production oriented as slaughter firms locate near concentrated sources of fed slaughter cattle. Results suggest that cattle feeders in the Southern and Central Plains may be faced with less favorable competitive positions when competing with western Corn Belt feedlots if transportation costs increase more than 50% relative to other input costs. Future increases in placements of feeder cattle would likely occur to a greater degree in the Corn Belt and to a lesser extent in the South.

Automatic synthesis of optimum heat exchanger network configurations

AbstractThis paper addresses the problem of automatically generating heat exchanger network configurations that feature minimum investment cost subject to minimum utility cost and fewest number of units. Based on the linear programming and the mixed‐integer linear programming (MILP) transshipment models for heat integration, a superstructure that has embedded many alternative configurations is proposed. This superstructure, which has as units the matches predicted by the MILP transshipment model, includes options for series and parallel matching, as well as stream splitting, mixing, and bypassing. Many of the implied stream connections in the superstructure are reduced to zero flow with a nonlinear programming formulation that leads to realistic and practical designs. Theoretical properties as well as the implementation aspects of the proposed procedure for the automatic generation of networks are presented. The method is illustrated with three example problems.

Synthesis of flexible heat exchanger networks for multiperiod operation

This paper addresses the problem of synthesizing heat exchanger networks that have the flexibility of coping with prespecified changes in flow rates, inlet temperatures and outlet temperatures in a finite sequence of time periods. A multiperiod version of the mixed integer linear programming (MILP) trans-shipment model is presented which accounts for the changes in pinch points and utility requirement at each time period. With use of this model as a basis, a systematic procedure is proposed for synthesizing network configurations that require minimum utility cost for each period of operation and involve the fewest number of units. Application of this synthesis procedure is illustrated with two example problems.

Transmission Network Planning Using Linear Programming

In long range transmission planning, where new load growth, new generation sites and perhaps a new voltage level are to be considered, a computer aided method of visualizing new circuits in a network context is needed. The new method presented meets this need by the combined use of a linear (dc) power flow transmission model and a transportation model (also known as a trans-shipment model). The dc transmission model is solved for the facilities network by obeying both of Kirchhoff's laws, flow conservation at each bus and voltage conservation around each loop. The transportation model is solved for the overloads by obeying only the bus flow conservation law while minimizing a cost objective function.

Totally balanced games arising from controlled programming problems

A cooperative game in characteristic-function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a (generally nonlinear) mathematical programming problem, either directly or through committee voting. Conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced. This assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers. In the linear case the core is closely related to the solutions of the dual problem. Applications are made to a variety of economic models, including the transferable utility trading economies of Shapley and Shubik and a multishipper one-commodity transshipment model with convex cost functions and concave revenue functions. Dropping the assumption of transferable utility leads to a class of controlled multiobjective or ‘Pareto programming’ problems, which again yield totally balanced games.

A Dynamic Plant Location Model: The East Florida Fresh Citrus Packing Industry

AbstractStatic location models provide a long‐run solution without the adjustments required over time. Dynamic programming allows incorporation of short‐ and long‐run adjustments in the same plant location model. A standard transshipment model with fixed quantities at supply and demand points is integrated with a dynamic program. Results indicate new large packinghouses are (are not) competitive with existing small (large) packinghouses even though (because) existing plants can forego a return on investment for a finite period.

A structural optimization approach in process synthesis—II

Several formulations of the transshipment model from Operations Research are proposed for the optimal synthesis of heat exchanger networks. The linear programming versions are used for predicting the minimum utility cost, and can handle restricted matches and multiple utilities. The mixed-integer programming version yields minimum utility cost networks in which the number of units is minimized, while allowing stream splitting and selection of most preferred matches. It is shown that the transshipment models can also be incorporated easily within a mixed-integer programming approach for synthesizing chemical processing systems. Several numerical examples are presented which show that the proposed models are computationally very efficient.

A comparison of two baseline screening approaches to regional energy facility siting

Of the many approaches that might be used by policy makers to simulate the future locational pattern of energy facilities, baseline screening is the most straightforward. Based upon some composite of siting criteria measured for appropriate areal units, decision rules are developed to site energy facilities needed for projected demands. Two baseline methods, one developed at Oak Ridge National Laboratory and the other at Teknekron, Inc. are computerized and applied to the six state Middle Atlantic region. An earlier multiobjective optimization model developed by The Johns Hopkins University for the same region is used as a benchmark against which to compare the screening approaches. Both baseline models are found deficient when a trade-off between environmental suitability and economic efficiency is desired. A multiobjective heuristic model and an optimal transshipment model are developed to overcome the deficiencies inherent in baseline screening approaches.

Distribution Cost Reduction as an Incentive for Coal Conversion

A linear transshipment model was used to determine the extent to which delivered coal prices could be reduced through gains in efficiency in coal transportation and distribution. Aggregate savings for coal users in southern Minnesota of as much as $10.8 million per year were shown to be possible. It was argued that the savings thus obtained would have the same effect as large direct subsidies to potential coal users in encouraging coal use. A program to reduce delivered coal costs would involve less public funding than subsidies in addition to providing coal delivery by truck to industries not able to receive it by rail. Furthermore, the benefits from reduced coal distribution costs would accrue to all local users, not just those selected for public payments.

The impact of changes in livestock supply on the optimum number, size and location of slaughterhouses in East Macedonia

The main aim of this paper is to determine the impact of changes in the livestock slaughterings in East Macedonia on the optimum number, size and location of the slaughterhouses in this area. To this end, the transshipment model has been employed. This is a transportation linear programming model which simultaneously minimizes the aggregate cost of product assembly, processing and distribution. The empirical results have shown that the changes in the supply (volume and pattern) of livestock slaughterings projected to 1980 do affect the optimum size and location of the slaughterhouses in the area.

Seasonal and Stochastic Factors in Water Planning

A transshipment model of water resources in a region is formulated which incorporates the seasonal variations in water uses and the stochastic characteristics of water supplies. The basic model is structured using nonlinear costs (by separable programming) for the objective function and solved for various combinations of annual or seasonal periods for water supply and demand, and deterministic or stochastic water supplies. Two levels of wastewater treatment are also specified corresponding to 1977 and 1983 requirements of PL 92-500. The results of the model runs give optimal allocations of water from the available sources to meet use sector requirements over a planning horizon from 1975 to 2020. The total minimum cost of water supply and wastewater treatment is reduced by taking into account seasonality of water requirements. Incorporating the stochastic nature of supplies generally results in a shift to more reliable but higher cost sources. A comparison of the model solutions indicates that improved sizing and timing of facilities can be achieved considering the stochasticity of water supplies and seasonality of water uses.

The Dual of a Cost Minimizing Linear Transshipment Model: An Economic Interpretation of an Assembly-Plant Processing-Distribution Network for a Firm

The general economic meanings and mathematical structure of the dual of a primal mathematical programming model have been discussed for many years. However, within the mathematical programming realm, many interesting formulization variations have developed partly in response to variations in particulars of problems.A number of authors have discussed the economic meaning and mathematical structure of the primal of a linear cost minimizing transportation model. Some authors discussed the economic meaning and mathematical structure of the dual as well as the primal of the transportation model. Several authors discussed cost minimizing transshipment models. Recently, greater interest has been shown in specific economic meanings of the dual of the cost minimizing transshipment model.