Optimal design of batch‐storage network with uncertainty and waste treatments

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An optimally designed of batch-storage network that uses a periodic square wave model provides analytical lot-sizing equations for a complex supply chain network characterized as a multisupplier, multiproduct, multi-stage, nonserial, multicustomer, cyclic system, with recycling or remanufacturing. The network structure includes multiple currency flows and material flows. The processes involve multiple feedstock and product materials with fixed compositions that are highly suitable for production processes. Transportation processes that carry multiple materials of unknown composition are included in this study, and the time frame is varied from a single infinite period to multiple finite periods to accommodate nonperiodic parameter variations. The objective function in the optimization is chosen to minimize the difference between the opportunity costs of currency/material inventories and stockholder benefits given in the numeraire currency. Expressions for the Kuhn-Tucker conditions for the optimization problem are reduced to a multiperiod subproblem describing the average flow rates and the analytical lot-sizing equations. The multiperiod lot-sizing equations are shown to differ from their single-period counterparts. The multiperiod subproblem yields a multiperiod planning model that has many advantages over existing planning models. For example, it contains terms that represent operation frequency dependent costs. Realistically sized numerical examples that deal with multinational corporations are formulated and tested. The effects of corporate income taxes, interest rates, and exchange rates are presented.

Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Optimal design of multiperiod batch‐storage network including transportation processes

Yi¹,

Reklaitis²

2011

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“…A previous study using the PSW model on a BSN developed analytical solutions of supply chain optimization dealt with uncertainty. 18 The sources of uncertainty were batch size and cycle time variations in raw material purchasing, batch production, transportation, and finished product demand processes. The processes were classified into three types according to their random characteristics: (1) processes that possess uncertainty only in the cycle time; (2) processes that possess uncertainty only in the batch size; and (3) processes that possess joint uncertainty in both the cycle time and batch size.…”

Section: Introductionmentioning

confidence: 99%

“…A multiperiod formulation to treat long-term trends of variables and parameters that was introduced in the previous study 18 is omitted in this study and, therefore, the derivation corresponds to single-period formulation that accounts for short-term variations of variables and parameters. The singleperiod formulation presented here can be easily expanded to the multiperiod formulation, as was done in the previous study.…”

Section: Introductionmentioning

confidence: 99%

“…The singleperiod formulation presented here can be easily expanded to the multiperiod formulation, as was done in the previous study. 18 The remainder of this article is organized as follows. First, the upper/lower bounds and average of the batch flow between a storage unit and a process exposed to joint uncertainties are found using basic probability theory and a unique graphical method.…”

Section: Introductionmentioning

confidence: 99%

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Optimal design of batch‐storage network under joint uncertainties

Yi¹

2008

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This study sought to find analytic solutions to the problem of determining the optimal capacity of a batch-storage network to meet demand for finished products in a system undergoing joint random variations of operating time and batch quantity. The raw material purchasing flow and final product demand flow are susceptible to joint random variations in the order cycle time and batch size. The production processes also have joint random variations in production cycle time and product quantity. Waste regeneration or disposal processes are included into the network to treat the spoiled materials from failed batches. The objective function of the optimization is minimizing the expected total cost, which is composed of setup and inventory holding costs as well as the capital costs of constructing processes and storage units. A production and inventory method, the PSW (periodic square wave) model, provides a unique graphical method to find the upper/lower bounds and average of random flows, which are used to construct terms of the objective function and constraints of the optimization model. The advantage of this model is that it provides a set of simple analytic solutions while also maintaining a realistic description of the random material flows between processes and storage units; as a consequence of these analytic solutions, the computation burden is significantly reduced. The proposed method has the potential to rapidly provide very useful data on base investment decisions during the early plant design stage. It should be particularly useful when these decisions must be made in a highly uncertain business environment.

Optimal design of batch‐storage network considering exchange rates and taxes

Reklaitis

2007

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in Wiley InterScience (www.interscience.wiley.com).This article presents an integrated analysis of the supply chain and financing decisions of multinational corporations. We construct a model in which multiple currency storage units are installed to manage the currency flows associated with multinational supply chain activities such as raw material procurement, processing, inventory control, transportation, and finished product sales. Temporary financial investments, bank loans, and currency transfer between multiple nations are allowed to increase the marginal profit. The core contribution of this study is its quantitative investigation of the influence of macroscopic economic factors such as exchange rates and taxes on operational decisions. The supply chain is modeled as a batch-storage network with recycling streams. The objective function of the optimization involves minimizing the opportunity costs of annualized capital investments and currency/material inventories minus the benefit to stockholders in the numeraire currency. The major constraints of the optimization are that the material and currency storage units must not be depleted. A production and inventory analysis formulation (the periodic square wave model) provides useful expressions for the upper and lower bounds and average levels of the currency and material inventory holdings. The expressions for the Kuhn-Tucker conditions of the optimization problem are reduced to a subproblem and analytical lot-sizing equations. The lot sizes of procurement, production, transportation, and financial transaction can be determined by analytical expressions once the average flow rates are known. We show that the optimal production lot and storage sizes are typically 20% smaller when corporate income tax is taken into consideration than when it is not considered. An illustrative example is presented to demonstrate the potential of this approach.