Optimal design of multiperiod batch‐storage network including transportation processes

Abstract

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.

Optimal Design of Generalized Batch‐Storage Network Considering Shortage Costs

“…Figure 3 of Ref. 21. Each transportation process moves multiple parcels of materials of undetermined composition from storage units in a source plant to storage units in a destination plant.…”

“…17,21 As depicted in Figure 1, a supply chain system that converts raw materials into final products through multiple physicochemical processing steps and subsequently transports them to customers is composed of a set of currency storage units (R), a set of material storage units (J), a set of semicontinuous production processes (I), and a set of transportation processes (L). Production process i ʦ I conducts multiple tasks in sequence, where n ʦ N(i) is the task index.…”

“…If only one task is involved in each process, the results of this study reduce to the case of a batch process. 21 The production process is fed from feedstock storage units j ʦ J and produces multiple products. Each task requires different feedstock materials and products.…”

“…The batch-storage network model introduced in this article extends our previous work 21 to include multitasking semicontinuous production processes which allow us to represent commodity polymer supply chain network. We refer to this extension as the generalized batch-storage network (GBSN).…”

“…In this study, the complex supply chain network is represented by a batch-storage network [12][13][14][15][16][17][18][19][20][21] that covers most supply chain structural components, for example, raw material purchasing, production, transportation, and finished product demand. The batch-storage network model introduced in this article extends our previous work 21 to include multitasking semicontinuous production processes which allow us to represent commodity polymer supply chain network.…”