ارزیابی ارزش فعلی خالص از سیستم های تولیدی ساخت برای سفارش و ساخت برای انبار

This paper shows the impact of using the net present value (NPV) on parameter selection in the ordering policy of a production planning and control system. Using a well understood and documented model, the net present value is used as an objective function to determine the discounted future variance costs resulting from the model's dynamics. The NPV of the variance (NPVvv) is defined and applied to the model under make-to-order and make-to-stock conditions. We show that the cost structure of the manufacturing system defines the NPVvv and hence aids in identifying the most appropriate control strategy to apply.

The net present value (NPV) is a financial measure that ascertains the time value of money invested in a business. Grubbström [1] has shown that where the economic consequences of production planning decisions need to be known then the NPV may be applied. In particular, the NPV discounting takes the form of an exponential function thus making the discounted cash flow analysis amenable to solution using the Laplace transform [2]. A number of production planning studies have subsequently been undertaken with the aim of maximising the NPV [3] and [4]. We aim to extend previous studies by researching the application of NPV on a generic dynamic model of a production planning and control system. Wikner [5] has undertaken some early analysis of the generic model using NPV. We will show that the standard NPV is not a sufficient criterion for analysing the dynamic behaviour of a closed-loop form of production planning and inventory control system. There is a need to extend the NPV criterion to encapsulate costs associated with the variances that occur in the system variables. The variance costs can be defined as all the “on-costs” [6] and [7] associated with not being in perfect control of a system. A perfectly controlled system is then defined as a system that faithfully tracks some reference or target signal. In addition to the “on-costs” we of course also have the base costs, so that our total costs=base costs+on-costscosts=base costs+on-costs. Base costs, that could include traditional fixed and variable costs, are those which the system suffers even when it perfectly tracks the target, so that in a make-to-order environment there are costs associated even with production faithfully tracking customer orders, which may be stable or fluctuating. In this paper, we are specifically addressing the “on-costs”. Two key “on-costs” are related to production and inventory: • Production on-costs are due to production's inability to match a given target and therefore will under produce in some periods and over produce in others. These variations put strain on production that needs to provide volume flexibility. • Inventory on-costs are based on deviations from a target inventory leading to excessive inventory holding in some periods and insufficient holding in others. The inventory on-costs are the increased costs of handling associated, say with the increased number of movements of stock within a warehouse or capacity fluctuation in the longer term. We use the inventory and order-based production control system (IOBPCS) archetype as a benchmark to determine the impact of using the NPV in assessing the “on-costs”. The IOBPCS was first developed by Towill [8] to show that the production and inventory model developed by Coyle [9] could be solved analytically. The dynamic characteristics of IOBPCS are now well documented and understood [8], [10] and [11]. Understanding the dynamic properties of the IOBPCS has been useful in extending knowledge of a whole suite of production planning and control systems as IOBPCS has been found to be an archetype for such systems [12], [13] and [14]. The IOBPCS archetype has also been used to extend our understanding of the dynamic behaviour of supply chains [15] and [16]. The IOBPCS archetype and its analysis is not only theoretical but has been applied in industry [8], [9] and [10]. By applying NPV to the IOBPCS we are extending the knowledge base associated with the model by studying the financial implications of its dynamic behaviour. Specifically, we focus our study on particular variants of the IOBPCS which lead to classic scenarios found in industry, namely make-to-stock (MTS) and make-to-order (MTO) systems. Therefore we are interested in some of the practical aspects of applying NPV to MTO and MTS systems. Theoretical studies on generic production planning and control systems are being investigated elsewhere (e.g., Disney and Grubbström [17]) and are beyond the scope of this paper. The paper next outlines our method and describes the model coding. This is followed by a presentation of the NPV formulae and its application. Next, we justify the need to use an alternative form of the NPV, which is then applied to MTO and MTS systems. Finally, we discuss our results and conclude.

We have shown the impact of the net present value criterion on parameter settings for a generic production planning and control system. Our analysis has shown that there is a need to develop an NPV criterion for the variance in both production and inventory costs. While hybrid solutions may be of theoretical interest we have focused our analysis on MTO and MTS systems. Parameter settings for the generic model have been utilised that replicate MTO and MTS dynamic behaviour. Relative variance costs for production and inventory have been defined that distinguish MTO and MTS behaviour. Our simulation study indicates that a given variance cost structure in our production planning and control system defines the control strategy a company should adopt. Thus where the production on-cost per item, cvcv is much smaller than the inventory variance cost per item and unit time period, hvhv, we should have the capability to flex our system and hence a MTO strategy is most suitable. If cvcv is much larger than hvhv then a MTS strategy would be better suited. Of course other factors have to be taken into account such as marketing and customer requirements. But our analysis indicates whether or not our current variance cost structure is appropriate from a dynamic perspective for given market circumstances. The research presented here is theoretical in nature. It determines the impact of using the NPVvNPVv criteria to judge the dynamic behaviour of a production and inventory control system. The NPVvNPVv criteria, in complete contrast to classical control theory criteria, penalises variances from a target the nearer to the time origin that variance occurs. Further theoretical work will require a full parametric experiment to evaluate the impact of changes in value in the NPVvNPVv parameters to compare and contrast with classical control theory criteria, such as the integral of time absolute error (ITAE). Empirical research should be undertaken to understand what the actual variance costs structures are in industry, and how they may be best evaluated. The cubic function utilised is based on a single source that, although requires validation, clearly penalises more harshly larger variances from a target. At the moment the NPVvNPVv parameters, cvcv and hvhv, are difficult to interpret cvcv and hvhv are required to transform variance variables, such as order requirements per week into monetary units, so their units and values have to be determined from specific cases to show the application of the method.