تعیین اندازه دسته تولید با تاخیر مجاز در پرداخت ها و هزینه آنتروپی

Although the lot size problem (i.e., the economic order quantity model) has been widely accepted and used by researchers and practitioners, it has also been criticized by others on the grounds that not accounting for some of the hidden costs in inventory systems often lead to poor results. This paper postulates that estimating these hidden costs may be attained by applying the first and second laws of thermodynamics to reduce system entropy (or disorder) at a cost. The applicability of this concept is demonstrated for the economic lot size problem with permissible delay in payments. Mathematical models are developed with numerical examples provided and results discussed.

The economic order quantity (EOQ) model, also known as the lot (batch) size problem, is the oldest scientific approach, and perhaps the simplest, to analyze inventory systems. The popularity of the EOQ model may have been attributed to the ease of manipulation and calculation (Woolsey, 1990). Since its development, there has been a plethora of work that extended the EOQ model in many directions with a good survey of these extensions provided in Silver, Pyke, and Peterson (1998). Among these extensions is the investigation of the lot sizing problem with supplier trade credit incentives. The rationale for such a business practice by many suppliers is to promote commodities and gain larger market shares by offering credit terms to their customers-the retailers. The EOQ model under permissible delay in payments is among the extensions found in the literature. The earliest reported works are those of Haley and Higgins, 1973, Kingsman, 1983, Chapman et al., 1984 and Goyal, 1985. Since, this research topic has been attracting the attention of researchers. Recent works, but not limited to, are those of Jamal et al., 2000, Teng, 2002, Salameh et al., 2003 and Chandrashekar and Gopalakrishnan, 2005. Although the EOQ model has been widely accepted and used by researchers and practitioners (Osteryoung, Nosari, McCarty, & Reinhart, 1986), it has also been criticized by others. Selen and Wood (1987) cautioned that substantial miscalculations or misinterpretations during parameter input determination often lead to poor results. Woolsey (1990) corroborated the conclusions of Osteryoung et al. (1986) that the assumptions necessary to justify the use of the EOQ model are never met. Jones (1991) cautioned that firms who fail to identify relevant costs in a system may result in over-estimating their lot sizes. Unfortunately, the usual cost parameters used in the EOQ model, particularly ordering cost, holding cost and shortage cost are difficult to estimate and so the results obtained may be misleading. For example, the holding cost is an aggregated cost that may include all (or some) of the following: cost of money tied up which is either borrowed (in which interest is paid) or could be put to other use (in which case there are opportunity costs), storage cost (supplying a warehouse, rent rates, heat, light, etc.), loss (due to damage, pilferage, and obsolescence), handling (including all movement, special packaging, refrigeration, putting on pallets, etc.), administration (stock checks, computer updates, etc.), insurance, and taxes (Waters, 2003). Some of these costs are difficult to estimate where other costs are hidden (Callioni, de Montgros, Slagmulder, Van Wassenhove, & Wright, 2005). In addition to these reported costs, there are hidden costs associated with inventory systems that are not usually accounted for (Pendlebury and Platford, 1988, Ullmann, 1982, Gooley, 1995, Crusoe et al., 1999 and Fisher and Siburg, 2003). This paper presents an analogy between the behavior of production systems and the behavior of physical systems. Such a parallel suggests that improvements to management systems may be achievable by applying the first and second laws of thermodynamics to reduce system entropy (or disorder). This paper postulates the concept of entropy cost to estimate some of the difficult-to-estimate or hidden costs outlined above. Few researchers in the discipline of industrial engineering have applied classical thermodynamics reasoning to analyzing management systems. For example, the thermodynamic entropy concept has been applied to analyzing decision trees (Drechsler, 1968), manpower systems (Tyler, 1989), logistics management (Whewell, 1997), business process management (Chen, 1999), product life cycle (Tseng, 2004), inventory management (Jaber et al., 2004 and Jaber et al., 2006), price-quality relationship (Nuwayhid, Jaber, Rosen, & Sassine, 2006), and coordinating orders in a supply chain (Jaber, et al., 2006). This paper incorporates the concept of entropy cost developed in Jaber et al. (2004) into the EOQ problem with permissible delay in payments, i.e., into the model of Goyal (1985). The remainder of this paper is organized as follows. In the next section, Section 2, a brief introduction to the first and second laws of thermodynamics is presented. Section 3 is for mathematical modeling of the inventory model of interest. Section 4 produces some numerical results that illustrate the behavior of the mathematical model. Section 5 provides further discussion of results. Finally, Section 6 presents a summary, conclusions and recommendations for future research.

This paper suggested that it might be possible to improve the performance of a production system by applying the first and second laws of thermodynamics to reduce system entropy (or disorder). This theory postulates that a production system resembles a physical system operating within surroundings, which include the market and the supply system. In this paper, the demand function (commodity flow function) was modeled in a manner similar to modeling heat flow in a thermodynamic system (production system), where heat (commodity) flows from a high temperature (low price) reservoir (inventory system) to a low temperature (high price) reservoir (market). The suggested demand rate function resembles in its form excess demand functions discussed in the mathematical economics literature, where demand is price dependent. Using the first and second laws of thermodynamics, an entropy cost expression was developed and added as a third cost component to the cost function, which classically includes the order and holding costs. The rationale for introducing this cost component is to account for some of the hidden costs not usually accounted for in inventory systems. The EOQ model with permissible delay in payments was extended by accounting for entropy cost. The results from this paper suggest that for a firm who is unable to estimate its cost parameters properly, may find ordering in larger lots an appropriate policy to counter entropy effects. These results also suggest that the lot size quantity is more sensitive to changes in the length of the delay period when including than when excluding the entropy cost, further suggesting that it is advantageous to both the supplier and the retailer. To the supplier, larger lots than recommended by the classical approach (EOQ model) are ordered by the retailer for the same length of a delay period. To the retailer, it is cheaper to control the flow of commodity from the system to its market. Further investigation of the model revealed that accounting for entropy cost may be more relevant for low demand and expensive items than for high demand and low-priced items. In this paper, commodity flow was assumed to be price driven, i.e., a firm provides the same quality product as its competitor at a lower price to sustain its market share. Investigating the model presented herein for a coupled commodity flow function, i.e., a quality and price driven model, is a possible extension. An immediate extension is to investigate the proposed model in a two-level (supplier-retailer) supply chain context.