Given the difficult nature of making purchase decisions, a linear programming model has been formulated to consider demand, space, and capital spending constraints.  It is primitive, with a lot more research required to make the model more meaningful, but it serves its purpose.  While the model’s objective function is to maximize profits, it seems to be also useful for a store that may be relocating with new space constraints; finding the optimal mix of inventory given the new space constraints, while assuming demand holds constant.  Additionally, it seems useful in looking at how spending constraints affect the optimal mix or even how changing the layout may be affected.  For example, seeing how the mix changes when available capital for particular product categories changes or seeing what the optimal mix will be if the space allocated for the class of products is changed. 


Something that complicates this model is the problem of inventory obsolescence. The demand that is input as a constraint is a result of previous demand, and the model does not consider the fact that as items become less popular so does the need for that item.  Therefore, historical demand data is not necessarily ideal and a more appropriate approach for calculating an optimal mix may be achieved through the use of a continuous order period model, Stochastic Programming, or simulation.   Stochastic Programming models allow the information to be evaluated under uncertain conditions and allow for probability assumptions; in this case demand.  Demand is receiving such an emphasis given the large degree of uncertainty and variability, and because it is the only uncertain element within our model.  It should also be noted that this model is for single order period decisions, which does not allow the model to consider excess inventory existing as a result of previous order periods.  Further research is required to transition the present LP model to a Stochastic Programming (SP) model. 


In addition to the aforementioned, it should be noted that the model has not been tested or proven, as this would require more extensive research.  At this point the results are theoretical and strictly for academic purposes.  However, there appears to exist a great opportunity to conduct further research with the possibility of creating software that not only considers the proposed LP/SP model, but also integrate the software with other useful business models (i.e. EOQ, ABC, Yield Management, and price sensitivity tools) and possibly add an ability for the software to establish optimal delivery routes given orders as they occur; as a result of point of sale data as sales occur.  In searching the Internet, there does not seem to be a software package specifically for the furniture industry that facilitates all of these business necessities.  Moving forward:


The first step of the model is to define the variables, as follows:


: Quantity of furniture item ἱ to order, ἱ=1, 2, 3…12 (1-3: Sofa, 4-8: Recliner, 9-12: Bedroom set)


: 1 if item ἱ is purchased, 0 otherwise


: Sale price of item ἱ


: Cost of furniture item ἱ


: Carrying cost of furniture item ἱ


: Transportation cost of furniture item ἱ


The objective function of this model is to maximize (net) profits, mathematically presented as follows:



Subject to the following constraints:



























Capital constraint per ordering period:








Purchase from California or Asia:










Industry Analysis pg. 3