Prysverlagings op voorraad met ’n dalende vraag

Abstract

The problem faced in this paper is a periodic pricing of inventory with obsolescence and an unknown time horizon. Typical inventory items with these properties are music CDs. The periodic pricing of music CDs is used as a tool to manipulate the demand thereof as they become less popular. A CD will, however, not perish in the time it is kept as inventory, as is the case with perishable inventory. This property accounts for the obsolescence. Other kinds of items in inventory that also become obsolete are typical fashion goods, like clothes. Contrary to CDs the demand for these goods do have a known time horizon (usually at the end of a season). The paper starts out by giving an introduction to the problems faced in a CD shop. Background information is given on how CD shops operate. The method of pricing CDs is explained. The current policy at a CD shop of when, and how many orders are placed is explained. This introduction is followed by an overview of relevant literature on various types of inventory problems. The review is structured according to the three properties of the problem. The first property is the pricing of items in inventory. The second property is that items in inventory may be considered as inventory with a random lifetime. The third property is that the items in inventory become obsolete. The subject of the pricing of inventory has received substantial attention in the operations research literature over the years. The conclusion after consultation of the references on the periodic pricing of inventory is that all these articles have two characteristics in common: the time horizon of the items in inventory are considered to be fixed and it is known by how much the price will change. In the problem under consideration only the second characteristic may be assumed. The objective in most of the literature is to find the time when, and how many times the price should be changed. The second property deals with inventory with a stochastic lifetime. By far the most literature on inventory with a stochastic lifetime appears under the banner of perishable inventory. Perishable inventory consist of inventories that deteriorates (damage, spoil, vaporise, etc.) as time elapses, regardless of how intensively it is used. Perishable inventory may be classified into three main groups, namely inventory with a fixed lifetime (sell-by date), stochastic lifetime inventory and inventory that deteriorates according to some law (for example, proportional to the number of items in inventory). CDs fall into the middle group, but do not deteriorate as such. A rich body of literature exists on the subject of perishable inventory with a stochastic lifetime. In this literature the main objective is to determine the optimal order quantity and reorder point. This is because deteriorating inventory is replaced by the same product on the shelf, which is not the case with CDs. CDs are replaced with a different product once it has become obsolete. This body of literature is thus not very relevant to this study, because the aim of the study is not to find optimal order quantities or reorder points, but the points in time at which the prices should be changed. The third property is obsolescence. Very little was found on this subject in the literature and most of the existing work considered clearance sales at the end of a season. A problem where these three properties are combined could not be found. Two heuristic approaches to minimise the loss made on inventory with the properties as described above, are presented. The first heuristic was developed in conjunction with the manager of a CD shop. This method allows one to set a date (T0) when the demand for a CD will vanish. The heuristic predicts whether or not the inventory in hand will be sold out before that date at the current price. If not, the price should be lowered. This method allows the manager to answer “what if†questions, by fixing T0 at different values. The second heuristic does not require manual input. It calculates the time (T(Pi)) when the inventory carrying cost is equal to the selling price less the buying price (profit), because after this point the CD must be sold at a loss. The heuristic then predicts the sales and calculates whether the inventory in hand will be sold out before or after T(Pi). If the inventory cannot be sold out before T(Pi), the price should be lowered to increase the demand. Finally a case study is presented. The performance of the different demand curves are tested with a simulation of actual data from a CD shop to measure the performance of the heuristics against the current mark-down strategies followed. The conclusion is that both heuristics outperform the current pricing policy of the shop management.