Análisis del marketing mix

Despite aspects of the CLSP resembling elements of the problem facing LTC planners, a number of important characteristics of our contracting problem are not considered. For example, the classical CLSP does not allow for any form of discounting and says nothing about the selection of suppliers for whom which orders will be made. Such considerations have to date been modelled through extensions to the classical CLSP and are referred to as CLSP models with supplier or vendor selection.

The more general supplier selection problem (SSP) concerns three related components, that is to say: (1) which products should be ordered, (2) from which suppliers and (3) in what quantities. Historically, previous work surrounding the supplier selection problem has focused on analysing each of these different aspects in relevant isolation of one another.

While (1) relates to strategic decisions that are made surrounding which products an organisation wishes to market and sell; (2) considers more the ability of sellers to meet shipment deadlines, the perceived quality of the products offered by different suppliers and the strength of relationship between purchaser and supplier; and (3) inventory management policies and sales forecasts. As we are interested in a very specific healthcare service, LTC, we consider only aspects (2) and (3). Apart from a few studies that consider purchasing

20 The introduction of Big Ms into the model does not yield particularly sharp lower bounds, leading to some loss of precision, despite reducing the computational complexity.

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decisions that form part of a services contract with a supplier, the vast majority of published works have investigated the SSP from the point of view of firms that intend to purchase raw materials (Aissaouia, Haouaria and Hassinib 2007).

Supplier narrowing

Earlier work in supplier selection placed more emphasis on choosing the initial suppliers to consider, perhaps prior to further negotiation of price, discounts and service level. The aim of such work is arguably to limit the number of suppliers for which it is possible to deliberate with, in cases where there are many, by eliminating suppliers according to either quantitative or qualitative metrics. One such approach was by (Timmerman 1986) who proposed a categorical ranking approach to sort suppliers into three classes; good, neutral or unsatisfactory, based on an evaluation of each supplier’s historic performance for different criterion. An approach that relied less on subjective opinion of supplier performance was proposed by (Hinkle, Robinson and E 1969) which used classification and clustering to identify groups of suppliers with similar performance characteristics. In this case, each supplier attribute was based upon a numerical performance indicator and the groupings could be used to identify groups of statistically related suppliers to consider.

Traditionally, once the supplier set has been narrowed sufficiently for further modelling, the supplier choice is then optimised so that the purchaser is able to minimise the total cost of ordering. However, given that a number of non-price based factors may also be Important in the purchasing decision, for example late delivery, quality of goods delivered and ability to consistently meet production, several researchers have developed methodologies to overcome these limitations and allow for some of these factors to be taken into consideration.

An approach that uses the total additional cost of purchasing from a supplier was proposed by (Roodhooft and Konings 1996) who added to the price of an item the expected total supplementary cost associated with using a given supplier’s materials. (Wind and Robinson 1968) proposed using a score card for each potential supplier under different criterion. For each criterion an appropriate weight could be assigned to reflect the importance the

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purchaser assigned to this particular aspect of the supplier. Based on the dot product of the score and weighting vectors an overall score could be obtained for each supplier and used to inform the decision making process. To overcome uncertainty in the criterion themselves, (Soukup 1987) has shown how the criterion weights may be represented by probabilities than can be adjusted to calculate a payoff matrix under different weighting scenarios.

Single and multiple sourcing models

Where a purchaser selects a single supplier from which to order the modelling approach is referred to as a single sourcing vendor selection model. One of the key approaches in this area was developed by (Morris 1959). In this case the purchaser must choose to purchase a product from one of several competing suppliers for the duration of the policy, during which time the price of a product is uncertain and modelled as a random variable. In this paper the problem is modelled using dynamic programming to analyse different purchasing strategies under price uncertainty. One of the many extensions to this approach was by (Polatoglu and Sahin 2000) whereby, in addition to future supplier price, demand for products in each period was modelled as a random variable dependant on selling price and the time period itself.

In contrast to single sourcing models, multiple sourcing models allow for the possibility of ordering from multiple suppliers. Reasons vendor selection models may be orientated around using several suppliers include being able to satisfy total demand where suppliers are capacity constrained and hence individually would be unable to satisfy total demand.

(Hong and Hayya J 1992) have also suggested that the use of multiple suppliers in specific inventory management policies, including Just-in-Time (JIT), allows for greater opportunities to reduce overall inventory and purchasing costs. One of the first papers which report the use of a multiple sourcing model was by (Gaballa 1974) in which case a mixed integer programming formulation was used to select suppliers for the Australian Post Office.

Discounting

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Two important extensions to multiple sourcing models have been made over the last few decades, the first of which concerns modelling the multiple supplier problem over multiple time periods and the second concerns modelling the discounting activity of suppliers.

Discounting of items may take one of several forms, to date the key forms that have been modelled within the literature include: discounts based upon a price-break, whereby the per-item price falls when an order reaches a certain threshold (Chaudhry, Forst and Zydiak 1993); total volume discounts, where the discount granted is based upon the total volume of all orders (Sadrian and Yoon 1994); and bundling, where the price of an item depends on the quantities of other items a supplier sells (Rosenthal, Zydiac and Chaudhry 1995).

Other extensions

To date, few papers have addressed the problem of multi-period supplier selection and multi-item problems simultaneously (Lee, et al. 2013). A theoretical formulation of the use of discounting with regards to production constraints under multiple suppliers was presented by (Bender, et al. 1985) using mixed integer programming. A model by (Basneta and Leungb 2005) attempted to bridge the gap between the classical CLSP model with more recent supplier selection models using discounting, in which case a mathematical programming formulation was presented to select the optimum number of items to order from each supplier taking into account ordering costs, quantity discounts and holding costs.

(Hassini 2008) has also considered the implication of limited supplier capacity and the discount rate to determine order quantity and frequency, in addition the cost of transporting products ordered to customers was also considered in the objective function.

Of the body of research that studies the supplier selection process, we find that the general direction has been in marrying the supplier selection decision with inventory planning models, including the CLSP, so that these two decisions can jointly be optimised. At the same time, while an increasing number of papers have investigated how features of the supplier selection and ordering process, for instance discounting, might be incorporated, a new wave of research has been directed towards defining and implementing more multi-objective style models and in treating demand for products, frequently taken as known and

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constant, in a more stochastic manner. The vast majority of existing research has also concerned the use of supplier selection and CLSP in production-type problems, those involving inventories and physical storage of goods, compared with for instance the optimum purchasing policy for services – items which cannot be stored or carried over to future periods.