Presentation of the book “Planificación y control de stocks” (Stock planning and control), by Joaquín Bautista-Valhondo

“Por tanto, provéase ahora Faraón de un varón prudente y sabio, y póngalo sobre la tierra de Egipto.
Haga esto Faraón, y ponga gobernadores sobre el país, y quinte la tierra de Egipto en los siete años de la abundancia.
Y junten toda la provisión de estos buenos años que vienen, y recojan el trigo bajo la mano de Faraón para mantenimiento de las ciudades; y guárdenlo.
Y esté aquella provisión en depósito para el país, para los siete años de hambre que habrá en la tierra de Egipto; y el país no perecerá de hambre”.

Gn 41, 33-36.

Description of the act

Why do we store assets? In principle, it does not seem that it is due to a biological necessity, since many living beings do not do it and survive. Among humans, the causes of this fact are diverse and in this book we will discuss them. We will also answer questions such as: what to save, how much to save and how often it is advisable to purchase an asset and in what quantity.

As consumers we buy goods in more or less quantity, and said quantity depends on the characteristics of the good, our purchasing power and our consumption needs, both immediate and short-term. Furthermore, intuitively, the quantity purchased is subject to the perception that We have about the effort it takes to get to where the good is, regardless of the number of units we acquire. When faced with the question of whether we should buy a lot rarely or buy a little often, without resorting to numbers, we try to find a balance between the effort (cost) of shopping and that of storing the purchases.

Thus, if the acquisition of the product involves trips of about 100 kilometers or having to pay for the corresponding transportation, it is reasonable to make few trips and buy many units on each trip; This last action involves saving the surplus naturally; If not, what are refrigerators, cabinets, display cases, book shelves, boxes and drawers and other domestic spaces intended for storing things for? In contrast, if the product is always available for purchase within 100 meters, the normal thing to do, if there are no special offers that attract us, is to purchase a few units, traveling as many times as necessary.

Similarly, a manufacturer produces items in larger or smaller batches depending on the characteristics of the item, its demand, and the productive capacity of the system. The size of the batches also depends on the effort involved in getting the production system ready and running, regardless of the number of units manufactured in a run. Now the question is whether to produce many small batches or few large batches, and the producer tries to strike a balance between the effort to start his system and the effort to save excess items to satisfy immediate orders.

Thus, if a mixed model manufacturing system requires preparation times with a machine stopped of 2 hours each time there is a model change, and the process time of a unit (piece) is of the order of 2 seconds, what is reasonable is to make few preparations and manufacture many pieces with each issue order, thus generating a surplus that will go to the warehouse until the contractual delivery dates agreed with the clients. On the contrary, if the preparation times are 2 minutes and the process times are 1 minute, the usual thing is to manufacture order by order, customer by customer, according to the order established by the contractual dates, making as many system preparations as necessary. .

In both cases, consuming and manufacturing, the best solution is obtained, from an economic perspective and in the absence of restrictions, when the balance is reached between the so-called costs of issuing an order and possession.

Sometimes it is convenient to accumulate a good in large quantities; To justify the high accumulation of this it is not necessary that it be expensive, it is enough that it is necessary.

Let’s think: what would happen if the Ministry responsible for the management of a country’s reservoirs tried to reduce the cost of maintaining them, eliminating the entire water stock, in accordance with the motto: if there is no content left over from the continent, therefore, it is cancelled. budget.

Normally, saving or accumulating products responds to a need or the possibility of reducing efforts (costs) in the medium long term, although the massive and specific accumulation of a good for later sale may also be motivated by speculative purposes, such as purchasing in mass of homes through investment funds in the expectation of rapid revaluation in the real estate sector. This type of motivation does not interest us because it is conducive to satisfying the ambition of a few to the detriment of the needs of many people, so it will not be the subject of study in this text.

Stock management is a fundamental topic in Industrial Organization Engineering, since stocks are present in all organizations and companies (public and private), whether they are goods or services, rarely can they be dispensed with. from them. Furthermore, stocks have special relevance in the modern economy and in some productive sectors (e.g. pharmaceuticals and consumer goods) they can represent more than 20% of the total assets to guarantee the quality of the service.

This text is focused on defining and describing the basic aspects related to stock management and the specific aspects related to stock planning and control using optimization models.

Thus, in the first section we will discuss the concept and typology of stocks, their usefulness in production and logistics systems, and the various types of stock in relation to the causes that generate them, the functions they perform inside and outside the system. and the nature of the goods being stored.

Sections 2 and 3 are dedicated to stock control and the factors involved in its management, among them: the demand for the products, the costs derived from stock management, the information system associated with management, delivery deadlines. delivery and supply, the various supply methods, and the way of classifying the stock according to the importance of the items within the production system to which they are subject.

From here we will dedicate ourselves to the optimization models to plan and control stocks, establishing their foundations and the basic nomenclature (section 4), and, subsequently, model after model, the hypotheses and formulations that govern them. Of course, so that the reader can acquire agility when applying the models, we will use various prototype examples with increasing degrees of difficulty in terms of resolution.

The first model that we will see (section 5) is the so-called economic lot (EOQ: Economic Order Quantity) or Harris-Wilson, whose basic application is illustrated with two examples, also including the treatment of investments in a project to improve the production system and the application of Game Theory in a collaborative environment between agents (e.g. supplier versus customer, manufacturers from the same industrial sector) with the goal of reducing relevant global management costs; everyone’s situation wins when they reach the Nash equilibrium point or, well, when they distribute the global profits through the Shapley value.

Sections 6 and 7 are dedicated to EOQ models with finite production rate and with the possibility of deferring demand, respectively. To apply these models we will solve several examples related to a stamping line, a reactor cooling system, a purchasing and selling company and a game between suppliers, deferring demand in two situations: competition and alliance between them.

In section 8 the models presented in sections 5, 6 and 7 are unified: generalized EOQ. Two prototype examples will serve to illustrate the application of the unified model: an electric battery manufacturing plant and an electronic components supplier.

The following models to deal with (section 9) contemplate the possibility of acquiring the units of the article with a unit cost dependent on the size of the lot. Three cases are distinguished: (i) homogeneous discounts, (ii) progressive discounts, and (iii) manufacturing costs based on the quantity produced in a run. The examples used to show the application of these models are related to a manufacturer of electric motorcycles and a mechanical workshop dedicated to the assembly of a component.

In section 10, two manufacturing models with production system preparation times are studied, being the first in which restrictions on management attributes appear explicitly: batch, frequency and replacement period. The first model corresponds to the treatment of a single article, while the second refers to multiple articles. Three examples illustrate the application of these models, which are related to a stamping line and the cooling system of a reactor.

Section 11 is dedicated to managing stocks of multiple products subject to linear technological and economic restrictions. To solve the problem, the Lagrange multiplier method is used using two illustrative examples based on the acquisition of 3 mechanical components, imposing limitations on the maximum stock and the economic value of the average fixed assets.

All the previous models are formulated under the assumptions of a continuous and homogeneous demand rate over time and an unlimited planning horizon. For its part, section 12 focuses on the dynamic lot sizing problem (DLS: Dynamic Lot Sizing) in which the assumptions are: discrete and heterogeneous demand over time and a limited horizon. To solve the problem, several heuristic methods and an exact procedure based on Dynamic Programming are used. The application of the methods is illustrated with two examples: one on the manufacturing of a component for vehicle fleets, and another on the supply of an item in which two merchants participate.

Section 13 includes some recommendations on the treatment of uncertainty when it affects some data of the problem such as: the demand rate, the production rate, the delivery time, the preparation time of the production system, the cost of issuing an order, the unit acquisition cost and the possession and breakage costs.

The conclusions and final comments derived from the development of this text are collected in section 14.

Finally, three additional sections are included in the book corresponding to selected references and some statements of problems to be solved and case studies.