Economic Lot Scheduling Problem

The Economic Lot Scheduling Problem ( ELSP ) is a model of lot size planning . In the German literature it is sometimes referred to as the problem of optimal brand switching or brand change problem . It is based on several goods to be produced, for which demand quantities or sales quantities are known, which are constant over time (so-called static-deterministic model). These products are produced on a single machine, whereby this machine can only produce one single product at a time. If a different type of product is to be manufactured, i.e. if a new batch is to be manufactured, setup costs are incurred , often in the form of setup times .

Description of the model

The model is based on the following assumptions:

One -step production of several products on one machine, which represents a bottleneck and can either be occupied by a single product or a set-up process
Finite production speed and sequence-independent set-up costs (sequence-dependent set-up costs result in a generalized round trip problem )
constant sales speed
infinite planning horizon

The aim is to determine a ticket circulation policy. The aim is to determine the times at which the individual lots are to be placed and how large they should be. Since the planning period is infinitely long, the time after which the corresponding lot is re-issued is usually specified for each product (so-called cycle duration). Most of the time, one restricts oneself in the literature to simplifications regarding the cycle duration: ${\ displaystyle \ tau}$

With stationary policies, the cycle times are identical for all products. ${\ displaystyle \ tau}$
In so-called basic policies, each cycle duration is an integral multiple of a basic cycle duration . ${\ displaystyle \ tau _ {B}}$
A special form of the basic policy is the policy, in which all cycle times are formed by multiplying a power of two with the basic cycle time, e.g. B. 1, 2, 4 or 8 times the base cycle. ${\ displaystyle 2 ^ {x}}$

The solution to the problem is extremely complex. Apart from special cases (e.g. only one product), it is one of the NP-hard problems. Even if the cycle times are given, the determination of a permissible machine occupancy is still NP-difficult. Often, therefore, only cases for 2 products are investigated or those with restrictions on lot circulation policies.

Individual evidence

↑ Domschke, Scholl, Voss: Production planning: process organizational aspects . 2nd edition, Springer, Berlin, 1997, p. 90.
↑ Domschke, Scholl, Voss: Production planning: process organizational aspects . 2nd edition, Springer, Berlin, 1997, pp. 90f.
↑ Domschke, Scholl, Voss: Production planning: process organizational aspects . 2nd edition, Springer, Berlin, 1997, p. 93.

literature

Elmaghraby: The economic lot scheduling problem (ELSP): Review and extensions Management Science 24, 1978, pp. 587-598.
Boctor: The two-product, single-machine, static demand, infinite horizon lot scheduling problem . Management Science 28, 1982, pp. 798-807.
Müller-Mehrbach: The determination of optimal batch sizes for multi-product production . Dissertation, Technical University of Darmstadt

[1] Domschke, Scholl, Voss: Production planning: process organizational aspects . 2nd edition, Springer, Berlin, 1997, p. 90.

[2] Domschke, Scholl, Voss: Production planning: process organizational aspects . 2nd edition, Springer, Berlin, 1997, pp. 90f.

[3] Domschke, Scholl, Voss: Production planning: process organizational aspects . 2nd edition, Springer, Berlin, 1997, p. 93.