Product lines constraints

The second step is to cut or remove some products allocated at the end of each sequence in the initial chromosome based on the production-line constraints in allocated labour, material and working capital. After the cutting operation, the N strings of number will become an intermediary chromosome. 

Below, the procedure for the determination of dominant campaigns in a version that was proposed by Lazaro et al. (1989) is outlined. Their methodology includes enumeration of feasible production sequences, selection of dominant production lines, task sequencing, and search for an optimum with constraints. All possible production variants are generated by an enumeration procedure that takes into account the possibility of available equipment working in parallel, initial and final task overlapping, and instability of intermediate products. Non-feasible sequences are eliminated so that only favourable candidates are subjected to full evaluation. Dominant production lines are selected by maximizing the criterion ... 

Currently Bayer Technology Services considers extending the software BayAPS PP to compute the optimal split of a product between several production lines or factories that can produce it. This split is influenced by uncertain demand with different characteristics in different regions, different cost oftransport and different production cost in the factories. This means that different marginal incomes for the same product occur depending on the place of production and/or the customer group which receives it. The mathematical formulation ofthe optimization criterion again is to maximize the expected service. This has already been solved for several types of constraints. 

A new or modernized production line must be provided (project 1 or 2). Automation is feasible only for the new line. Either project 5 or project 6 can be selected, but not both. Determine which projects maximize the net present value subject to the various constraints. 

The dual price of the slack variable sm on this constraint indicates the effect of selling this product at the margin, that is, it indicates the marginal profit on the product. Ifthe constraint is slack, so that the slack variable is positive (basic), the profit at the margin must obviously be zero and this is in line with the zero dual price of all basic variables. Since cost + profit — realization for a product, the sum of the dual prices on its balance and requirement constraints equals its coefficient in the original objective function. 

The total investment expenditures incurred at a site have to be calculated in two steps. Equation (3.10) calculates the investments per plant. These are aggregated to the site level and adjusted for government investment incentives, defined as percentage of total investments, in equation (3.11). Investment expenditures are allocated to the time period preceding the commissioning of the technical capacity. A non-negativity constraint (3.54) ensures that plant/production line shutdowns do not lead to negative investment expenditures. 

Equation (3.24) requires that the production volume allocated to a plant does not exceed technical capacity of the plant. Capacity consumption factors are site-specific to account for productivity differences and time dependent to allow for discrete process improvement projects. A plant s technical capacity is calculated by multiplying the number of production lines installed with the capacity per line (3.25). It can be varied between a lower and an upper bound (3.26). Restriction (3.27) states that from each plant class only one plant can be open at a site. The rationale behind this restriction is that only one plant type (size and degree of automation combination) should be put in place at a given site and capacity can be adjusted via the number of production lines. It is not implied that all production lines necessarily have to be in one building. For sites with utility capacity restrictions, constraint (3.28) ensures the available capacity is not exceeded. 

The additional capacity restriction (3.98) accounts for the capacity of the shared resource. In order to determine shared-resource capacity, restriction (3.99) can be used if the number of equipment units is correlated with the number of production lines installed at a plant. In combination with the integrality restriction (3.100) it enforces the step-wise increase of the shard resource capacity in line with the development of overall plant capacity. For example, if for every three production lines one equipment unit is to be installed, the second unit will be installed once the fourth production line is put into operation. If the model is to select the number of equipment units independently, restriction (3.99) has to be deactivated. Finally, for the option to temporarily shut down production lines capacity constraint 24 needs to be modified as shown above. 

The integration of capital expenditures for the shared resources as shown in equation (3.11a) rests on the assumption that the number of equipments is correlated to the number of production lines. If the model can independently select the shared resource capacity, it is theoretically possible that the number of shared resources operated increases while the number of production lines used decreases. In this case a separate calculation of the investment expenditures for shared resources is required to avoid that "negative" capital expenditures from capacity reductions that are eliminated via the non-negativity constraint (3.54) offset the expenditures for shared resource installations. 

Either / or minimum constraints are considered at the production lines level, at the packaging lines level, at the semi-product transport, and at the product transport. In each case, existence of a rninimrun constraint means that the quantity of produced /packaged / transported semi-product / product either has to reach a defined rninimrun level or has to be zero. In each case this rninimum constraint expresses the economical consideration that it is not worth to produce, package, or transport, below a rninimum quantity (e.g. one truck, in the case of transportation). 

A solution for the above class of problems is a selection of products to produce, which production line to be used and in what order, so as to maximise the total profit of the company as well as customer satisfaction index while satisfying simultaneously all the given constraints. 

The problem is to do the planning for next month by (1) selecting what products to produce, (2) allocating the selected products to which production line and (3) selecting the producing sequence in three production lines to maximise the profit of the company as well as its customer satisfaction index while satisfying simultaneously all constraints above. 

The second step is to cut the initial chromosome based on three constraints of labour, working capital and material in each production line. Output of this step is intermediary chromosome, which looks like as shown in the cells shown in the highlighted cells in Table 6.3. 

It should be noted that, in the other case, if the number of different products in intermediary chromosome is less than 20 as required minimum number of different products, the three-step proposed must be repeated until all of the given constraints are satisfied, which means that feasible chromosome is achieved. In addition, the length of each string corresponding to each production line in the feasible chromosome is different from the one in initial chromosome and different from time to time. 

After swapping the two selected genes, constraint-based cutting operations are then applied to every production line in the obtained chromosome to ensure feasibility. As a result, a feasible chromosome output of mutation operation is achieved as shown in the last sub-table in Table 6.6. 

In this chapter, a class of soft precedence-constrained production sequencing and scheduling problems for multiple production lines has been modelled. Due to the nature of constraints, the multi-objectives GA with new strategies for chromosome encoding, feasibility of chromosome, crossover as well as mutation operations have been developed to optimise the model. 

Product lines and customers products and customers, whether they are profitable or not, that must be supplied the source of the constraint. 

The simple production capacity constraint (11.5) could be enhanced in a number of ways using standard techniques depending on the complexity of the production environment. For example, allocation among multiple factories or production lines within a factory could be made. The possibility of overtime could be included. Also, production scheduling factors, such as lot sizing, could be modeled (e.g., see Constantino (1996) and Wolsey (1997)). Ozdamar... 

In addition, a solver alone does not solve the variability problems in industry because there is a strong need for a visualization that represents the solver results in an adequate way to the user. The visualization of product line models and their dependencies that represents the far end in product Une engineering has to deal with huge variability models and often an incredible number of constraints (more than 200,000) for a complete product line. To the best knowledge of the authors there is currently no tool with an appropriate user interface available able to visualize such models, their constraints and analysis results from a solver in an effective and efficient way. 

Major corporate decisions are shown as fuzzy gates in the model, implying that teams involved in the PD must collectively decide on the next phases for a product line or product style. The system constraints may vary depending on the type of product line and business model. Some of the examples for these constraints are vendor reliability, raw material availability, customer constraints such as personal consumption expenditures, consumer wants, marketing channels, and available technology. The reader is encouraged to refer to this model to have an in-depth examination of... 

The final, and major constraint of the designer is that the cell and battery designs which evolve shall be amenable to mass production techniques at realistic costs. This is too extensive a topic to discuss here suffice it to say that each proposed material of construction and component design must be reviewed critically in the light of this criterion. The size of the operation can be gauged by considering a modest market for 60,000 urban delivery vans with a battery life of 3 years. The annual requirement would then be for 20,000 traction batteries containing, say, 15-20 million cells. If a production line assembled cells at the rate of two per minute and operated three shifts, all the year, it would still require 20 such production lines to manufacture this number of cells. The need for simplicity and automation is evident. 

Production Expansions Binary Decision Variables Equations 3.33 and 3.34 ensure that a new production line t, proposed as a capacity expansion, is activated only when all the existing machines of similar technology t are operating. If at least one production line of type t is idle at a given plant, then no capacity expansion can be done. Note that these constraints can be relaxed if the analyst wants to evaluate the replacement of equipment. In such a case, new production lines could be opened even when the existing equipment is idle. 

Employment of instrumentation is much the same in industrial research laboratories as it is in academic institutions, although of course the aims of the former are necessarily more focused to particular objectives. But elsewhere in industry both time and money, within the constraints of safety, are of prime importance and the usefulness of information provided by any technique must be Judged primarily by these criteria. The nearer the production line, the greater is the degree of rigour with which these criteria are applied. Rapid measurement, high degree of automation and reliability, all at minimum cost, are therefore demanded of manufacturers of spectroscopic equipment. 

Two major distinctions may be justifiably drawn for further discussion. First, it is important to consider the repeatability of the task when characterizing potential decision aids (Slovic 1982). Decisions that are repeatable can be handled quite effectively by precise rules, or standard operating procedures. If on the other hand the task of the decision is unique, it requires to allow for the time available for deliberations prior to action (see Tab. 5.5). Second, time-dependent decisions such as in ongoing processes at a chemical plant have to have other treatments and support systems than decision making under no such time constraints, like planning the lay-out of a new production line. Several procedures for decision analysis in time-invariant situations are available today (Zimolong Rohrmann 1987). 

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