Production capacity constraints

One of the first papers to incorporate production capacity constraints in a pricing and inventory model is Lai [88]. Under linear deterministic demand and quadratic production costs, Lai shows that price is more responsive to demand shocks when a stockout is realized or when capacity is soon to be exhausted, and that considering production capacity constraints reduces the asymmetry in price behavior. 

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... 

Constraint set (6) is the production capacity constraints at the plants. The left-hand-side term of the constraint represents the sum of products transported to warehouses from plant m which should be less than or equal to its capacity. 

Purchasing organizations are exposed to numerous risks associated with their supphers and their supply network. Supply side risks reside in purchasing, suppher activities and supplier relationships. These include suppher business risks, production capacity constraints on the supply market, quahty problems, technologic changes, and product design changes (Zsidisin et al. 2000). 

Jung, J. Y., Blau, G. E., Pekny, J. E, Reklaitis, G. V., Eversdyk, D. (2008). ntegrated safety stock management for multi-stage supply chains under production capacity constraints. Computers and Chemical Engineering, 32, 2570-2581. 

The types of facilities bottleneck which appear late in field life depend upon the reservoir, development scheme and facilities in place. Two of the most common capacity constraints affecting production include ... 

For a given subset of chemicals, where cp CP, these constraints control the production of different processes based on the upper and lower demands of the petrochemical market for the final products. In constraint (4.3), defining the binary variables yp cm for each process m Mpet is required for the process selection requirement as y ( m will equal 1 only if process m is selected or zero otherwise. Furthermore, if only process m is selected, its production level must be at least equal to the process minimum economic capacity B for each m Mpet, where Ku is a valid upper bound.. This can be written for each process m as follows ... 

Overall volumetric productivity Qp (mol.m s ) (it is also common to use a yearly basis) is the average production capacity per unit volume and time of the bioreactor. The overall volumetric productivity is confined, on the one hand, by physical constraints, such as mass and heat transfer, and, on the other hand, by biocatalyst concentration... 

A third type of innovation is concerned with attempts to weaken the capacity constraints at both upper and lower limits. At the upper limit, weakening a constraint will reduce unit costs on the assumption that the production relationship holds at greater sizes with approximately the same coefficients that characterized smaller outputs. Production beyond existing upper limits, as noted above, may be associated with difficult engineering problems. Expansion of output by moving along a process curve may not be possible because of additional stresses put on equipment. In addition, attempts to reduce the minimum scale at which a process may be operated may also be worthwhile because of local conditions which both justify a smaller output than may be produced by a given process and make a process attractive... 

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. 

On the other hand, the constraints require to meet the demand of every customer every period capacity constraint at each EXi every period. The upper and lower bounds on the production ability of each plant every period, and the material balance at each DC every period. Additionally, non-negative conditions are imposed on the material flows and binary condition on the open/close selection. Finally, the model has the problem size such that number of integer variables is J, continuous variables T (IJ+J +JK+IK+J), and constraints T U+2J+K) where notation /, J, K and T denote number of plants, DCs, customers and terms, respectively. 

There are several cases where it is necessary to determine the optimum conditions for maximum production rate (1) when the demand for a product exceeds the production capacity, and (2) when the capital cost of the purification is significant compared to the operating costs and to the cost of the unrecovered crude. As a matter of fact, sales, hence production, can rarely be kept for a long period at any predetermined level. There must be alternative strategies to adjust the production rate and the recovery yield, while minimizing costs. The absolute maximum production rate can be looked for, or the maximum production rate with a recovery peld constraint. Other combinations will permit the minimization of the production costs. Alternatively, since we know from the literature [12] that the costs associated with the loss, the processing, and the regeneration of the solvent used often accoimt for nearly 40% of the total production costs, we can choose as... 

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