Capacity allocation models

Wong, W.K., 2003. A fuzzy capacity-allocation model for computerised fabriccutting systems. International Journal of Advanced Manufacturing Technology, 21(9), 699-711. 

One option to deal with the situation is to neglect setup times and setup carryover. This results in a situation, in which the available capacity is overestimated. On the other hand, if setup times are modeled, but setup carry-overs are not in the scope of the model formulation, the available capacity would be underestimated. Both results are not satisfactory in the first situation plans will result which are too optimistic and not feasible, whereas in the second situation in which capacity estimation is too conservative, resources will be underutilized. Consequently, only a model formulation which takes setup times and setup carry-overs into account captures the characteristics of the real world adequately and provides a realistic capacity allocation. 

The problem of selecting the optimal location and capacity allocation is very similar to the regional configuration problem we have already studied in Phase II. The only difference is that instead of using costs and duties that apply over a region, we now use location-specific costs and duties. The supply chain team thus decides to use the capacitated plant location model discussed earher to solve the problem in Phase IV. 

Use optimization for facility location and capacity allocation decisions. Gravity location models identify a location that minimizes inbound and outbound transportation costs. They are simple to implement but do not account for other important costs. Network optimization models can include contribution margins, taxes, tariffs, production, transportation, and inventory costs and are used to maximize profitability. These models are useful when locating facilities, allocating capacity to facilities, and allocating markets to facilities. 

Additionally, as indicated by Varma et al. (2007) there is a need to model financial planning decisions, R D resource allocation, as well as capacity expansion decisions within an integrated model, so that capital and capacity allocation can be performed simultaneously with R D projects selection and prioritization in order to enhance value generation. Certainly, R D decisions necessarily impact the design and the regular activities of the entire SC. Thus, such operational impact should be considered and assessed at the time R D and SC decisions are taken. 

The reactors are not considered individually but they are aggregated to a group of identical processing units with an overall capacity of four. The allocation of the reactors is not modeled explicitly, but they induce constraints on the start times of the polymerizations. Based on the as sumption that all four reactors can be used and that they are allocated in turns, the intervals between tn and tn+4 [n = 1... N — 4) must be greater than or equal to the processing time of a polymerization dp (with dp= 17) ... 

Fleischmann et al. (2006) provide a global production network planning model used at BMW that extends the simpler load planning model proposed by Flenrich (2002). The model is a multi-period, multi-product model with an objective function that maximizes the pre-tax net present value of the network. It includes decisions on product-plant allocation, production volumes, material sourcing volumes by supply region, structural and product-specific investments and use of overtime capacity. A major contribution of the model is the incorporation of the time-distribution of investment expenditures typically observed in automobile production networks. While tariffs are included in the transportation costs, the model does not consider further aspects of international trade such as currencies, duty drawbacks or local content rules which play a major role in practice. 

Business valuation literature provides various other methods for estimating terminal values (for an overview see Koller et al. 2005, pp. 271-290). Unfortunately, as cash flows cannot be allocated to individual decisions in a network design model, a cash flow-based estimate is not possible. Instead, book value or liquidation value at the end of the planning horizon could be used. For example, Fong and Srinivasan (1981, p. 790) include a terminal value function in the unit capacity acquisition cost function. However, they do not specify how this function can be quantified in real-world applications. The major disadvantages are that it is difficult to justify the assumptions underling the terminal value estimate and that restructuring expenditures cannot be properly evaluated. 

Since scope economies are especially hard to quantify, a separate class of optimization models solely dealing with plant loading decisions can be found. For example, Mazzola and Schantz (1997) propose a non-linear mixed integer program that combines a fixed cost charge for each plant-product allocation, a fixed capacity consumption to reflect plant setup and a non-linear capacity-consumption function of the total product portfolio allocated to the plant. To develop the capacity consumption function the authors build product families with similar processing requirements and consider effects from intra- and inter-product family interactions. Based on a linear relaxation the authors explore both tabu-search heuristics and branch-and-bound algorithms to obtain solutions. 

In a model developed to analyze the trade-off between scale advantages from product-focused factories and reduced transport costs from market-focused factories Cohen and Moon (1991) and Moon (1989) consider a fixed charge incurred for each product-plant allocation and a concave production cost function. The cost function is transformed into a piecewise linear function. In a model developed for the paper industry, Philpott and Everett (2001, pp. 229-230) use pre-determined product mix "clusters" that are selected using binary variables and for which the effects on unit production costs and technical capacity are specified exogenously to model scope effects. 

As discussed in Chapter 3.3.4 product mix complexity effects can be modeled with a fixed cost charge incurred for every product allocated to a plant and/or via an estimation of the capacity lost due to more frequent/more complex changeover processes. Since strategic models such as the one proposed here do not simultaneously determine production campaigns, the latter approach requires an estimation of the number of changeovers occurring at a plant. 

In some cases, product mix-dependent effects might have to be considered. For example, only a subset of the products requires processing step t5. Reflecting this fact, the installed capacity of the equipment used for t5 was found to be less than the overall plant capacity at most plants. In situations like these, an additional capacity restriction is required to ensure that only feasible product-plant allocations are proposed by the model. If task t5 requires substantial resources such as dedicated equipments or personnel, the model has to be further extended to explicitly model this resource and the costs associated with its utilization based on the production volumes allocated to the respective plant. 

Fixed costs are modeled in a similar fashion. For each plant class a default model containing plant fixed costs and production line fixed costs is created. Site specific copies of this default plant are created and the default cost structure is updated based on the actual values observed at the individual sites. The plant model additionally contains the capacity of the plant and the number of employees required to operate a production line. Based on the capacity consumption factors contained in the product description and the number of operators required per capacity unit, variable personnel costs are allocated to the products. If required, variable costs associated with additional resources contained in the BOM are allocated to the products in identical fashion. 

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