Do you mean set up costs?

I would think that there is no single answer to this question. One would like both of these to be small. Perhaps you are looking at the utilization of facilities. If SC is the setup cost and OC is the operating cost, you are possibly looking at OC/SC as the utilization. A better question may be what will be impact factor of the facility i.e. how many lives it may save, or how much damage to property it may save. I would think that higher the ratio of impact factor to set up cost (say 10), the easier it is to justify.

I am concerned about both setup and operating costs. I want to analyze the impact of increasing operating and setup costs on the objective function value and optimal solution e.g., with the increase in operating cost, some facilities may get closed during the planning horizon.

In this regard, I am indirectly also concerned about the impact of this increase on the lives saved. I actually want to investigate the impact of this increase on the overall deprivation of the affected population.

All of the above-mentioned investigations are possible if the optimization model and its parameter setting are pertinent to real-world operations. So I am in search of realistic model parameter values of operating and setup costs/

1. Cost Parameters for Temporary Relief Logistics Facilities

A. Setup Costs:

• Construction and Installation: These include the costs of setting up temporary facilities such as tents, mobile units, or modular buildings. Costs can vary significantly based on the type and scale of the facility. Typical Ranges: Setup costs can range from a few thousand dollars for simple tents to several million dollars for larger modular units with full amenities. Factors Influencing Costs: Location, infrastructure requirements (e.g., utilities, access roads), and the facility's scale.

B. Operating Costs:

• Maintenance and Utilities: These cover expenses for maintaining the facility and providing utilities such as electricity, water, and sanitation.Typical Ranges: Operating costs might range from $500 to $5,000 per day, depending on facility size and complexity. Factors Influencing Costs: Duration of use, local utility rates, and facility size.
• Staffing and Supplies: Costs related to personnel (e.g., security, administrative staff) and supplies (e.g., medical equipment, food).Typical Ranges: Staffing costs can vary widely based on the number and type of staff. Supplies costs depend on the nature of relief activities.

2. Relationship Between Costs and Facility Capacity

• Scaling Costs: As the temporary relief facility's capacity increases, both setup and operating costs generally increase, but not necessarily in a linear fashion. Larger facilities may benefit from economies of scale, where the cost per unit decreases as the size increases. For example, a larger facility might have a higher initial setup cost, but the per-person cost of providing services may decrease.
• Capacity Planning: To optimize costs, it's essential to match the facility’s capacity with anticipated demand. Underestimating capacity can lead to higher per-unit costs due to inefficiencies and overcrowding while overestimating can lead to higher fixed costs.

3. Effect of Planning Horizon’s Length on Costs

• Short-Term vs. Long-Term Costs: The length of the planning horizon affects both setup and operating costs. Short-Term Planning: Short-term facilities might have higher per-day costs due to the temporary nature of the setup and possible lack of economies of scale. Long-Term Planning: Longer-term facilities might benefit from more efficient resource use and lower per-day costs, but they also incur additional costs related to long-term maintenance and staffing.
• Cost Trade-offs: Longer planning horizons might allow for more permanent or semi-permanent solutions that reduce daily operating costs but increase upfront setup costs. Balancing these trade-offs is crucial for cost-effective planning.

4. Practical Recommendations

• Benchmarking: Review case studies and reports from similar disaster response scenarios to understand realistic cost ranges. Organizations like the World Health Organization (WHO), the United Nations (UN), and various NGOs often publish cost data related to disaster response facilities.
• Cost Modeling: Use cost models that account for both fixed and variable costs and incorporate scenarios for different facility sizes and durations. Tools like Excel or specialized optimization software can help develop these models.
• Consult Experts: Engage with experts in disaster response logistics and facility management to get accurate cost estimates and insights into cost management strategies.

Summary

• Setup Costs: Typically range from thousands to millions of dollars, depending on facility type and scale.
• Operating Costs vary from $500 to $5,000 per day, influenced by facility size and local conditions.
• Capacity Relationship: Larger facilities may have higher setup costs but lower per-unit operating costs.
• Planning Horizon: Longer horizons might reduce per-day costs but increase initial setup costs. Your model should consider both short-term and long-term implications.

Understanding these cost parameters and their relationships will help you optimize your disaster response logistics model effectively.