Kelmarsh Valley Irrigation District: Allocating a Short Supply

Driving question. When a fictional irrigation district cannot fill every request, what rule should it use to divide the water, and how should it report the result to growers?

The client. You are staff analysts for the Kelmarsh Valley Irrigation District, a fictional district that delivers surface water to thirty farm parcels and to the town of Kelmarsh. The district board will hear your recommendation at the end of the project.

The supply. This season the district expects 4,200 acre-feet in total. A standing contract sends 900 acre-feet to the town before any farm water is delivered. That leaves 3,300 acre-feet for the thirty parcels.

The requests. The thirty parcels asked for these amounts, in acre-feet: 40, 55, 62, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 140, 150, 160, 170, 180, 200, 220, 240, 260, 290, 320, 380, 450, 600. The requests total 5,217 acre-feet, well above what the district can deliver.

The money. The district's fixed costs for the season are $780,000 in this fictional scenario. The district recovers costs through a single price per acre-foot delivered, charged the same to the town and to every parcel.

Constraints your model must carry. Total deliveries cannot exceed 4,200 acre-feet. The town must receive its 900 acre-feet. No parcel may receive more than it requested. Revenue must at least cover the $780,000 in fixed costs. Your board also insists that no parcel receive less than 25 percent of what it asked for.

What you turn in. A written proposal of four to six pages containing your quantity memo, both data displays, your system of inequalities with a graphed feasible region for two decision variables, a table of three candidate allocation rules marked viable or non-viable, your recommended rule, and your recommended price per acre-foot. You also give an eight-minute presentation to the fictional board, and you must answer one question from the board about a grower who is unhappy with your rule.

1. Session 1, quantity memo. Write one page naming the quantities your team will report and defending each choice. Candidates include acre-feet delivered per parcel, percent of request filled, and dollars per acre-foot. Choose two as your primary reporting quantities and explain what question each one answers for a grower. Turn in the memo at the end of the session.

2. Session 2, data displays. Build a histogram of the thirty fictional parcel requests, stating the bin width you chose and why. Build a box plot of the same thirty values, marking the median and both quartiles. Write two sentences on what the histogram shows that the box plot hides, and two sentences on the reverse. Turn in both displays.

3. Session 3, constraint model. Choose two decision variables, such as a flat amount given to every parcel and a percentage of each request. Write at least four inequalities from the constraints in the brief, graph them on labeled and scaled axes, and shade the feasible region. Turn in the graph with each boundary labeled by the constraint it carries.

4. Session 4, candidate rules and price. Test three allocation rules against your model: an equal share for every parcel, a fixed percentage of each request, and a rule of your own design. Build a table showing, for each rule, the water each of the thirty parcels receives, the total delivered, and whether the rule is viable. Compute the price per acre-foot that recovers the $780,000 in fixed costs under your recommended rule. Turn in the table and the price.

5. Session 5, board presentation. Present for eight minutes to the fictional board, using your two reporting quantities from Session 1 throughout. Answer one challenge question from the board about the grower who requested 600 acre-feet. Turn in the finished written proposal at the end of the session.