Chap

Network Design in the Supply Chain Exercise Solutions1. SC consulting, a supply chain consulting firm, has to decide on the location of its home offices. Their clients are primarily located in the 16 states as given in the following table. There are four potential sites for home offices: Los Angeles, Tulsa, Denver, and Seattle. The annual fixed cost of locating an office in Los Angeles is $165,428, Tulsa is $131,230, Denver is $140,000, and Seattle is $ 145,000. The expected number of trips to each state and the travel costs from each potential site are shown in table . Table: Travel cost and number of trips for Sc consulting Tota l # of trips Cost from Tulsa Cost From Denver Cost from Seattle State Cost from LA Washington Oregon California Idaho Nevada Montana Wyoming Utah Arizona Colorado New Mexico North Dakota South Dakota Nebraska Kansas Oklahoma 15 40 35 10 0 25 40 25 50 30 50 65 40 30 20 30 40 55 0 15 0 75 15 0 10 0 17 5 15 0 15 0 75 15 0 12 5 30 0 30 0 25 0 25 0 25 0 25 75 00 75 00 25 25 50 00 75 75 00 00 50 00 50 2 00 2 00 2 50 2 25 2 25 1 25 1 00 1 00 2 00 1 25 1 75 2 50 1 25 1 25 75 2 25 2 75 1 25 1 25 1 50 1 25 1 50 1 00 1 50 2 50 3 00 1 00 1 00 1 50 3 00 1 25 00 3 2 2 2 2 2 1 1 1 1 1 1 so as to minimize the overall network cost. (a) if there are no restriction on the number of consultants at a site and the goal is to minimize costs.n (5. Optimization model: n m Dj Ki fi cij yi xij = 4: possible home office locations. it is easy to see that this might not save on trip costs. The first constraint set requires that a specified number of trips be completed to each state j and the second constraint set prevents trips from a home office i unless it is open. note that there is no capacity restriction at each of the home offices. where should the home office be located and how many consultants should be assigned to each office? What is the annual cost in terms of the facility and travel? Solution The objective of this model is to decide optimal locations of home offices. There are two constraint sets in the model.2) (5.m (5. Thus. in this model there is no restriction = Annualized fixed cost of setting up a home office = Cost of a trip from home office i to state j = 1 if home office i is open. we need an optimization model to handle this.1} for i = 1.... it will be used in answering (b).. since trip rates vary between home offices and states.. and number of trips from each home office..3) yi ∈ {0.. However. We need to identify better ways to plan trips from different home offices to different states so that the trip costs are at a minimum..1) ∑x j=1 ij ≤ K i yi for i = 1.. Also. 0 otherwise = Number of trips from home office i to state j. The overall network cost is a combination of fixed costs of setting up home offices and the total trip costs.2) is not active in this model since K is as large as needed.. = 16: number of states. While a feasible solution can be achieved by locating a single home office for all trips to all states. It should be integral and non-negative Min ∑ i =1 ij n f i yi + ∑∑ cij xij i =1 j =1 n m Subject to ∑x i =1 m n = D j for j = 1.. = Annual trips needed to state j = number of trips that can be handled from a home office As explained. 2 .n Please note that (5.Each consultant is expected to take at most 25 trips each year. xls) 3 .H7:H22.1 demand constraints (Sheet SC consulting in workbook exercise5.SYMBOL INPUT Annual trips needed to state j Transportation cost from office i to state j fixed cost of setting up office i number of consultants from office i to state j.1. objective function 5.M7:M22 G26. K7:K22.M26 F7:F22. Dj cij fi xij CELL E7:E22 G7:G22.K26.I7:I22. J7:J22.L7:L22 M31 N7:N22 obj.I26. 2 50 137.With this we solve the model to obtain the following results: Tota l # of trips Trip s from LA Trip s from Tulsa Cost from Tulsa Trips from Denver Cost From Denver Trips from Seattle Cost from Seattle State Cost from LA Washington Oregon California Idaho Nevada Montana Wyoming Utah Arizona Colorado New Mexico North Dakota South Dakota Nebraska Kansas Oklahoma # of trips # of Consultants Fixed Cost of office Cost of Trips Total Office Cost 15 40 35 10 0 25 40 25 50 30 50 65 40 30 20 30 40 55 67 5 10 0 4 0 5 0 0 75 15 0 12 5 30 0 30 0 25 0 25 0 25 0 19 0 8 165.87 5 1 1 131.00 0 20.00 0 9.8 75 154.67 8 0 10 5 5 5 5 25 0 2 75 3 00 75 00 25 25 00 0 17 5 15 0 15 0 50 75 75 75 15 0 10 00 00 00 0 15 0 50 50 2 2 2 2 2 1 1 0 1 0 2 1 5 1 0 2 0 1 0 1 1 5 1 50 75 25 2 25 3 50 4 75 6 25 00 3 00 5 00 25 25 25 50 00 00 2 0 2 5 1 1 5 1 1 5 1 1 1 1 1 1 1 25 2 - 4 25 3 75 1 25 2 25 1 50 2 25 1 50 2 00 2 50 2 50 3 00 2 00 2 00 2 50 3 00 3 00 1 25 5 145.75 0 160. I. The task : Solution to the problem is given to you. You have to do it with Solver & Excel.25 0 180. 4 .23 6.48 0 10 140.75 0 The number of consultants is calculated based on the constraint of 25 trips per consultant.42 8 15. Explain each step in the class. As trips to Kansas cost the same from Tulsa or Denver there are many other solutions possible by distributing the trips to Kansas between these two offices. 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