You have finally been promoted to Senior Manager for the nuts and bolts category at Locky Locke Inc., a manufacturer with a large demand for bolts at

You have finally been promoted to Senior Manager for the nuts and bolts category at Locky Locke Inc., a manufacturer with a large demand for bolts at its three (3) factories. You have surveyed the market and found four (4) suppliers for a certain steady selling SKU, ZA27R46.  Your factories’ weekly demand for bolts are:

• Factory 1: 9,500 cases/week
• Factory 2: 6,500 cases/week
• Factory 3: 17,000 cases/week

Each of the four suppliers can provide the ZA27R46, but they differ in unit price, weekly capacity, and distance to Locky Locke Inc. three factories. The unit prices and the weekly capacity for each of the four suppliers are shown below: 

• Supplier 1:  U.S. Ainbolt  – Unit cost:  2.50 $/case  Capacity  9,500 cases/week
• Supplier 2:  Der Bolt, Thun  – Unit cost:  3.20  $/case  Capacity  10,000 cases/week
• Supplier 3: Li Tningbolt –  Unit cost:  1.90  $/case  Capacity  7,000 cases/week
• Supplier 4:  M. Bolton –   Unit cost:  2.80  $/case  Capacity  9,000 cases/week

You are trying to plan the weekly flow of bolts from these suppliers to your factories. Based on the current contract with your transportation carrier, the unit transportation cost for a case of bolts is $0.05 per mile from any of the suppliers to any of the factories.  The distances between the four suppliers and the three factories are given in the table below.

Q1: Currently, the factories operate independently. Disregarding any of the other factories, which supplier should Factory 2 select in order to have the lowest total (purchase and transport) cost for them?

Select the best answer

Supplier 1: U.S. Ainbolt

Supplier 2: Der Bolt, Thun

Supplier 3: Li Tningbolt

Supplier 4: M. Bolton

Q2: You want to take a holistic view of bolt sourcing instead of having each factory select its supplier on its own. You decide a model to help you select the optimal sourcing assignment for all of the factories for the ZA27R46 bolts. Based on this optimization model, what is the total weekly cost for supplying bolts for Locky Locke Inc.? Be sure to include the purchase price as well as the transportation costs. 

Q3: Based on your optimization model, which supplier should Factory 2 select in order to have the lowest total (purchase and transport) cost for Locky Locke Inc.?

Supplier 1: U.S. Ainbolt

Supplier 2: Der Bolt, Thun

Supplier 3: Li Tningbolt

Supplier 4: M. Bolton

Q4: You want to discuss the situation with the general manager of Factory 2. How much is the difference between Factory 2’s total (purchase and transport) cost per week in Q1 compared to the total cost per week from  Q3?

Q5:

a) You decide to re-negotiate with Supplier 1 (U.S. Ainbolt) to increase their capacity. They agree to increase it to 14,000 cases per week. How many cases per week does Supplier 1 (U.S. Ainbolt) send to Factory 2 in the new optimal solution? Input your answer in integers. 

b) Based on this optimization model, what is the total weekly cost for supplying bolts for Locky Locke Inc.? Be sure to include the purchase price as well as the transportation costs. Round to the nearest integer.