Problem statement: The company currently shipping from its distribution center and warehouse in Riyadh. To all the targeted other twenty-one cities the company has warehouse that is appropriate with size of the business in the region. In each city the warehouse is equipped for receiving and storing products, and with sleeping area for the drivers. Although theses warehouses cannot be used as distribution centers without upgrading the facilities to reach the company quality standards. Marketing department has done market research about opportunities of selling the company's new porcelain glue. The research has concluded that there is a huge demand on all the construction materials, including porcelain glue, especially in Riyadh, Jeddah, Mecca, and Dammam due to the large growing in construction sector. Including Riyadh distribution center which has fixed cost of 200,000 SAR, operations department nominated Either Jeddah or Dammam warehouses or both to be upgraded to facilitate the distribution process. Upgrading Jeddah warehouse will add a fixed cost of 150,000 SAR and upgrading Dammam warehouse will add a fixed cost of 120,000 SAR. The company has Mercedes trucks that consume 19.44 liters of diesel per 100 km, each truck is equipped with 40 feet container of maximum load of 26 tons The company's safety policy states the following 1. Total time of round-trip delivery less than 12 hours is allowed 2. One-way trip of more than 14 hours is not allowed, driver must sleep (costs the company 250 SAR per trip) For quality purposes delivery must not exceed 25 tons The company wishes to satisfy all demand. Table [1] below shows the weekly demand of all twenty-two cities City Index D F H M N V Destination Riyadh Jeddah Ad Damam Mecca Medina Taif Tabuk Abha Hail Al Hafuf Buraydah Al Baha Al kharj Wadi Al-Dwasir Bishah Najran Sakakah Ara'r Jizan Hafer Al Batin Al Majma'ah Al Quwaiiyah Delivering Cost Service fee: 30 SAR 243 86 216 212 196 335 236 160 81 94 219 21 162 149 230 245 265 283 125 53 46 One-way time Round-trip time 10.5 4.5 10 9.5 8.5 16 12 7.5 4.5 10.5 2 7 7.5 12 10.5 12.5 14 9 3 2.5 66 21 20 19 17 32 24 15 00 21 + 14 15 24 21 25 28 12 s City Index D G H I K L M Destination Riyadh Jeddah Ad Damam Medina Taif Tabuk Abha Hail Al Hafuf Buraydah Al Baha Al kharj Wadi Al-Dwasir Bishah Najran Sakakah Ara'r Jizan Hafer Al Batin Al Majma'ah Al Quwaiiyah Delivering Cost 86 331 Service fee: 30 SAR 313 303 294 427 334 250 37 184 315 119 249 275 330 339 255 380 118 145 141 One-way time 4.5 15 14 13 13 19 15 11 2 8 14 5.5 12 12 15 13 12 17 6.5 Round-trip time 30 HE 28 26 26 38 30 22 16 28 11 24 24 30 28 24 34 12 12 13 City Index D E F G H K L M P Q R Destination Riyadh Jeddah Dammam Mecca Medina Taif Tabuk Abha Hail Al Hafuf Buraydah Al Baha Al Kharj Wadi Al-Dwasir Bishah Najran Sakakah Ara'r Jizan Hafer Al Batin Al Majma'ah Al Quwaiiyah Delivering Cost 234 Service fee: 30 SAR 331 23 101 42 238 162 206 314 225 96 255 211 133 228 299 340 174 314 258 331 One-way time Round-trip time 10.5 21 14 28 1.5 3 5 10 2.5 5 12 24 8.5 17 9 18 13.5 27 10.5 21 5.5 11 12 24 11 22 7.5 15 12 24 13 26 14 28 9 18 14 28 10.5 21 9 18 7 Formulation: Sets: Warehouses i: a,b,c Distribution a..v Constant: Cij:Cost deliver form I to j Dj: Demand j 01j: One way time trip 1 j RIj:Round-trip time Ij Decision variables: k-Riyadh distribution center oi-upgrading warehouse i to be a distribution, i- Jeddah warehouse, Dammam warehouse. Binary xij-amount of porcelain to be deliver from distribution center i to warehouse j in (tone) i-a.b.c.j-a...v objective function: min total cost min z zsumx 1j "Cij const xlj-oi sum xij>-Dj for all j, i not-1 9