Final Report Requirements:

• • Problem Formulation (Modeling):
    • Define the decision variables.
    • Write and explain the objective function. Identify and explain all objective function coefficients (cj).
    • Identify and explain all constraints, which includes:
      • Identify and explain all constraints attributes (aij).
      • Identify and explain all right-hand side values (bi).
      • Identify and explain any other supporting data, if available.
  • Problem Solution: Generate an optimal solution for the problem using a software (Excel Solver ) package. Attach the software input and output in the appendix of the report.
• • Results and discussion: Analyze the output of the optimal solution. Explain the results and the suggested decisions. Answer all the questions from the case study here.
  • Conclusion: What was learned from the considered problem and the results.

Al-Batal: A Facility-Location Problem

Al-Batal (AB) is a well-known Saudi snacks company that produces high quality chips. Basically, AB processes raw materials like potatoes, corn, and rice to make ketchup flavored and salt & vinegar flavored chips. AB is expanding into the western and southern regions of Saudi Arabia and has to study several locations to build their production facilities.

AB currently are considering five different sites. In Table 1, the second column shows the land rent prices and the last three columns show the purchase and delivery cost per ton of each material to each of the locations under consideration. Each production facility can produce as much as 12,000 tons of all products per year.

The largest four companies conducting business with AB, their distribution center location, and their yearly demand quantities are listed in Table 2. The demand is shipped by trucks from each production facility to each customers distribution center. The shipping cost from each production facility to each distribution center is SR0.10 per ton per km. Demand for each distribution center has to be fulfilled completely.

The amount of each raw material that goes into the making of each flavored chips is given in Table 3. Your task is to determine how AB should expand. In addition, you are expected to answer the following questions:

• Which locations should be selected? How should the distribution centers receive AB service?
• If fuel cost increases and our shipping costs between production facilities and customers distribution center are affected, will your recommendation change? Explain. (Hint: Sensitivity analysis is not required)
• If shipping costs for raw material increase, will your recommendation change? Explain using sensitivity analysis.
• Are their any other sensitivity-analysis issues that you feel might be important to address? Conduct your experiments if so.

Table 1 Site Information and Material Shipping Cost

		MaterialShipping Cost(SR/Ton)
Site Location	Land Renting Cost (SR/Year)	Corn	Rice flour	Potato
Rabigh, Makkah	250,000	20	10	32
Taif, Makkah	240,000	24	16	22
Yanbu, Madinah	270,000	18	20	30
Dahban, Makkah	320,000	22	14	28
Al Bahah, Al Bahah	230,000	28	30	16

Table 2 Demand Information

		Demand (Tons)
Company	Location	Ketchup	Salt & Vinegar
Aseer CO	Abha, Aseer	2,000	1,600
Taibah CO	Al Madinah, Madinah	2,600	2,200
Al Rahma CO	Makkah, Makkah	2,300	1,800
Red Sea CO	Jeddah, Makkah	3,600	2,400

Table 3 Product-Ingredient Mix

Product	Ingredient (%)
	Corn	Rice flour	Potato
Ketchup flavored chips	65	25	10
Salt & vinegar flavored chips	30	15	55

This table 4 shows the distances between the distribution center and the location of the receiving company.

Distribution center	Company	Km
Rabigh makkah	Red sea CO	175 Km
Dahaban makkah	Red sea CO	80 Km
Taif makkah	Al Rahmah CO	140 Km
Yanbu madinah	Taibah CO	220 Km
Al bahah al bahah	Aseer CO	185 Km