Optimization Of Electric Manufacturing And Distribution Plant

In the current distribution system, demand at the Dhahran, Manama, Riyadh, and Kuwait customer zones can be satisfied by shipments from Damam and/or KIZAD distribution centers.  In a similar manner, the Salalah, Muscat, Nizwa, and Sohar customer zones are served by the Jabal Ali and/or KIZAD distribution centers.  In addition, the Jeddah customer zone can be covered by all the three distribution centers.  To determine how many units to ship from each plant, the quarterly demand forecasts are aggregated at the distribution centers, and a transportation model is used to minimize the cost of shipping from the production plants to the distribution centers.

(a)Provide a Linear Programming Model (in both algebraic and spreadsheet formats) for the above case.  You model should clearly state the Decision Variables, objective function, and constraints.
 
(b)Use SOLVER module on Microsoft Excel to solve your model in part (a) and interpret your results.  

(c)Use the sensitivity report(s) and solver table(s) results to make recommendations for improving the distribution system. Your report should address, but not limited to, the following issues:


(1)If the company does not change its current distribution strategy, what will its distribution costs be for the following quarter?

(2)Suppose the company is willing to consider dropping the distribution center limitations; that is, customers could be served by any of the distribution centers. Can costs be reduced? If yes; by how much?

(3)The company wants to explore the possibility of satisfying some of the customer demands directly from the production plants. In particular, the per-unit shipping cost is $0.30 from RAK to Nizwa, and $0.7 from RAK to Sohar.  The per-unit cost for direct shipments from Musafah to Manama is $3.50.  Can distribution costs be further reduced by considering these direct plant-customer shipments?

(4)Over the next five years, the company is anticipating moderate growth (around 5000 meters). Would you recommend that they consider plant expansion at this point in time? And why?

(5)Provide your own free style analysis based on what you learnt in class to come up with relevant set of recommendations for the GCC company. The recommendations must be supported by the results of your analysis.

Production and Distribution of Electric Meters

This report presents the solution to the problem being faced by the joint GCC company. The company initially set up an electric manufacturing plant at Musafah. It supplied power to the five cities of Dhahra, Manama, Riyadh, Kuwait and Jeddah from the Damam distribution center. With the growth of customer base another distribution centre was set up at Khalifa Industrial Zone in Abu Dhabi (KIZAD). Subsequently when the demand rose it set up another plant at Ras-al-Khaimah (RAK). In addition, another distribution centre was set up at Jabal Ali. At present the company supplied electric meters to 9 cities from three distribution centres and two production plants.  

1. Input analysis and assumptions (if any)

The production plants of Musafah and Rak generate different amounts of meters. Musafah produces 30000 meters and Rak produces 20000 meters. Moreover, the production costs of Musafah and Rak are $10.50 and $10.00 respectively.

The following table presents the cost to ship meters from the production to plant to the distribution center.

	D i s t r i b u t i o n   C e n t e r s
Plant	Damam	KIZAD	Jabal Ali
Musafah	3.2	2.2	4.2
RAK	--	3.9	1.2

The following table presents the cost to ship meters from the distribution center to the customers zone.

	C u s t o m e r   Z o n e s
Center	Dhahran	Manama	Riyadh	Kuwait	Jeddah	Salalah	Muscat	Nizwa	Sohar
Damam	0.3	2.1	3.1	4.4	6.0	--	--	--	--
KIZAD	5.2	5.4	4.5	6.0	2.7	4.7	3.4	3.3	2.7
Jabal Ali	--	--	--	--	5.4	3.3	2.4	2.1	2.5

Further, the requirements of each of the customer zones is given below:

Customer Zone	Dhahran	Manama	Riyadh	Kuwait	Jeddah	Salala	Muscat	Nizwa	Sohar
Demand	6300	4880	2130	1210	6120	4830	2750	8580	4460

1. Definitions of all decision variables

The decision to be taken by the GCC company is how much power should be generated by each the two manufacturing units. The organizations need to take a decision on how much meters is to be generated from the two manufacturing centres of Musafah and Rak.  Moreover, the organizations also need to decide the quantity of meters to be distributed to the three centers of Damam, Kizad and Jabal Ali. Further, the organization also needs to decide on the meters to be distributed from the three distribution centers to the nine customer zones.

1. Detailed development of the objective function

The objective function has three parts.

1. The product of the manufacturing cost of meters at the two plants and the quantity of production.
2. The product of distribution cost from plant to distribution center
3. The product of shipping cost from distribution plant to customer zone
4. Existing constraints and their significance

The constraint is that Musfah plant can produce only 30000 meters while Rak can produce only 20000 meters.

1. Model Summary – number of Variables and Constraints

There are 24 variables.

Minimize

0.3*Damam Dhahran + 2.1*Damam Manama + 3.1*Damam Riyadh + 4.4*Damam Kuwait + 6*Damam Jeddah + 5.2*KIZAD Dhahran + 5.4*KIZAD Manama + 4.5*KIZAD Riyadh + 6*KIZAD Kuwait + 2.7*KIZAD Jeddah + 4.7*KIZAD Salalah + 3.4*KIZAD Muscat + 3.3*KIZAD Nizwa + 2.7*KIZAD Sohar + 5.4*Jabal Ali Jeddah + 3.3*Jabal Ali Salalah + 2.4*Jabal Ali Muscat + 2.1*Jabal Ali Nizwa + 2.5*Jabal Ali Sohar + 13.7 *Musafah Damam + 12.7*Musafah KIZAD + 14.7*Musafah Jabal Ali +

13.9*RAK KIZAD + 11.2*RAK Jabal Ali

There are 14 constraints:

1. Musafah-Damam + Musafah-Kizad + Musafah-Jabal Ali <= 30000
2. Rak-Kizad + RakJabal Ali <= 20000
3. Damam-Dhahara + Damam-Manama + Damam-Riyadh + Damam-Kuwait + Damam-Jeddah = Musafah-Damam
4. Kizad-Dhahran + Kizad- Manama + Kizad-Riyadh + Kizad-Kuwait + Kizad- Jeddah + Kizad – Salalah + Kizad – Muscat + Kizad - Nizwa + Kizad – Sohar = Musafah-Kizad + Rak-Kizad
5. Jabal Ali-Dhahran + Jabal Ali-Manama + Jabal Ali-Riyadh + Jabal Ali-Kuwait + Jabal Ali-Jeddah + Jabal Ali-Salalah + Jabal Ali-Muscat + Jabal Ali-Nizwa + Jabal Ali-Sohar = Musafah-Kizad + Rak-Kizad
6. Damam-Dhahran + KIZAD – Dhahran = 6300
7. Damam-Manama + KIZAD – Manama = 4880
8. Damam-Riyadh + KIZAD – Riyadh = 2130
9. Damam-Kuwait + KIZAD – Kuwait = 1210
10. Damam-Jeddah + KIZAD – Jeddah + Jabal Ali-Jeddah = 6120
11. KIZAD – Salalah + Jabal Ali-Salalah = 4830
12. KIZAD – Muscat + Jabal Ali-Muscat = 2750
13. KIZAD – Nizwa + Jabal Ali-Nizwa = 8580
14. KIZAD – Sohar + Jabal Ali-Sohar = 4460

1. Optimal solutions and their interpretations

The following table shows the amount of electric to be generated and distributed.

	D i s t r i b u t i o n   C e n t e r s
Plant	Damam	KIZAD	Jabal Ali
Musafah	14520	6740	0
RAK	0	0	20000

Costs Involved

The following table shows the meters to be shipped from the distribution center to the customer zones.

	C u s t o m e r   Z o n e s
Center	Dhahran	Manama	Riyadh	Kuwait	Jeddah	Salalah	Muscat	Nizwa	Sohar
Damam	6300	4880	2130	1210	0	0	0	0	0
KIZAD	0	0	0	0	6120	0	0	0	620
Jabal Ali	0	0	0	0	0	4830	2750	8580	3840

1. Effect of Model Assumptions.

The assumptions in the model signify that:

1. There would be optimum utilization of meters. No excess meters would be left at distribution centers.
2. Optimum amount of meters would be produced and distributed from the plant to distribution center.
3. Optimum amount of meters would be shipped from distribution centers to customer zones.

1. Introduction

The total cost of manufacturing, distribution and shipping meters is $600942

1. Responses to parts C-1 through C-4

The total cost of manufacturing, distribution and shipping meters is $600942

Dropping the distribution center limitation would lead to a reduction in distribution costs. The decrease in distribution costs would be : $600942 - $537174 = $63768

Considering the fact that the per-unit shipping cost is $0.30 from RAK to Nizwa, and $0.7 from RAK to Sohar and from Musafah to Manama is $3.50 the total cost would reduce since the costs from plant to customer via distribution would be reduced.

There would not be any need for plant expansion since the total productions from the two plants is 50000 while the total demand from the 9 customer zones is 41260. Considering the fact that there is an increase of 5000 meters demand the total demand would be 46260 which is below the total production level.

1. Analysis of variations in (RHS)

The RHS provides information about the each of the constraints corresponding to the shadow price within the limits of allowable decrease and increase.

Damam distribution has a capacity of 145520. The allowable increase is 14520 and the allowable decrease is 8740.

Similarly, Kaizad distribution has a capacity of 6740. The allowable increase is 6740 and the allowable decrease is 8740.

Further, Jabal Ali distribution has a capacity of 20000. The allowable increase is 620 and the allowable decrease is 3840.

1. Analysis of variation in objective function coefficients

The objective function coefficient provides information to the fact that when the value of the coefficient is changed within the allowable increase and decrease limits then the final objective value would not change.

1. Analysis of variation in other input parameters
2. Some of the input parameters are zero. When the values of the zeros are changed to non-zero values then reduced cost column provides us information of the changes in objective function.
3. Summary of the analysis results  

Musafah plant can produce 30000 meters. However the optimal solution provides information that Musafah should produce 14520 meters and distribute to Damam and 6740 meters and distribute to Kizad. Rak should ship all its meters to Jabal Ali.

Further it is found that the total shipping costs is $600942.

In addition, the optimal solution shows that from Damam distribution center the customer zones of Dhahran, Manama, Riyadh and Kuwait are served. From the Kizad distribution center Jeddah and Sohar meters are shipped. The customer centers of Salalah, Muscat, Nizwa and Sohar are provided meters from Jabal Ali.

Conclusion

From the analysis it can be recommended that looking at the future demand over five years there is no need to plant expansion. Further a reduction in shipping costs from Rak to Nizwa and Sohar and Musafah to Manama would reduce the total costs.