Case Analysis Operations Research Red Brand Canners [Download to View Full Presentation]

Operations Research [Red Brand Canners] 

Submitted by:

Kavya SS

Group V

Kritika Gupta

Kulbhushan Baghel

Lokesh Singh

Mahtaab Kajla

Case Facts

Red Brand Canners  – medium sized, fruit and vegetable cannery Decide the optimal product mix for tomato products  – Canned whole tomatoes, Tomato Juice and Tomato Paste Two grades of tomatoes available  – Grade A and Grade B whether to purchase the 80,000 pounds of grade A tomatoes

Decision Variables •Xaw – Pounds of “Canned Whole Tomatoes” produced using grade A tomatoes •Xaj – Pounds of “Tomato Juice” produced using grade A tomatoes •Xap – Pounds of “Tomato Paste” produced using grade A tomatoes Xbw – Pounds of “Canned whole tomatoes” produced using grade B tomatoes Xbj – Pounds of “Tomato Juice” produced using grade B tomatoes Xbp – Pounds of “Tomato Paste” produced using grade B tomatoes

Objective function

Contribution from various products: Cw = $1.48 $1.48 / 18 = 0.082 Cj = $1.32 / 20 = 0.066 Cp = $1.85 / 25 = 0.074 Hence the Objective function is to maximize the contribution : Maximize Z = 0.08222(Xaw + Xbw) + 0.066(Xaj + Xbj) + 0.074(Xap + Xbp)

Constraints

Demand Constraints : Whole tomatoes, Xaw + Xbw < = (800000*18) Tomato Juice, Xaj + Xbj< = (50000*20) Tomato Paste, Xap + Xbp< = (80000*25) Quality constraints : For Canned whole tomatoes, 9Xaw + 5Xbw >= 8(Xaw+Xbw) For tomato Juice, 9Xaj + 5Xbj >= 6(Xaj + Xbj)

Constraints cont.

Quantity Constraints: A grade tomatoes are 20% of the total produce, (Xaw+Xaj+Xap) < = 600,000 B grade tomatoes are the rest 80 %, (Xbw + Xbj + Xbp) <= 2400,000

Optimal Solution

Using Excel Solver, the optimal solution obtained is: Xaw = 525000 Xaj = 75000 Xap = 0 Xbw = 175000 Xbj = 225000 Xbp = 2000000 Objective function, Z = $225355.56

Additional A grade tomatoes

When extra 80,000 pounds of grade A tomatoes tomatoes are available: The sensitivity report shows that the allowable increase in the quantity constraint is 600000 With an increase of 80000 pounds, the increase in contribution becomes = (80000*0.090333 (80000*0.090333)) = $7226.64, where 0.090333 is the shadow price Hence, net contribution = $232582.2

Profit calculation

Cost of Tomatoes = 3 million * 6 cents = $180,000 Profit in normal scenario = $225355.56 - $180000 = $45355.56 Profit with costs as proposed by Myers = $225355.56 $180240 = $45115.56 Profit in scenario 2 = $232582.2 – (180000 + 6800) = $45782.8

More grade A Tomatoes?

Since the profit in scenario 2, with 80000 more grade A tomatoes is higher than normal scenario, the company should opt for buying the extra tomatoes

Analysis

Myers had proposed a product mix as following: 2 million grade B tomatoes for paste, remaining grade A and B tomatoes for juice Contribution = 2000000*0.074 + 1000000*0.066 = $214000 Profit = $214000 = $180000 = $34000 The profit in the optimal solution is greater than that of solution as proposed by Myers

Thanks!!!