IDS-552 Assignment 2

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School

University of Illinois, Chicago *

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Course

552

Subject

Economics

Date

Feb 20, 2024

Type

pdf

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Uploaded by ChancellorFogGull33

?????’? 𝐴𝑔𝑔?𝑒𝑔??𝑒 ?????𝑖?𝑔 𝐹???????𝑖?? Parameters: D t = Number of units demanded in time period, t. (t = 1, 2 …, 12) Price for each period from the problem description Cost Parameters from problem description (defined in the Excel sheet ‘Data’) Decision Variables: W t = Number of workers employed in month t. (t = 1, 2 …, 12) O t = Number of hours of overtime in month t. (t = 1, 2 …, 12) I t = Number of units held in the inventory at the end of the month t. (t = 1, 2 …, 12) P t = Number of units produced in month t. (t = 1, 2 …, 12) The objective is to minimize the total cost of production. Total cost components are Regular Time labor, Overtime labor, Inventory holding cost and Material/Production Cost. Minimize ∑ 10 ∗ 20 ∗ 8 ∗ 𝑊 𝑡 12 𝑡=1 + ∑ 15 ∗ ? 𝑡 12 𝑡=1 + ∑ 4 ∗ ? 𝑡 12 𝑡=1 + ∑ 35 ∗ ? 𝑡 12 𝑡=1 The final objective function is, Minimize 1600 ∑ 𝑾 𝒕 ?? 𝒕=? + 15 ∑ ? 𝒕 ?? 𝒕=? + 4 ∑ 𝑰 𝒕 ?? 𝒕=? + 35 ∑ ? 𝒕 ?? 𝒕=? Subject to: Initial Conditions: W 0 = 250 I 0 = 4000 Workforce Constraint: W t = 250 W t -250 = 0 ; t = 1, 2, …, 12 Inventory balance Constraints: I t = I t-1 + P t - D t I t-1 + P t - D t - I t = 0 ; t = 1, 2, …, 12 Production Constraints: 2P t ≤ 160W t + O t P t ≤ 80W t + O t /2 P t - 80W t - O t /2 ≤ 0; t = 1, 2, …, 12 Overtime constraints: O t ≤ 20W t O t - 20W t ≤ 0; t = 1, 2, …, 12 Terminal Conditions: I 12 = 4000

(a) The optimal production plan for Jumbo is the one that minimizes the overall cost of production. Using Solver in excel, we have calculated the overall profits generated by Jumbo and the production plan that works best as shown below. Period (t) Production Pt 1 9000 2 20000 3 20000 4 20000 5 20000 6 20000 7 20000 8 20000 9 15000 10 10000 11 11000 12 14000 The total profit generated is $3,907,000.00. (b) If Shrimpy promotes in April and Jumbo doesn’t , Jumbo ’s demand drop by 40% in that month. The profit, in that case, is $3,615,000.00. The below table shows the production and demand in a given month. Demand in April has dropped to 12,000. Period Production Demand 1 8000 12000 2 13000 11000 3 20000 14000 4 20000 12000 5 20000 25000 6 20000 27000 7 20000 24000 8 20000 20000 9 15000 15000 10 10000 10000 11 11000 11000 12 14000 10000 If Jumbo promotes in April and Shrimpy does n’t , Jumbo sees demand increase by 40% as well as forward buying of 10% from May and June. The profit, in this case, is

$4,103,000.00. The below table shows the production and demand in a given month. Demand for April, May and June has changed. Period Production Demand 1 17000 12000 2 20000 11000 3 20000 14000 4 20000 33200 5 20000 22500 6 20000 24300 7 20000 24000 8 20000 20000 9 15000 15000 10 10000 10000 11 11000 11000 12 14000 10000 The benefit of running the promotion is $488,000.00. This demonstrates the positive impact of Jumbo's promotions on profit, especially when the competitor is not actively promoting. In a competitive market where the total demand for a product is relatively stable, one company's gain from a promotional activity is likely to come at the expense of its competitors. If Jumbo gains customers due to its promotion, it might mean that some of those customers were previously buying from Shrimpy or other competitors. When Shrimpy promotes but Jumbo does not, Jumbo's profit is lower compared to the scenario where both don't promote. This indicates a loss in profit for Jumbo when the competitor engages in promotions and Jumbo does not respond. This emphasizes the importance of adapting marketing strategies to remain competitive in the face of promotional activities by rivals. (c) If both Shrimpy and Jumbo promote in April, the optimal production plan is as shown in the table below. The total profit is $3,871,000.00. Period Production Demand 1 9000 12000 2 20000 11000 3 20000 14000 4 20000 27800 5 20000 21250 6 20000 22950 7 20000 24000 8 20000 20000 9 15000 15000 10 10000 10000

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