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MULTI-PERIOD PRODUCTION-SMOOTHINGG MODEL Example 2.4.4 on page 65 of Taha's book A company will manufacture a product for the next four months: March, April, May, and June. The demands for each month are 520, 720, 520, and 620 units, respectively. The company has a steady workforce of 10 employees but can meet fluctuating production needs by hiring and firing temporary workers at the beginning of each month, if necessary The extra costs of hiring and firing in any month are $200 and $400 per worker, respectively. A permanent worker can produce 12 units per month, and a temporary worker, lacking comparable experience, only produce 10 units per month. The company can produce more than needed in any month and carry the surplus over to a succeeding month at a holding cost of $50 per unit per month. . Decision variables: i= 1 (March), 2 (April), 3 (May), 4 (June) X : number of units produced in month i 1 : inventory level at the end of month i H : number of temporary workers hired at the beginning of month i L : number of temporary workers fired at the beginning of month i W number of temporary workers for month i LP model: Inventory balance constraints: inventory level at the end of a period i - inventory level at the end of period i-1 + number of units produced in period i demand of period i Workforce balance constraints: temporary workforce level of period i- temporary workforce level of period i - 1 number of temporary workers hired at the beginning of month i number of temporary workers fired at the beginning of month i Capacin, constraints LP model: Minimize 2 - 50 (+1+1, 1) +200 (H + H + H2 + H) + 400 (4 +L++La) subject to 1.-X, -520 1,-1, + Xx - 720 Inventory balance constraints 1,-1+X- 520 1,-1,+ XX-620 w, -H- W -W,+H-4 Workforce balance constraints W - W + H-4 W. - W+H - X, s 120 + 10 W, X; $ 120+ 10 W Capacity constraints X; s 120 + 10 W, X. 120 + 10 W, X20,1,20, W20, H,20,4, 2 0 for 1-1.2.3.4