Question

The Mr. Meadows Cookie Company can obtain accurate forecasts for 12 months based on firm orders. These forecasts and the number of workdays per month are as follows: Month Workdays Demand Forecast in thousands of cookies 850 1260 436 980 770 850 1050 1550 1350 1000 970 680 26 24 20 18 4 23 21 23 24 21 13 12 During a 46-day period when there were 120 workers, the firm produced 1,700,000 cookies. Assume that there are 100 workers employed, and 436 cookies in inventory at the beginning of month 1 (January). Further assume that the inventory carrying cost s 872 Do the following: $0.10/cookie/month, employee hiring cost cu S100/work, and cost of firing one worker cE- S200/worker. It is required that the inventory level at the end of month 12 (December) is (1) Mixed strategy (allowing inventory and workforce changes from month to month): Find an optimal plan (using linear programming) to meet all monthly demands (assuming back order not allowed) in order to minimize the total cost including employee hiring and firing costs and inventory carrying cost. (2) Repeat (1), assuming backlog is allowed at a cost of e S0.2/cookie/month.

Answer 1

13c Ca ime peaod46 a ota paodactonoo.coo tiec ーAssume , u36 cookeg araying cost ^ メo.ld plovee bia ore coat : 20 ttero hoe ro Padection cost No.of xoube 46 1a0 : 0 308

|Ab. 1961-19. h19 Ise.bee ii | io.bool hnl 01811 5S) bbl S 5-1 | b9.it | th.9|-& ob lll > t | ti.tt_b | 0).Son otib 098) 0 ese 0991 ht15 5 8 8 C% 8 Sib -86-58TS 어 ! ve -art 09t I

b) Gototal ottox bioai pe cote : 156-100 : 56 hiod tapo mon-ia 56 cost f 十60 constant anah-toto plan." umabforse plar (fiaing cost toouter bied) t r 5600 540500 546100

minimum coanl coat oace plan わ(2 an beloc -lable Dtao hided contea,8: Cs Scanned with CamScanner

ve Coromolativemnioo co o units oa darronddarand 8.01 9.38 G.16 26 to + 8 50 2r0 20 /55.40 2110 | 1864 |วเป | 64 2620 20 8 3 6 10 980 ЭРО | 4370 5163- LA 3600 330 510 311-63 16 6. 33.89 10-96 44.28 11 0 2.3 2.08 12.0 80 S236 6 6 220 tu LOSO SSO G.49 2.0R OuO 2820 58.83 9t 350 1703539193 93 Lo 2.4 . 39 66 22 136 tyo0 692 26 ,83020 2.69 ISD 920 13 46.69 680 ouing n ble besn' ao ny momia in a Cs Scanned with Camšcaanertotol endigven

6 Dtal cost Total Cost nvarioay cost otal edin nvento F 3 2g0 51800 2250o Scanned with CamScanner