Question

Northwest General, a large hospital in Providence, Rhode Island, has initiated a new procedure to ensure that patients receive their meals while the food is still hot as possible. The hospital will continue to prepare the f now deliver it in bulk (not individual servings) to one of three new serving stations in the building. From there, the food will be reheated, meals will be placed on individual trays, loaded onto a cart, and distributed to the various floors and wings of the hospital ood in its kitchen, but will The three new serving stations are as efficiently located as possible to reach the various hallways in the hospital. The number of trays that each station can serve is shown below: Location Capacity (Meals) Station 5A Station 3G Station 1S 200 225 275 There are six wings to Northwest General that must be served. The number of patients in each follows Wing Patients 80 120 150 60 80 The purpose of the new procedure is to increase the temperature of the hot meals that the patient receives. Therefore, the amount of time needed to deliver a tray from a serving station will determine the proper distribution of food from serving station to wing. The table below summarizes the time associated with each possible distribution channel

Answer 1

Objective	Minimize delivery time (sum product of Supply delivery constraints and distribution time
Constraints	1) Capacity utilised<= Capacity available
	2) Patients served = Patients available
Supply delivery constraints
	Ward 1	Ward 2	Ward 3	Ward 4	Ward 5	Ward 6	Capacity utilised		Max capacity
Station 5A	0	52	39	0	29	80	200	<=	200
Station 3G	80	0	1	113	31	0	225	<=	225
Station 1S	0	68	110	97	0	0	275	<=	275
Patients served	80	120	150	210	60	80
	=	=	=	=	=	=			Total time	4825	min
Patients available	80	120	150	210	60	80
Distribution time
	Ward 1	Ward 2	Ward 3	Ward 4	Ward 5	Ward 6
Station 5A	12	11	8	9	6	6
Station 3G	6	12	7	7	5	8
Station 1S	8	9	6	6	7	9

Q1) Distribution recommendation (Highlighted above)

Q2) Serving time per patient =Total time/Total no of patients = (4825/700) = 6.89 min

The question above has been solved using solver in excel, the screenshot of which is given below (objective and constraints)

Solver Parameters Set Objective: SKS27 O Min 0: Max Value Of: By Changing Variable Cells: SFS8:SK$10 Subject to the Constraints: $F$11:$K$11 $F$13:$K$13 SF$8:$K$10 integer $L$8:$L$10 <= $N$8:$N$10 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: GRG Nonlinear Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close