Business Optimization Models Text Chapters 13 14 Motivation

Business Optimization Models Text: Chapters 13 -14

Motivation 1: Cash Flow Financing Many firms earn revenues which do not synchronize with monthly bills. The CFO of Hongguo has forecasted revenues and bills for the next 6 months as tabled below. Clearly, Honguo must borrow money to cover the negative net cash flow in Jul-Sep. There are 3 options available: 1. At the beginning of July, take out a 6 months loan, to be paid back end Dec together with 4% interest (i. e. 8% annual rate ; no discount for early payback) 2. Month-to-month revolving loans (i. e. 1000 in July, 3100 in Aug, 4200 in Sep, …), for which the interest charge is 1% monthly (i. e. 12% annual rate). 3. A combination (which? ) of 6 months and month-to-month loans Which option minimizes Hongguo’s interest charges? Explain. $’ 000 Jul Aug Sep Oct Nov Dec Revenue 600 900 1200 1400 2800 3500 Bills 1600 3000 2300 1200 800 500 Net Cash Flow -1000 -2100 -1100 +2000 +3000

SOLVER 3

Business Optimization Models: Market-Driven Optimal Allocation of Resources Efficient Allocation of Resources: HOW? Optimal Product Mix Optimal Advertising Impact Yield / Revenue / Cash Flow Management Supply Chain Optimization Outsourcing Portfolio Optimization Worker Rosters / Assignment Minimizing CO 2 emission Helping Singapore Firms to be cheaper, better, faster…

Motivation 2: Drone Delivery • • • The recommendations of Singapore’s Committee on the Future Economy (CFE) has motivated you to launch a drone delivery service. You have a strategic client located 37 kms from Changi Airport and you’ve promised to deliver its air cargo within 2 hours of reception. Your fleet of drones use biodiesels to fuel their dual 2 -engine or 4 -engine motors which have maximum speed of 18 and 20 km/h. Their biodiesel consumption varies according to motor type and speed of travel as shown below. Challenge: How long will you program the 2 and/or 4 engine motors and at what speed in order to deliver the cargo on time and simultaneously, minimize biodiesel consumption? e. g. Run 2 /4 engines at 17/20 km/h and use 130+450=580 cc: Is there a BETTER solution?

Optimization=> Cheaper, Better, Faster • Managerial focus on modeling rather than mathematical intricacies. • Models are abstractions: they make assumptions ; they can be rigid ; they ignore “soft” factors e. g. people, politics, . . .

LP Motivation: Profit Maximization Primo Concierge is introducing 2 new services: A and B. Their respective expected profit are $5 and $2 per unit. Their departmental resource requirements are: Work-Hours per unit Department Service A Service B Work-Hours Available X 3 2 2400 Y 0 1 800 Z 2 0 1200 Advise management on sales quotas for services A and B in order to maximize the total expected profit. Common sense says (? , ? ): WHY?

Optimal Location for Warehouse The table and graph below display the (x, y) co-ordinates of four sales outlets as well as the number of daily truck deliveries to them. Outlet #Daily Deliveries A 8 B 6 C 2 D 5 (x, , y) (8, 2) (3, 10) (8, 15) (14, 13) ? Cisco Lab relocates from Sydney to Singapore Delivery cost is $1 per unit distance. Your company intends to build a warehouse within the rectangle zone bounded by the (x, , y) co-ordinates: (10, 6), (12, 10) and (10, 10). Advise on the optimal (x, y) location of the warehouse so as to minimize delivery costs. • Why is this called a non-linear programming problem?

PWC: Which Capital Projects to select? Your firm has short listed 6 potential projects for investments. Their NPV annual capital expenditures and cash flows are tabled below. (a) Which projects would you select given the annual capital expenditure budget? (b) Which projects would you select if un-spent budget can be carried forward? Capital Expenditure ($m) Cash Flow ($m) Project Yr 1 Yr 2 Yr 3 Yr 4 Yr 5 Yr 6 A 5 6 20 0 -5 -6 -16 12 14 15 B 9 6 0 0 -9 -6 6 4 5 5 C 12 10 5 5 0 0 -12 -10 -5 -5 25 15 D 7 5 20 10 15 0 -7 -5 -20 -15 75 E 20 0 0 -20 6 6 6 F 18 15 15 15 0 0 -18 -15 -10 35 35 Budget 45 30 20 20 0 0

SOLVER Limitations • “Free” Solver in Excel can handle – 200 unknown variables – 100 constraints • For BIGGER problems, use – Solver. Plus – Open. Solver